Watching Materials Form: Particle Formation and Growth in Hydrothermal Synthesis. Kirsten Marie Ørnsbjerg Jensen PhD Dissertation

Transcription

1 Watching Materials Form: Particle Formation and Growth in Hydrothermal Synthesis Kirsten Marie Ørnsbjerg Jensen PhD Dissertation

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3 Watching Materials Form: Particle Formation and Growth in Hydrothermal Synthesis PhD Dissertation Kirsten Marie Ørnsbjerg Jensen Department of Chemistry Aarhus University July 2013

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5 Contents Preface iii Acknowledgements v List of Publications vii Abstract ix Dansk Resumé xi (ydrothermal Synthesis of Nanomaterials Motivation Nanomaterials for Li ion Batteries (ydrothermal Synthesis of )norganic Nanomaterials Particle Nucleation and Growth Theory Characterization of Nanoparticles by Scattering Techniques )ntroduction X ray and Neutron Scattering Sources of X rays and Neutrons for Scattering Experiments Powder Diffraction Total Scattering and Pair Distribution Function Analysis Small Angle Scattering Summary In situ X ray Scattering Studies of (ydrothermal Synthesis )ntroduction In situ X ray Powder Diffraction Experiments The Aarhus In Situ Capillary Reactor What can be Learned from In Situ X Ray Studies Formation and Growth of Nanocrystalline LiCoO )ntroduction Experimental Methods Data Analysis Results and Discussion Conclusions Defect Formation During (ydrothermal Synthesis of LiFe x Mn x PO )ntroduction In Situ Experiments In Situ Results and Discussion Questions Raised in the In Situ Study Ex situ Characterization i

6 Ex situ Results and Discussion Conclusions Mechanisms of SnO Nanoparticle Formation and Growth )ntroduction Experimental Methods Data Treatment Results and Discussion Conclusions Formation and Growth of Fe O Nanoparticles )ntroduction Experimental Methods Results and Discussion In Situ Studies Results and Discussion Ex Situ Studies Conclusions and Outlook Concluding Remarks References Appendix ) Experimental considerations Appendix )) LiCoO Appendix ))) LiFePO Appendix )V SnO Appendix V Fe O Appendix V) Published papers ii

7 Preface This dissertation has been submitted to the Graduate School of Science and Technology GSST at the Faculty of Science and Technology Aarhus University in order to fulfil the requirements for obtaining the PhD degree in Chemistry The research presented has been conducted under the supervision of Professor Bo Brummerstedt )versen at the Department of Chemistry and )nterdisciplinary Nanoscience Center inano Aarhus University as part of the year (onours PhD programme from August to July During this time ) spent month in Professor Simon Billinge s research group at Columbia University in New York The overall topic for my research is elucidating the mechanisms of particle formation and growth during hydrothermal synthesis The dissertation has been divided into two parts describing first the methods used and subsequently my main research projects Part I Theory and Methods consists of three chapters Chapter 1 is an introduction to material structure nanoparticles and hydrothermal synthesis The chapter serves as the motivation for performing in situ studies and detailed structural characterization of nanoparticles Chapter 2 presents the X ray and neutron scattering techniques applied for in situ and ex situ structural characterization Chapter 3 describes in situ studies of hydrothermal synthesis A short review of previous work is included as well as a description of the experimental setup used for my own research Part II Research Projects includes studies of four different materials Chapter 4 presents an in situ X ray powder diffraction study of the hydrothermal synthesis of LiCoO nanoparticles Chapter 5 concerns studies of the defect formation of LiFePO and LiFe x Mn x PO during hydrothermal synthesis The project includes both extensive in situ and ex situ structural characterization using X ray and iii

8 neutron powder diffraction total scattering small angle scattering as well as microscopy and spectroscopy Chapter 6 presents an in situ total scattering and powder diffraction study of the formation and growth of SnO nanoparticles Chapter 7 concerns the hydrothermal synthesis of magnetic Fe O nanoparticles Both in situ and ex situ total scattering and powder diffraction studies are included General conclusions and an outlook for further work are given in Chapter 8. For clarity ) have chosen to include only projects where ) consider myself the main responsible in the dissertation Apart from the research presented in Part )) ) have thus been involved in a number of other studies Many of these studies have been published and all relevant manuscripts can be found in Appendix V) During my research stay at Columbia University ) worked on sequential analysis of in situ total scattering data as well as a study of the lattice dynamics of PbTe (owever for the sake of coherence ) have chosen not to include the latter project in my dissertation )nstead the paper concerning the study published in Physical Review B in can be found in Appendix V) iv

9 Acknowledgements Over the last five years ) have been extremely privileged to benefit from supervision and interactions with engaged and excellent researchers and fellow students First of all ) am deeply grateful to my supervisor Prof Bo Brummerstedt )versen for his guidance and supervision since ) started in his group for my bachelor s project in (is enthusiasm and deep understanding of crystallography and materials science have been a true inspiration ) thank him for trusting in me allowing me freedom in my studies and for providing me with the best possible conditions for conducting my research Apart from building up an excellent environment for materials science research in Aarhus through Center for Materials Crystallography CMC and Center for Energy Materials CEM Bo has over the last years sent me on numerous beamtimes workshops and conferences around the world and ) am very grateful for the opportunities During my PhD studies ) have worked with fantastic colleagues Ass Prof Mogens Christensen has been an invaluable source regarding both the experimental side of the project as well as data analysis ) am very grateful for all the time he has spent helping me with refinements and experiments as well as discussing results and new projects Fellow PhD student Christoffer Tysted and ) have worked side by side planning and executing in situ synchrotron experiments Working with someone as competent as Christoffer has been a privilege and our collaboration has expanded the scope of my research significantly ) equally thank the rest of DreamTeam )n Situ Dr Nina Lock Espen Drath Bøjesen and (enrik Lyder Andersen as well as guest stars to the team over the years Performing challenging experiments during a beamtime is a true team effort and all the hard work they have done day and night is highly acknowledged Apart from the many beamtimes scientific discussions and study groups concerning data analysis and results ) am grateful for all the good times we have had touring the world in the quest for data Christoffer Mogens and Espen as well as Sebastian Christensen and Dr Sofie Kastbjerg are also thanked for their help proofreading the dissertation ) also acknowledge the help ) received from Dr Martin Bremholm and Dr Jacob Becker in the initial stages of my research Martin who finished his PhD when ) started mine developed in situ studies in the group build the first v

10 version of the experimental setup and taught me many aspects of scattering data analysis Jacob has helped developing the technical site of the project Furthermore the beamline staff at i MAX lab )D B and )D C APS P PETRA ))) )D and BM ESRF NPDF LANL and NOMAD ORNL are thanked for technical support during the many beamtimes )n ) spent months in Prof Simon Billinge s group at Columbia University in New York (ere ) learned total scattering from the pioneers in the field and ) am very grateful to Simon as well as Dr Pavol Juhas Dr Emil Bozin and the rest of the group for the opportunity and for patiently answering all my questions The stay expanded the scope of my research and allowed us to go in new directions Apart from being an amazing place to do research the social environment at Center for Materials Crystallography in Aarhus is outstanding and being a part of such a thriving research centre has been extremely motivating (ence everybody participating in study groups group meetings cake sessions game nights Friday Bars Cocktail Nights Christmas Parties and all other social or educative events is sincerely thanked Especially the legendary girls office in all its various constellations over the years is thanked for all the good times Many of my colleagues have over the years become great friends and this has made my time in the CMC unforgettable Aarhus, July 2013 Kirsten Marie Ørnsbjerg Jensen vi

11 List of Publications The list is given chronologically with the most recent publications listed first All published manuscripts are appended in Appendix V) marks that the work is presented in the dissertation Gilles Philippot Kirsten M. Ø. Jensen Mogens Christensen Catherine Elissalde Mario Maglione Bo B )versen Cyril Aymonier Growth mechanisms of Ba1 xsrxtio3 (0 x 1) nanoparticles in supercritical ethanol/water mixtures Submitted to ACS Nano Peter Nørby Kirsten M. Ø. Jensen Nina Lock Mogens Christensen and Bo B )versen In Situ Synchrotron Powder X ray Diffraction Study of Formation and Growth of Yttrium and Ytterbium Aluminum Garnet Nanoparticles in Sub and Supercritical Water RSC advance doi C RA E Kirsten M. Ø. Jensen Mogens Christensen (araldur P Gunnlaugsson Nina Lock Espen D Bøjensen Thomas Proffen Bo B )versen Defects in hydrothermally synthesized LiFePO4 and LiFe1 xmnxpo4 cathode materials Chemistry of Materials Jakob R Eltzholtz Christoffer Tyrsted Kirsten M. Ø.Jensen Martin Bremholm Mogens Christensen Jacob Becker Christensen Bo B )versen Pulsed supercritical synthesis of anatase TiO2 nanoparticles in a water isopropanol mixture studied by in situ powder X ray diffraction Nanoscale,,, Christoffer Tyrsted Kirsten M. Ø. Jensen Espen Drath Bøjesen Nina Lock Mogens Christensen Simon J L Billinge and Bo B )versen Understanding the Formation and evolution of Ceria Nanoparticles under Hydrothermal Conditions, Angewandte Chemie )nternational Edition Kirsten M. Ø. Jensen Mogens Christensen Pavol Juhas Christoffer Tyrsted Espen D Bøjesen Nina Lock Simon J L Billinge and Bo B )versen Revealing the Mechanisms behind SnO2 Nanoparticle formation and Growth during Hydrothermal synthesis: An In Situ Total Scattering Study, Journal of the American Chemical Society Kirsten M. Ø. Jensen Emil S Bozin Christos D Malliakas Matthew B Stone Mark D Lumsden Mercouri G Kanatzidis Stephen M Shapiro and Simon J L Billinge Lattice dynamics reveals a local symmetry breaking in the emergent dipole phase of PbTe. Physical Reviews B Jian Li Mi Casper Clausen Martin Bremholm Nina Lock Mogens Christensen Kirsten M. Ø. Jensen Bo B )versen Rapid Hydrothermal Preparation of Rutile TiO2 Nanoparticles by Simultaneous Transformation of Brookite and Anatase: An in situ Synchrotron PXRD Study Crystal Growth and Design vii

12 Christoffer Tyrsted Brian Pauw Kirsten M. Ø. Jensen Jacob Becker Christensen Mogens Christensen and Bo B )versen Watching Nanoparticles Form: An In Situ (Small /Wide Angle X ray Scattering/Total Scattering) Study of the Growth of Yttria Stabilised Zirconia in Supercritical Fluids Chemistry a European Journal Kirsten M. Ø. Jensen Mogens Christensen Christoffer Tyrsted and Bo B )versen Real time synchrotron PXRD study of the anti site defect formation during sub and supercritical synthesis of LiFePO4 and LiFe1 xmnxpo4 nanoparticles Journal of Applied Crystallography Andreas Laumann Kirsten M. Ø. Jensen Christoffer Tyrsted Martin Bremholm Karl Thomas Fehr Michael (olzapfel and Bo B )versen: In situ synchrotron X ray diffraction study of the formation of cubic Li2TiO3 under hydrothermal conditions European Journal of )norganic Chemistry Kirsten M. Ø. Jensen Mogens Christensen Martin Bremholm and Bo B )versen Structure, Size and Morphology control of nanocrystalline LiCoO2 Crystal Growth Design,, Nina Lock Mogens Christensen Kirsten M. Ø. Jensen Bo B )versen: Rapid One Step Low Temperature Synthesis of Nanocrystalline Al2O3 Angewandte Chemie )nternational Edition Jian Li Mi Mogens Christensen Christoffer Tyrsted Kirsten M. Ø. Jensen Jacob Becker Peter (ald and Bo B )versen Formation and Growth of Bi2Te3 in Biomolecule Assisted Near Critical Water: In Situ Synchrotron Radiation Study Journal of Physical Chemistry C Jacob Becker Martin Bremholm Christoffer Tyrsted Brian Pauw Kirsten M. Ø. Jensen Jakob Eltzholt Mogens Christensen and Bo B )versen Experimental setup for in situ X ray SAXS/WAXS/PDF studies of the formation and growth of nanoparticles in near and supercritical fluids Journal of Applied Crystallography In preparation, with major contributions: Kirsten M. Ø. Jensen (enrik L Andersen Christoffer Tyrsted Espen D Bøjesen Bo B )versen Mogens Christensen Formation mechanism of Fe2O3 nanoparticles in hydrothermal synthesis: An in situ total scattering study, (*) (enrik L Andersen Kirsten M. Ø. Jensen Christoffer Tyrsted Espen D Bøjesen Mogens Christensen Size control of Fe2O3 magnetic nanoparticles: An in situ PXRD study of the hydrothermal synthesis (*) viii

13 Abstract The hydrothermal method is a low cost and environmentally benign synthesis technique for inorganic nanomaterials By adjusting simple parameters such as temperature pressure or precursor concentration it is possible to alter the characteristics of the product particles e g crystalline phase and particle size (owever the fundamental mechanisms dictating particle formation and growth are not fully understood )n order to synthesize tailor made nanoparticles with specific properties it is crucial to obtain further knowledge of these processes (ere in situ studies of nanoparticle formation and growth during hydrothermal synthesis are presented The studies employ Powder X Ray Diffraction PXRD Small Angle X ray Scattering SAXS and Total X ray Scattering TS with Pair Distribution Function PDF analysis to probe different length scales in the samples To complement the time resolved studies detailed ex situ characterization of samples synthesised by the hydrothermal method have been done using X ray and neutron scattering as well as microscopy and spectroscopy The synthesis of four different materials is illuminated LiCoO LiFePO SnO and Fe O Detailed knowledge of each of the compounds has been obtained along with a broader understanding of the complexity of the processes in a hydrothermal synthesis First in situ PXRD was used to study the growth of LiCoO nanoparticles The studies showed that LiCoO forms from CoOO( nanoparticles through a dissolution recrystallization process Analysis of the particle growth revealed that the particle size and morphology is highly temperature dependent and can be controlled within few nanometres In situ PXRD as well as SAXS and TS studies were also used to investigate the defect formation in LiFe x Mn x PO during hydrothermal synthesis The formation of the material happens from an iron phosphate gel over an intermediate phase of small iron phosphate nanoparticles to a highly disordered Li x Fe y PO phase where excess iron partly occupies the Li site With longer synthesis time and higher temperature the structure orders and stoichiometric LiFePO is obtained The defect chemistry was further investigated through ex situ analyses The studies show that the defect is in fact Fe excess and not Fe Li anti sites as previously proposed Total scattering data revealed that a large fraction of the sample is amorphous when the synthesis is quenched after short reaction times and the presence of defects is closely related to the coexistence of the amorphous phase ix

14 The formation and growth mechanisms in the hydrothermal synthesis of SnO nanoparticles from aqueous solutions of SnCl ( O were elucidated by means of in situ X ray total scattering The analysis of the data reveals that when the tin )V chloride precursor is dissolved chloride ions and water coordinate octahedrally to tin )V forming aquachlorotin )V complexes as well as hexaaquatin )V Upon heating ellipsoidal SnO nanoparticles are formed uniquely from hexaaquatin )V The nanoparticle size is dependent on both the reaction temperature and the precursor concentration and particles as small as nm can be synthesized In situ total scattering studies were also used to investigate the formation of maghemite Fe O nanoparticles As the ammonium iron citrate precursor decomposes a large cluster with local order to ca Å forms )t contains two distinct iron sites which corresponds to the octahedral and tetrahedral iron sites in the final maghemite spinel structure The clusters condensate along the tetrahedral iron to form loose nanostructures that grow further into defective Fe O nanoparticles with low occupancy of the tetrahedral site As the synthesis proceeds crystalline ordered particles form Ex situ studies of hydrothermally synthesized samples were used to characterize the vacancy ordering in maghemite nanoparticles Clear Bragg peaks corresponding to ordering in the P space group are seen whereas superstructure peaks from P are not readily observed x

15 Dansk Resumé (ydrotermal syntese er en lovende metode til fremstilling af uorganiske nanopartikler Ved at justere simple synteseparametere f eks temperatur tryk eller reaktantkoncentration kan vigtige karakteristika af produktet partikelstørrelse krysatllinitet mv ændres Mekanismerne der kontrollerer partikeldannelse og vækst er dog langt fra fuldt ud forståede og for at kunne syntetisere skræddersyede partikler med specifikke egenskaber er det essentielt at opnå viden om disse processer (er præsenteres in situ røntgensprednings studier af hydrotermale processer Til studierne er anvendt pulverdiffraktion PXRD småvinkel spredning SAXS samt total spredning TS Detaljerede ex situ studier neutron og røntgenspredning samt mikroskopi og spektroskopi har yderligere været benyttet ) det første studie blev PXRD benyttet til at følge dannelse of vækst af LiCoO Resultaterne viste at både størrelse og morfologi af de dannede LiCoO partikler kan styres præcist ved at ændre syntesetemperaturen PXRD samt SAXS og TS blev også anvendt til at studere dannelse af defekter i LiFe x Mn x PO (er dannes krystalstrukturen fra en amorf jernfosfat gel over en intermediær fase af jernfosfat nanopartikler til en uordnet LiFe x Mn x PO struktur Med længere syntesetid og højere temperatur ordnes strukturen og LiFePO opnås Defektkemien blev yderligere undersøgt gennem detaljerede ex situ analyser Defekten er Fe overskud og ikke Fe Li antisites som tidligere foreslået Data viste yderligere at en stor fraktion af prøver fremstillet ved kort syntesetid ikke er krystallinsk og tilstedeværelsen af defekter hænger tæt sammen med sameksistensen af den amorfe fase Dannelse og vækstmekanismer i hydrotermal syntese af SnO nanopartikler fra vandige opløsninger af SnCl blev belyst ved hjælp af total spredning Når tin )V klorid opløses koordinerer klorid og vand oktaedrisk til tin )V og danner aquachlorotin )V komplekser samt hexaaquatin )V Efter opvarmning dannes SnO nanopartikler udelukkende fra hexaaquatin )V Total spredning blev også brugt til at undersøge dannelsen af Fe O nanopartikler Når ammonium jern ))) citrat nedbrydes dannes et nanocluster med lokal orden til ca Å Strukturen indeholder to forskellige jern sites hvilket svarer til de oktaedriske og tetraedrisk jern sites i den endelige spinelstruktur Nanoclusterne kondenseres langs de tetraedriske koordinerede jernatomer og danner løse nanostrukturer der vokser videre til defektfyldt Fe O med lav okkupans af det tetraedriske site Ved yderligere reaktion dannes krystallinske defektfri partikler Studier af vakancer viste tydelige Bragg toppe svarende til P ses mens superstruktur toppe fra P ikke kan observeres xi

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17 Part I Methods and Theory Part ) introduces the methods and theory applied in the dissertation First a motivation for the studies is given whereupon hydrothermal synthesis is presented This is followed by a brief introduction to the scattering methods used for material characterization and finally the use of in situ scattering techniques for studies of hydrothermal processes is discussed

18 Chapter (ydrothermal Synthesis of Nanomaterials 1 Hydrothermal Synthesis of Nanomaterials 1.1 Motivation Life in the twenty first century is more than ever dependent on an unlimited variety of advanced materials Complex building materials as well as functional materials for e g electronics and batteries have all made daily life more comfortable and it is difficult to imagine modern society without them (owever there are many new challenges ahead for materials science With the growing world population developing economies and limited fossil fuels the world is in need of new advanced technologies for energy conversion and storage The key to these technologies is improved materials To compete with fossil fuel based technologies batteries need to have higher energy densities while being cheaper and safer the energy conversion rate of solar cells must be improved and fuels cells must become more cost efficient Researchers around the world are therefore working to develop new and enhanced energy materials A major goal in modern materials chemistry is to establish the link between synthesis structure and properties of a given functional material Currently novel advanced synthesis methods and exotic materials are being developed but without detailed structural characterization and understanding of the structure synthesis property relation we cannot take the development in materials chemistry to the next level where tailor made materials with specific properties can be produced on a large scale at low costs and in an environmentally benign manner Mapping the relation between especially synthesis and structure has been the main focus point in my research Specifically ) have studied the hydrothermal synthesis of a range of inorganic materials to understand some of the underlying mechanisms governing the formation and growth of advanced nanomaterials This first chapter serves to introduce main concepts such as material structure and hydrothermal synthesis and to define the terminology applied in the dissertation Firstly the importance of nanostructure in materials chemistry is briefly discussed (ere special focus is given to Li ion battery materials and nano electrodes as this has been a reoccurring theme throughout my PhD studies Secondly an introduction to the hydrothermal synthesis method is given along with the classical theories of particle nucleation and growth

19 Chapter (ydrothermal Synthesis of Nanomaterials 1.2 Nanomaterials for Li ion Batteries While traditional solid state chemistry up until the s was mainly concerned with the synthesis and characterization of bulk crystalline compounds a rapidly growing interest in structural design on the nanometer scale appeared in the s and the following years At this point nanoparticles had actually been synthesized and used for centuries e g as paint pigments in ancient Mesopotamia and years before the nanotechnology revolution front runners in science such as Richard Feynman had predicted the scientific possibilities when working on the nanoscale Before discussing the properties of nanomaterials the various types of structures in solid state chemistry are briefly introduced )n the context of this dissertation solid materials are divided into three categories Crystalline nanocrystalline and amorphous as illustrated by simplified two dimensional atomic arrangements in Figure The distinction is made based on the extent of spatial atomic order in the structure A bulk crystalline solid Figure A is a highly ordered three dimensional repetition of a smaller atomic motif termed the unit cell and the structure thus possesses long range order The translational symmetry is described by the three vectors defining the unit cell a 1, a 2 and a 3 Within the cell the atomic positions may be constrained by further symmetry restrictions such that only a small number of atomic positions the asymmetric unit the symmetry given by the crystallographic space group and a 1, a 2 and a 3, are needed to describe the total crystal structure The counterpart to a crystal is an amorphous structure Figure C where no long range order is present The local order i e the first atomic coordination shells however is usually relatively well defined due to the nature of chemical bonding Figure 1.1: Atomic arrangements in crystalline nanocrystalline and amorphous solids

20 Chapter (ydrothermal Synthesis of Nanomaterials A nanocrystal often just termed a nanoparticle is a crystalline structure where at least one dimension is smaller than nm Figure B )t thus possesses translational symmetry like bulk crystalline materials but the finite size of the crystal limits the structural coherence and the range of atomic order The whole concept of crystallinity breaks down when dealing with particles with dimensions of less than unit cells and it can therefore be challenging to describe nanocrystalline structures using only traditional crystallographic terminology and methods The nanostructure of advanced functional materials affects almost all material characteristics such as mechanical strength and electrical and optical properties and much attention is therefore directed towards the synthesis and characterization of new nanomaterials This also applies for battery materials Figure shows a simple illustration of a rechargeable Li ion battery )t consists of three parts An anode here graphite a cathode here LiCoO and an electrolyte The cathode and anode electrodes have different chemical potentials such that when connected electrons spontaneously flow from the more negative to the more positive potential Simultaneously Li ions are transported between the electrodes through the electrolyte thereby maintaining charge balance The rate and efficiency of the battery are dependent on the reactions between Li and the cathode and anode particles For LiCoO and graphite these happen through intercalation in the layered structures and the Li diffusion in the D layers thus determine the reaction kinetics which in turn affects the charge discharge rate of the battery Figure 1.2: )llustration of Li ion battery

21 Chapter (ydrothermal Synthesis of Nanomaterials By nanosizing the electrode crystallites the pathway for lithium diffusion in the particles is reduced resulting in faster lithiation delithiaion Furthermore the contact area between the electrolyte and the electrode particles is increased for nanoparticles compared to larger crystallites due to the particle surface volume ratio This supplies the Li ions with more entries into the particles again speeding up the reactions and making it feasible to take full advantage of the capacity of the electrode materials Nanoparticles also accommodate strain related to the lithium intercalation de intercalation better than bulk materials making the reversibility of electrode reactions higher and thus enhancing the cycle life of the batteries )n recent years much attention has been given to the development of new electrode materials Studies of alternative intercalation electrodes such as LiFePO have emphasized the need for nanostructures due to relatively low electronic and ionic conductivity of the compound Furthermore metal and metal oxide nanoparticles are now studied extensively as candidates for high capacity anodes Some metals and semimetals e g Si Sn and Al can react with Li to form alloys in a partly reversible electrochemical process where large amounts of Li can be accommodated in the final structure (owever the volume change from the lithiated to delithiated state is very high giving rise to extensive mechanical strain in the battery By applying nanoparticles this problem can be reduced and both Sn and Si based nanomaterials are believed to become important in the next generation of batteries Studies of the reaction of various nanoparticles with Li have also shown that chemistry changes when working on the nanoscale For example Fe O nanoparticles can react reversibly with Li per Fe O while larger crystallites react irreversibly with Li per Fe O )n other energy technologies nanostructure plays an equally large role )n thermoelectric materials for example nanostructuring can reduce the thermal conductivity thus increase the thermoelectric efficiency )n catalysts for e g fuel cells the large surface volume ratio for nanoparticles increases the active area compared to bulk materials The goal in nanotechnology is thus to be able to engineer functionalized material on a nano meter scale i e nm Due to the close relation between size and properties being able to synthesize tailor made particles as well as understanding the size structure relationship is crucial

22 Chapter (ydrothermal Synthesis of Nanomaterials 1.3 Hydrothermal Synthesis of Inorganic Nanomaterials Nanoparticles can be synthesized in numerous ways and it is well beyond the scope of the dissertation to give a review of the field )nstead ) will focus only on the hydrothermal method which has been applied in my research The method is by no means a new invention the term hydrothermal has its origins in geological science and was first used in the beginning of the th century describing hydrothermal circulation This process where hot pressurized water circulates under the crust of the Earth is responsible for the formation of rocks and minerals and investigating these reactions was the starting point for research in hydrothermal processes The knowledge acquired led to interest in using similar conditions for synthetic chemistry and the first records of hydrothermal synthesis were by Robert Bunsen in (is synthesis of BaCO and SrCO crystals thus marked the beginning of a huge research field which is still continually developed (ydrothermal synthesis is now used throughout inorganic and materials chemistry and novel takes on the traditional techniques such as continuous supercritical synthesis are believed to be promising methods for advanced material production )n the following a short description of the technique as employed for inorganic materials synthesis is given For further details on the method development and theory the reader is referred to i a Handbook of Hydrothermal Technology by Byrappa and Yoshimura as well as several reviews The Hydrothermal Method A hydrothermal synthesis is a special case of a solvothermal process which is generally defined as a chemical reaction taking place in a solvent at temperatures above the solvent boiling point and at pressures above bar The medium used in a solvothermal synthesis can thus be anything from water hydrothermal to ammonia ammonothermal an alcohol alcothermal glycothermal or any other organic or inorganic solvent The hydrothermal method exploits that by increasing temperature and pressure the fundamental properties of water and thus its abilities as a solvent changes )mportant characteristics such as the ionic product density thermal conductivity viscosity heat capacity and the dielectric constant are all highly p,t dependent and by tuning the synthesis parameters specific solvent properties can be obtained As an example Figure shows the dielectric constant of water as function of temperature for different pressures With temperature the dielectric constant drops rapidly This drop has large implications for the solubility of polar and ionic species which are often used

23 Chapter (ydrothermal Synthesis of Nanomaterials Figure 1.3: Dielectric constant of water at various temperatures and pressures The dielectric constants for solvents at ambient conditions are indicated with arrows From Bremholm in the synthesis of inorganic materials As the dielectric constant decreases when the temperature is increased the ionic species can precipitate to a solid phase The precipitation and following particle nucleation is discussed further in section The precursor used in the synthesis of inorganic compounds is often aqueous solutions of simple salts such as metal chlorides nitrates or acetates Depending on the specific synthesis these can be precipitated to the corresponding metal hydroxides prior to the synthesis using a base often NaO( KO( or N( O( and other additives for e g p( control reduction or oxidation coating etc can equally be added prior to the hydrothermal treatment The reaction mechanisms are naturally highly system dependent but when considering a simple and classic example namely the synthesis of metal oxide particles Adschiri et al have in suggested the following step formation mechanism for particles from a simple metal salt Step (ydrolysis MXx aq x( O l M O( x s x(x aq Step Dehydration M O( x s MOxs x ( O l (ere M denotes the metal and X the anion As the temperature is increased the equilibria shift to the right leading to the formation of metal oxide particles (owever even in this simple example several aspects of the reactions are not known The intermediate phase M O( x is hard to characterize as the second reaction often happens quickly after the formation

24 Chapter (ydrothermal Synthesis of Nanomaterials of the hydrated phase Furthermore as the intermediate phase is often amorphous and nano sized it is difficult to obtain structural information from traditional characterization methods The mechanisms controlling the reactions are thus not well understood Supercritical Synthesis of Nanoparticles As was seen in Figure the most drastic changes in the solvent properties occur around the critical point of water at o C and bar Above this point in the supercritical state there is no longer a distinction between the gas and liquid phase and the properties of supercritical water lies between those of the two phases At o C and bar the dielectric constant is below and in this respect supercritical water can be compared to an nonpolar organic solvent As a further development of the hydrothermal method supercritical synthesis has become a well established technique for nanoparticle production and the method is already used commercially (ere an aqueous solution of e g a metal salt is very rapidly brought to temperatures above the critical point and instantaneously the low dielectric constant will force nanoparticles to precipitate Because all the metal ions present in the precursor will precipitate in numerous particle nuclei simultaneously very small homogenous particles with a narrow size distribution can be obtained This is illustrated in Figure where it is compared to a synthesis at lower temperatures subcritical during which the precipitation happens much slower )n subcritical synthesis nucleation does not happen instantaneously The fraction of the precursor that does not immediately precipitate will slowly crystallize around the particle nuclei and thus result in particle growth giving much larger particles with wide size distributions Figure 1.4 Growth of MOx particles under sub and supercritical conditions Adapted from Adschiri

25 Chapter (ydrothermal Synthesis of Nanomaterials Reactors for Hydrothermal Synthesis A conventional hydrothermal synthesis is performed in a batch reactor (ere the precursors are simply dissolved or suspended in water in an autoclave Figure A which can withstand high temperatures and pressures The autoclave is subsequently sealed and heated to the desired temperature while the pressure is most often autogenously generated Depending on the degree of autoclave filling pressures of up several hundred bar can be obtained even at low temperatures This is illustrated in Figure B where the autogenously generated pressure is plotted as function of temperature for various filling fractions The volume of the autoclave varies from few milliliters for laboratory scale synthesis to thousands of liters for industrial scale material production Depending on the reactor construction the maximum temperatures and pressures can be as high as o C and bar (owever in general temperatures below o C are preferred for commercial applications The autoclave sketched in Figure A is typical lab scale version as is also used at Aarhus University )t simply consists of a Teflon cup inserted in a steel shell which can be sealed with a steel lid For these types of autoclaves the maximum temperature is limited to ca. o C Although batch reactors have proved to be very powerful for material production there is a general interest in developing flow reactors where material can be continuously synthesized Flow reactors are especially well suited for supercritical synthesis where rapid heating rates are required This first continuous flow hydrothermal reactor was developed by Adschiri et al in at Tohoku University and since then several groups around the world have built and developed continuous apparatuses including the )versen group in Aarhus Furthermore a continuous pulsed reactor combing the merits from batch and flow synthesis has recently been developed in Aarhus Figure 1.5: A Schematic drawing of a lab scale autoclave B Pressure obtained in autoclaves at different filling fractions Adapted from Rabeneau

26 Chapter (ydrothermal Synthesis of Nanomaterials Merits and Shortcomings of the Hydrothermal Method (ydrothermal synthesis is a green environmentally friendly and simple method for material production Due to the physical and chemical properties of pressurized and heated water the temperatures needed to synthesize specific inorganic compounds are much lower than in a conventional solid state synthesis Additionally purer and defect free materials are often obtained As extended high temperature treatment is not required thermodynamically metastable phases can be obtained and because it is easy to change the chemical environment in the synthesis by altering e g the p( value or oxidation potential it has been shown possible to synthesize complex inorganic materials The crystallite size and morphology can furthermore often be altered on the nanoscale by simply adjusting the synthesis parameters i e temperature precursor concentration p( etc Additionally the process is easily scalable especially when using continuous apparatuses The precursors are often simple metal salts which are cheap and readily available Compared to advanced soft chemical techniques hydrothermal synthesis uses no toxic solvents and often expensive and toxic additives such as organic surfactants or harsh reductants are not needed in the reaction The hydrothermal method thus shows great promise for several different applications and fields )n recent years much attention has also been given to improvements of the method The continuous flow approach is in fast progress with new mixing technologies setups for core shell nanoparticle synthesis etc being built Also the batch method is developing with new approaches to synthesis appearing The microwave hydrothermal synthesis method was first reported in by Komarneni et al, and has since then been used for several different systems Other combinations of technologies include ultrasonic hydrothermal synthesis electrochemical hydrothermal synthesis as well as mechanochemical hydrothermal synthesis The method thus has many merits but there are also drawbacks Often extensive exploratory trial and error studies are needed to map the parameter space precursor composition p( oxidation potential temperature pressure and reaction time for a specific synthesis as it is hard to predict the outcome of a reaction This illustrates that even years after the first laboratory hydrothermal synthesis we still do not understand some of the most central processes taking place in the reactor )n addition to developing new advanced synthesis equipment and synthesizing novel complex and exotic materials it is thus necessary to take a step back in complexity in order to understand some of the underlying chemistry that happens during particle formation and

27 Chapter (ydrothermal Synthesis of Nanomaterials growth Before discussing methods for obtaining this understanding in Chapter and some of the classical theories for particle nucleation and growth will be introduced followed by a discussion describing the difficulties implementing these to hydrothermal methods 1.4 Particle Nucleation and Growth Theory Nucleation of Particles in a Liquid Classic text book nucleation theory builds on theoretical considerations for solid particles in melts but these are often extended to other solid liquid systems e g hydrothermal synthesis Although many approximations are done when considering a hydrothermal synthesis in this context the approach is useful when trying to understand the basic processes The theory uses simple thermodynamic functions to describe the formation of the nuclei that lead to particles Two different mechanisms are often considered namely homogenous or heterogeneous nucleation and here homogenous nucleation is introduced Generally atoms in a melt or another liquid phase will fluctuate in the liquid phase due to thermal motion Sometimes these fluctuations will lead to formation of atomic assemblies with local structures resembling that of a solid phase )f there is a thermodynamic gain related to this cluster formation the assembly might stay stable and act as nuclei for particle formation (owever when forming a new particle an interface between the liquid and solid phase is created This costs energy and the total expression for the change in Gibbs free energy can be written as (ere V s is the volume of the solid particle G V the energy gain by forming the solid A SL the area of the interface and the interfacial energy Assuming that this energy is isotropic and that the particles are spherical with radii r the following expression is obtained This function is plotted in Figure where a maximum is seen at

28 Chapter (ydrothermal Synthesis of Nanomaterials Interfacial energy G(r) G* 0 r* Volume free energy 0 Cluster radius r Figure 1.6: The size dependent change in Gibbs free energy for nucleation as function iof the radius of the formed of solid cluster Thus only above this limit it is thermodynamically favorable to form particle nuclei Below it the clusters are unstable in equilibrium with the species still in solution The local fluctuations and the amount of species in the liquid phase therefore have to be large enough for clusters above the critical size to form The critical cluster size may be considered in terms of supersaturation of dissolved species The relative supersaturation is given as where AP is the activity product for dissolved species ready to precipitate while K is the solubility product The change in Gibbs free energy is related to the supersaturation as and higher relative supersaturation will thus decrease the critical nucleus radius required for stable cluster formation The equilibrium constant K is heavily dependent on the dielectric constant of the solvent and a revised (elgeson Kirkham Flowers (KF model can be used to calculate equilibrium constants for several inorganic compounds under hydrothermal conditions (ere and 0 are the dielectric constants at the actual temperature pressure and standard ambient conditions respectively K 0 is the equilibrium constant at standard conditions and is a constant parameter specific for the reaction system As discussed above the dielectric constant drops with temperature and pressure most dramatically around the supercritical point The solubility dependence on the change in dielectric constant and temperature as described by the (KF model have been shown to give a small increase in metal oxide

29 Chapter (ydrothermal Synthesis of Nanomaterials solubility up to the supercritical point whereupon it drops dramatically This is illustrated for CuO in Figure The sudden drop in solubility above the critical point is exploited in supercritical synthesis Even though the solubility increases up to the critical point thereby implying an increase in the cluster critical radius the increased temperature ensures that the energy required to overcome the nucleation barrier is more than provided Subcritical conditions will therefore similarly provide the means for nucleation of dissolved metal ions but the extreme burst in nucleation expected for supercritical synthesis will not occur Figure 1.7: Solubility of CuO as function of temperature Points represent measured data while the solid line arises from theoretical calculations From Sue Growth of Particles in Solution When stable nuclei have formed in the liquid the particles will start growing to minimize the energy loss related to the newly formed high surface area This can happen through several different growth mechanisms again depending on the chemistry and local environment Classically particle growth is described based on differences in surface energy of small and large particles For solid species present at a solid liquid interface the chemical potential increases with decreasing particle size following the thermodynamic theory presented above This leads to re dissolution of the smallest newly formed particles creating a concentration gradient in the solution Uniformity of the concentration is reestablished by material diffusion towards the larger particles thus leading to particle growth The process illustrated in a simple diagram in Figure A was first described by Ostwald in and the mechanism is therefore known as Ostwald ripening Since the growth rate is dictated by material diffusion between particles the process is often termed diffusion limited growth

30 Chapter (ydrothermal Synthesis of Nanomaterials Figure 1.8: Particle growth by Ostwald ripening The full mathematical treatment of the process was done in the s by Lifshitz and Slyozov followed by work by Wagner and is known as LSW theory )t was shown that the diffusion limited growth process leads to time growth dependence of the form (ere t is the time r the particle radius r 0 the particle radius at time t and K a constant containing the interfacial energy the diffusion constant of the system the average concentration of the species and the temperature among other parameters )f the diffusion of material to the growing particles is faster than the actual reaction of the material with the particle surface the growth is reaction limited )n this case it can be shown that the time dependency of the size is Analysis of the growth curves can therefore give indications of which step in the particle growth determines the growth rate Real Life Nucleation and Growth Classical nucleation and growth theory can thus provide information on the main processes related to particle synthesis (owever in many cases the theories fail to supply any details about the further mechanism and classical modelling is often insufficient in describing experimental observations )n the case of particle nucleation the classical expressions regarding the nucleation energy are very approximate for example further calculations show that for many systems the critical nuclei often consist of less than atoms and at this size the particles cannot be considered spherical The interfacial energy is most likely particle size dependent and moreover cannot necessarily be assumed isotropic Consequently chemical considerations regarding the interaction of the liquid phase with the solid particles are required to fully understand the nucleation processes Additionally the nucleation happening in a hydrothermal synthesis is much

31 Chapter (ydrothermal Synthesis of Nanomaterials more complex than the solidification of a metal from a melt as the reaction energies related to e g hydrolysis and condensation need to be taken into account Several attempts of describing nucleation in solution hydrothermal synthesis in general terms based on both experiments and theory have been done but it is now widely accepted that the nucleation process is highly system dependent and cannot easily be generalized New theories such as the Two step models where an initially disordered cluster transform to an ordered crystallite have also been proposed Following LSW theory the coarsening phenomenon has been studied both theoretically and experimentally in several systems and more complex models for particle growth have been developed by several different groups A lot of the work has concerned particle size distribution developments with reaction time The newer models have used more advanced theoretical models describing the dissolution and diffusion and interestingly the resulting parameters and time growth relations seem to be very dependent on the theoretical approach used This shows that the LSW theory is really an over simplification of the growth mechanism and that many more factors affect the particle growth More recently non classical mechanisms have been used to explain growth of smaller nanocrystals )n Penn and Banfield first reported oriented attachment (ere it is proposed that particles grow when two nanocrystals are oriented such that they share crystallographic orientation and can thus be attached to each other forming a single crystal Generally with the developments in characterization methods further advanced models regarding nucleation and growth of nanoparticles are likely to appear in the coming years As will be seen in the following chapters in situ X ray scattering studies of the mechanisms can yield important information on the chemical reactions happening during the synthesis First the characterization methods applied are introduced

32 Chapter Characterization of Nanoparticles by Scattering Techniques 2 Characterization of Nanoparticles by Scattering Techniques 2.1 Introduction Just years after Wilhelm Röntgen discovered X rays in Max von Laue showed that when shining these through a crystal a distinct diffraction pattern appears due to the internal periodic arrangement of atoms This marked the birth of crystallography and led to the derivation of the Bragg law in by W ( and W L Bragg Since then the field has continued to grow and crystallography is today a multidisciplinary technique used in everything from biological to materials science Since the use of scattering and diffraction has thus led to Nobel Prizes and the field is continuously developing with new applications constantly appearing )n the following a short introduction to X ray and neutron scattering will be given As the topic has been described in depth in numerous textbooks detailed derivations of the theory will not be presented in the dissertation and the present chapter mainly serves to introduce how scattering techniques can be used for structural characterization of nanomaterials Section contains a short description of X ray and neutron scattering processes where the nomenclature used in the dissertation is introduced X ray and neutron sources are introduced in section )n Powder X ray and Neutron Diffraction PXRD and PND is described followed by an introduction to Total Scattering TS and Pair Distribution Function PDF analysis in section A brief description of Small Angle X ray Scattering SAXS is a included in section followed by a short summary of the various techniques in section The chapter is based mainly on the books by Als Nielsen McMorrow Warren scattering theory Billinge Dinnerbier Young powder diffraction and Billinge Egami total scattering where further details may be found

33 Chapter Characterization of Nanoparticles by Scattering Techniques 2.2 X ray and Neutron Scattering Scattering of X rays When a beam of X rays propagates through a sample the material is subjected to a sinusoidal varying electric field This field interacts with the electrons in the sample which consequently start oscillating and emit radiation according to electromagnetic theory The process can either be elastic or inelastic and incoherent or coherent and several processes may occur simultaneously )n the following only coherent elastic scattering will be considered as this is the process mainly exploited in the investigation of material structure The term scattering will in this section been used to describe the process happening when X rays interact with an electron distribution (owever in the context of elastic interactions of X rays the term can be used interchangeable with diffraction and both terms will be used throughout the dissertation A general scattering process is sketched in a simple 2D diagram in Figure (ere an X ray beam is scattered by a point scatterer such as a single electron The scattering vector q is defined as the momentum transfer in the process and is usually expressed in units of Å Figure 2.1: Scattering process from electron at position r For elastic scattering the wavelengths of the incoming and outgoing waves are equal i = f, k i =k f and the magnitude of the scattering vector is therefore given as sin The intensity of the scattered radiation at a certain point in q space is contained in the coherent scattering cross section d /d. )t expresses the

34 Chapter Characterization of Nanoparticles by Scattering Techniques fraction of photons scattered into a detector area d in the direction q The scattering cross section is proportional to the square of the amplitude of the scattered waves (q): Coherent elastic scattering is uniform in space around a point scatterer )n a coherent scattering process from matter however the radiation scattered from the individual electrons in the atoms will interfere and the scattering amplitude will no longer be uniform but dependent of q )f first considering scattering from a single atom the electron cloud surrounding the nucleus will result in phase differences between the waves scattered from different parts of the continuous electron distribution (r). )t can be shown that the amplitude of the total scattered wave from a specific atom is given by the atomic form factor, f(q) which is the Fourier transform of the electron density exp The atomic form factors for ( C and F are plotted as function of q in Figure The X ray scattering power increases with electron number but decreases with increasing q. 4 C 2 0 H q (Å 1 ) Figure 2.2: Atomic form factors for ( C and F as function of q f 8 6 F )f now considering a material consisting of a collection of atoms v at positions r v the q dependent sample scattering amplitude is given by the Fourier transform of the atomic positions exp

35 Chapter Characterization of Nanoparticles by Scattering Techniques This assumes the kinematic approximation which ignores any multiple scattering processes Due to interference effects the amplitude of the coherently scattered waved thus contain information on the atomic structure of the scattering matter By analysing the scattering intensity proportional to 2 structural information can be extracted X ray Scattering from Crystals )n a crystalline material the atomic structure is periodic and the radiation scattered from the individual atoms or molecules in a crystal will interact in a particular simple manner and give constructive or deconstructive interference at specific points in q space )n terms of a three dimensional lattice where the translational symmetry is described by unit cell vectors a 1, a 2 and a 3, it can be shown that constructive interference will only occur when the Laue condition is fulfilled for the q vector (ere a i * are the reciprocal lattice vectors defined so that a i a j *= where ij is the Kronecker delta i e ij = for i=j and ij = otherwise The Miller indicies h, k and l are integers and the K vector represents reciprocal lattice points A simple way to illustrate under which circumstances the Laue condition is fulfilled is through the Ewald sphere as shown in D in Figure The radius of the sphere is k, and the origin of the reciprocal lattice is placed on the sphere surface The Laue condition is fulfilled only when the reciprocal lattice is oriented in a way such that a reciprocal lattice point falls on the sphere surface By rotating the reciprocal lattice i e rotating the crystal in certain directions this can be achieved Figure 2.3 The Ewald Sphere in two dimensions

36 Chapter Characterization of Nanoparticles by Scattering Techniques )f projecting the three dimensional Laue conditions to one dimension it can be shown that it is equivalent to the simpler Bragg law sin (ere d hkl is the spacing between crystal lattice planes with Miller indices hkl defining the translational symmetry is the scattering angle and the radiation wavelength The amplitude of the scattered beam for q=k is given by the crystallographic structure factor which is the Fourier transform of the electron density in the unit cell in accordance with exp The sum is over all the N atoms in the unit cell where the position of each is given by the vector r and the form factor of the specific atom f Since atoms are not static but vibrate around their equilibrium position the Debye Waller factor is introduced to account for this giving exp exp The vector u describes the thermal displacements of the scattering centres Equation and summarizes how scattering experiments can be used to study structures of crystalline materials The positions of the scattered radiation in q space contain information about the translational symmetry i e unit cell vectors while the intensity of the scattered beam proportional to 2 is determined by the contents of the unit cell By means of modelling precise crystal structures can thus be solved or refined The specific use in powder diffraction will be described in section Only coherent scattering was so far described but incoherent processes happen equally (owever incoherently scattered radiation contains no structural information due to the lack of a definite phase relationship of the scattered waves and incoherent effects are therefore seen as a background signal underneath the coherent scattering arising from equation

37 Chapter Characterization of Nanoparticles by Scattering Techniques Furthermore scattering is not the only process occurring when shining X rays on an object A part of the X ray radiation is absorbed by the material which means that the photon energy is completely transferred to an electron in the sample which can then leave the specific atom ionized The degree of absorption depends on the X ray energy as well as the electron density of the material Absorption processes can be used for local structure analysis through EXAFS Extended X ray Absorption Fine Structure spectroscopy (owever it is beyond the scope of the dissertation to discuss absorption any further Neutron Scattering The scattering theory introduced in section concerned interactions of X rays with matter but the basic principles can be equally applied to neutron scattering Where X rays interact with electrons neutrons interact with the atomic nuclei The scattering power of a specific element thus depends on the nuclear structure and can vary significantly with e g different isotopes of the same element Figure shows a representation of neutron scattering power for the first elements As can be seen some light elements scatter just as strongly as heavy elements and some have negative scattering lengths This makes neutron scattering very powerful in characterization of structures containing light elements such as hydrogen or lithium which can be difficult to study with X rays Neutron scattering is also very useful for distinguishing between elements with adjacent atomic numbers such as Fe or Mn Furthermore magnetic structures can be studied due to the magnetic moment of the neutron Where the atomic X ray form factor was seen to decrease with q because of the spatial distribution of electrons around the atom the neutron scattering length denoted b is constant in q and structural information from high scattering vectors can be obtained b (barns) D He H He Li N Cl Be B C OF Mg NeNa Al SiP K Ca S Ar z Figure 2.4: Coherent neutron scattering length for the first elements Sc Ti V Ni Fe Cu Zn Cr Co Mn

38 Chapter Characterization of Nanoparticles by Scattering Techniques 2.3 Sources of X rays and Neutrons for Scattering Experiments X rays can be generated in the laboratory using a standard sealed tube source (ere electrons produced by a heated W filament are accelerated towards a metal anode by a potential difference When the electron beam hits the metal the electrons in the target atoms are excited and in order to return the ground state energy is released as X rays Depending on the electronic structure of the target material intense X rays of specific wavelengths will be emitted as well as bremsstrahlung of a broad spectrum of wavelengths A monochromator or filter can be used to eliminate radiation of all unwanted wavelengths The most common anode material for laboratory powder diffractometers is Cu where the K electron transition gives a characteristic wavelength of Å corresponding to kev While laboratory diffractometers are extremely useful for day to day sample characterization much of the work done today in advanced X ray crystallography uses synchrotron radiation )n a synchrotron X rays are generated when charged particles travelling at relativistic speeds are made to follow a curved trajectory by means of a magnetic field Figure A shows a sketch of a synchrotron ring )t consists of straight sections where electrons are accelerated and of sections constructed such that the electrons deviate from their straight path thus emitting electromagnetic radiation owing to the transverse acceleration of the charged particles These constructions can either be bending dipole magnets or insertion devices wigglers or undulaters )n an insertion device the alternating magnetic field placed in the straight section of the storage ring forces the electrons to oscillate Figure B providing X ray beams with very high flux and narrow angular range The energy of the emitted X rays depends on the gap between the magnets and can therefore easily be changed With advanced optic components the resulting beam can be monochromatized focused and collimated Figure 2.5: A Sketch of synchrotron storage ring From Kastbjerg B Top view of the electron pathway in an insertion device with alternating magnets After Als Nielsen MacMorrow

39 Chapter Characterization of Nanoparticles by Scattering Techniques Compared to the radiation generated in a standard laboratory source synchrotron radiation is extremely intense and brilliant making it possible to rapidly obtain high quality data Furthermore a synchrotron beam is highly collimated and very good q resolution can therefore be achieved in a scattering experiment The tuneable X ray energy makes it possible to change the wavelength for a specific purpose e g spectroscopy or anomalous diffraction experiments At rd generation synchrotrons such as the Advance Photon Source APS ARNL Chicago the European Synchrotrons Radiation Facility ESRF Grenoble or PETRA))) DESY (amburg X ray energies of several hundred kev can be obtained allowing novel types of experiments to be performed For these reasons all the X ray studies presented in the dissertation have been done using synchrotron radiation around the world While X ray diffractometers are standard equipment in any material science laboratory intense neutrons beams cannot be produced in the lab Neutron experiments must therefore be performed at large facilities where neutrons are produced in either nuclear reactors or spallation sources The neutron experiments described in this dissertation have been done at pulsed spallation sources namely The Lujan Center at Los Alamos National Laboratory USA and the Spallation Neutron Source SNS at Oak Ridge National Laboratory USA )n a spallation source a heavy metal target such as Pb W Ta or (g is bombarded with energetic particles usually protons accelerated to energies of up to GeV This bombardment results in spallation i e release of high energy epithermal neutrons from the target To obtain neutrons in the energy range suited for diffraction experiments the neutrons are cooled down by means of collisions in a moderator in the neutron pathway The neutrons are then led to the experimental instruments in evacuated guide tubes

40 Chapter Characterization of Nanoparticles by Scattering Techniques 2.4 Powder Diffraction )n this section the use of X ray and neutron scattering for materials characterization by means of powder diffraction is described further The technique was developed in by Debye and Scherrer just years after the derivation of Bragg s law and the first single crystal diffraction experiments Since then it has become an indispensable characterization method for materials scientists )t provides an easy non destructive way of identifying crystalline compounds and even solving and refining crystal and nano microstructure (ere a short introduction to the method is presented with particular focus on the use of powder diffraction for nanomaterials Special attention will be given to the treatment of profile broadening in Rietveld refinement and how nanostructural information can be extracted Diffraction from a Powder For a sample to qualify as a powder a very large number of small crystallites must be randomly oriented with respect to each other such that every possible crystalline orientation is represented equally in the sample When this is fulfilled there are numerous crystals that satisfy any possible Bragg condition with respect to the incoming beam The principle is illustrated in terms of the Ewald sphere in Figure A D and B D )nstead of having discrete reciprocal lattice points as for a single crystal the reciprocal lattices of the many randomly oriented crystallites form a series of concentric spheres that intersect the Ewald surface with each intersection circle representing a particular reciprocal lattice point The measurable signal is thus cones of scattered radiation which will show up as circles on a D detector Usually these data are integrated to yield a D diffraction pattern as shown in Figure C When doing a powder diffraction experiment the three dimensional nature of the scattering amplitude q is therefore condensed into one dimension q )n order to obtain accurate intensities of the Bragg peaks it is crucial that the sample is in fact a powder graininess few crystallites can cause severe problems )n this case the number of lattice planes oriented to diffract differs for the various reciprocal lattice points and the spheres intersecting the Ewald surface are not complete Another issue is preferred orientation that arises when there is a stronger tendency for the crystallites to be oriented in a specific direction This can happen if e g the particles are disk or rod shaped and will change the relative intensities of the Bragg peaks

41 Chapter Characterization of Nanoparticles by Scattering Techniques Figure 2.6 a The Ewald circle in dimensions The different colours of the reciprocal lattice points correspond to crystallites with different orientation b The Ewald sphere in three dimensions The crystallites produce concentric diffraction rings c When integrated the D data result in D diffraction patterns X ray Powder Diffraction Experiments )f considering the Bragg law two parameters can be varied to fulfil the conditions for a certain lattice spacing d the wavelength or the scattering angle Corresponding to this two options for powder diffraction experiments are used angular dispersive or energy dispersive mode )n the latter the signal is collected at a fixed scattering angle as function of energy whereas in angular dispersive mode the wavelength is kept fixed while the scattering signal is measured as function of scattering angle This can be done either using a moving point detector a line detector or a flat plate D detector Generally the angular dispersive mode is now most widely applied for X ray studies and has been used for all the experiments described in the dissertation Conventional powder diffraction experiments are done in either reflection Bragg Brentano or transmission Debye Scherrer geometry For synchrotron studies the simplest option is to use transmission geometry as illustrated in Figure B Neutron Powder Diffraction Experiments Just as for X rays neutron powder diffraction data can be measured either as function of scattering angle with a monochromatic beam or as function of neutron wavelength at a fixed scattering angle The neutron experiments described in the dissertation have been done using the latter technique i e Time of flight TOF neutron powder diffraction A TOF experiment uses the polychromatic beam at the pulsed neutron source and exploits the fact that

42 Chapter Characterization of Nanoparticles by Scattering Techniques the neutron wavelength is inversely proportional to its velocity v according to the De Broglie relationship By recording the arrival time of each neutron of a particular pulse in the detector its wavelength and therefore the corresponding d spacing of the diffracting planes can be calculated (ere t is the time of flight L is the length of the flight path m n is the neutron mass and h is the Planck constant The scattered neutrons are usually detected at several banks covering a large proportion of the volume around the sample Since the TOF technique makes use of a large wavelength band high quality data can rapidly be obtained at high flux sources Compared to X ray experiments additional considerations have to be done in the experimental preparation for neutron studies For example incoherent neutron scattering occur due to differences in scattering lengths between spin states of the nucleus For ( there is a large difference in the scattering length between the spin up and spin down states of the protons leading to a considerable incoherent scattering cross section i e a large background Therefore if possible hydrogen is often substituted with deuterium ( for neutron experiments Where X ray absorption depends on the number of electrons in the sample the neutron absorption again depends on the nuclei structure The neutron absorption can thus vary significantly with isotopes While Li is a strong neutron absorber the absorption in Li is negligible and the latter is thus preferred for neutron diffraction experiments Information in the Powder Diffraction Pattern The research presented in the dissertation has applied both X ray and neutron powder diffraction experiments )n the following section the X ray approach and nomenclature is generally used but the main principles also apply for neutrons When doing a standard angular dispersive PXRD experiment of an isotropic crystalline sample the result is a plot of intensity as function of diffraction angle or scattering vector qsin As shown in equation the Bragg peak q values are determined by the translational symmetry of the crystal lattice and the peak positions are therefore solely dependent of the size and symmetry of the unit cell )nformation about the content of the unit cell lies in the intensities of the peaks which within the kinematical

43 Chapter Characterization of Nanoparticles by Scattering Techniques approximation are proportional to the norm of the crystallographic structure factor in equation The intensity of the hkl family peak is given by (ere S is a constant containing parameters related to the geometry used in the experiment I 0 is the intensity of the incoming beam the wavelength r the sample to detector distance V the unit cell volume and L the Lorentz factor correcting for the intensity dependency arising from the integration of the diffraction cones p corrects for incomplete polarization of the incoming beam M is the multiplicity of the hkl reflections while F hkl is the structure factor (ence all information about the crystal structure of the sample lies in the diffraction peak positions and intensities (owever one of the strengths of PXRD is that it also gives information about the sample microstructure which is contained in the line profile of the Bragg peaks Theoretically a perfect crystalline sample and a perfect instrument would cause Bragg peaks to be infinitely narrow functions with intensities given by equation (owever many factors contribute to the broadening of peaks )n general the contributions can be divided into instrumental profile g and sample profile j and the full profile h is the convolution of the two Several effects such as beam divergence sample size slit widths etc contribute to the instrumental broadening Sample broadening is caused by limitations of the coherently diffracting crystalline domains and all sorts of crystal imperfections can give rise to this Using a generalized approach the effects are traditionally divided into crystallite size and crystallite strain and the contributions from each can theoretically be distinguished by the angular dependence of the peak width Strain broadening occurs due to crystal defects and can thus take many different forms depending on the specific type (owever macrostrain broadening due to lattice defects can be shown to generally take the form tan (ere is the macrostrain

44 Chapter Characterization of Nanoparticles by Scattering Techniques Size broadening is expressed in the Scherrer equation derived in cos (ere is the profile width K a constant the diffraction angle and <D> the parameter expressing the crystallite domain size The original Scherrer derivation was done for an ideal powder of small monodisperse cubic crystallites and in this case <D> has the physical meaning of being the volume weighted crystallite size The constant K is dependent on the particle morphology but often this dependency is ignored The value is subject for much confusion and are all used widely When deriving the formula from monodisperse cubic crystals using the integral breadth the result is K )f the full width at half the maximum intensity FW(M is used in the size analysis K should be set to )n practice however this has no large implications as the Scherrer derived particle size should only be used to study trends in crystallite sizes rather than exact dimensions )n this context it is also important to note that the apparent size obtained from the Scherrer equation cannot directly be compared to the particle size found from e g electron microscopy Firstly it is not the same quantity <D> is the volume weighted size whereas an average size found from e g TEM is number weighted Secondly <D> refers to the crystallite domain size whereas the particle size as seen by TEM can include amorphous parts of the sample or be the size of aggregates or polycrystalline grains rather than single crystals Furthermore since it is often hard to distinguish size broadening from strain broadening conclusions regarding absolute size of particles should be made with great care Still much information about trends in crystallite size i e crystallite growth can be obtained from Scherrer analysis The Rietveld Method Rietveld refinement is a powerful way of extracting the structural and nano microstructural information mentioned above from a powder diffraction pattern Since its development in the s by (ugo Rietveld it has become a standard analysis technique for powder diffraction data Today several Rietveld software packages exist making the method highly accessible The work presented in the dissertation has applied different programs namely FullProf Suite and GSAS )n the following sections the Fullprof nomenclature is used

45 Chapter Characterization of Nanoparticles by Scattering Techniques A Rietveld refinement requires two inputs A structural model from which a theoretical diffraction pattern can be calculated and an experimental pattern from which the structural parameters are to be extracted The quantity to minimize by refinement of the parameters in the model is then the difference between the two diffraction patterns (ere the sum is over all the observations in the data w i is the weight of the observation y i is the observed intensity and y ci is the calculated intensity of the i th step For a certain phase the calculated intensities are determined from the norm of the structure factor calculated from the given model Often there will be overlap of several Bragg peaks and the intensity in a certain point q is therefore a sum over the intensity from the neighbouring peaks s is here the scale factor gathering all the non dependant terms that affect the intensity Lp is the combined Lorentz and polarization correction factor is the profile function describing the peak shapes F is the structure factor and y bi is the background intensity in the i th step The summation goes over the M neighbouring peaks to the i th step For multi phase models an additional summation over all phases is made Two approaches for the background description are generally used )nterpolation between a number of refinable points or a smoothly varying function such as a linear combination of a number of polynomials with refinable coefficients The best model describing the experimental data is found by using the least squares method for the minimization of S y The model is improved by refining the appropriate structural parameters such as the unit cell parameters atomic positions Debye Waller factors etc The quality of the fit is expressed by the residual factors given by

46 Chapter Characterization of Nanoparticles by Scattering Techniques Note that R F and R Bragg are actually deduced with the help of the model This means that they are in fact biased in favour of the model being used While these are the most quoted R values R p or R wp gives the best idea of the quality of the fit Treatment of Peak Broadening in Rietveld Analysis Several different functions can be applied to describe the powder diffraction peak shape when modelling the diffraction pattern Traditionally pure Lorentzian and Gaussian profiles have been used (ere ( is the full width at half maximum FW(M of the peak (owever these functions are not always sufficient to individually model the complex shape of the diffraction peak )nstead the Voigt function which is a convolution of a Gaussian function with H G and a Lorentzian function with H L has been shown to give a good fit As the Voigt function is computationally heavy it is often replaced by the pseudo Voigt function given by a sum of a Gaussian and Lorentzian function both with FW(M H The pseudo Voigt function is thus characterized by parameters and H To correlate the pseudo Voigt parameters with Voigt parameters H g and H L the Thomas Cox (astings TC( formulas can be used

47 Chapter Characterization of Nanoparticles by Scattering Techniques The total profile of the peaks is the convolution of the sample and instrumental broadening eq and the total profile must therefore be corrected for the instrumental contribution before any information about the sample broadening can be extracted The instrumental contribution can be characterized for a specific setup using ray tracing where the X ray beam is followed from the source to the detector and the various contributions to the broadening are convoluted (owever a simple and often sufficient way of finding the instrument broadening parameters H G and H L is to measure the diffraction pattern from a sample that is free from sample broadening usually N)ST LaB or Si By determining the TC( peak shape parameters for the instrument the sample broadening can then simply be found as The instrument broadening is dependent on the scattering angle and thus has to be characterized for the entire range As was seen in equation and the sample peak width arising from size and strain have different dependencies The following functions are used to model the dependence of H G and H L : tan cos tan cos The nomenclature from FullProf Suite is here applied U I G X and Y are all refinable parameters in the Rietveld model This description allows one to separate the size and strain contribution to the broadening U and X have a tangential angular dependence and in accordance with these are related to strain I G and Y represent broadening from size because of the reciprocal cosine function )f anisotropic sample broadening effects occur the hkl dependant functions D( D ) strain and F( F ) size are needed )n the case of size anisotropic broadening occurs for non spherical particles because the crystallite size <D> in the Scherrer formula is dependent on the number of unit cells in the direction parallel to the scattering vector q )n this case the simple angular dependence from the Scherrer formula will not be sufficient to describe the broadening as it is now hkl dependent A simple way to model

48 Chapter Characterization of Nanoparticles by Scattering Techniques this and thus extract information about particle morphology is to describe the broadening through a linear combination of the spherical harmonic functions F( z ) in equation is for this model given by (ere A lmp are refinable coefficients while Y lmp are the spherical harmonic functions with the polar angles of the vector [hkl] with respect to the crystal cartesian coordinate system as arguments The spherical harmonic functions used are chosen so that they possess the same symmetry elements as the internal crystal structure as this is retained in the diffraction pattern By refining the different parameters U X Y I G and F the apparent sample strain and size can be extracted More specifically the apparent crystallite size is calculated by determining the ) G Y and F contributions to H G and H L and then using the TC( formulas to determine the common H FW(M which can be used in the Scherrer formula )n order to robustly determine crystallite size and strain from powder diffraction it is clearly important to measure data to high q values to be able to distinguish between the different hkl and q dependencies of the sample broadening (owever even when this is done care should be taken when interpreting the results Often reality is not as simple as equation and because crystallite size distributions and various kinds of strain can give very different angular broadening dependencies Furthermore the Voigt and Pseudo Voigt function are purely mathematical and do not have any direct physical meaning in the fitting process Therefore only trends should be considered when analysing Scherrer crystallite size results Peak broadening in Whole Powder Pattern Modelling A more physical modelling of size and strain effects is used in Whole Powder Pattern Modelling WPPM (ere peak profiles are described directly in terms of physical models of the microstructure and lattice defects present in the sample Rather than fitting mathematic expressions to the data the diffraction pattern is modelled with real physical effects and the method can thus be considered a bottom up approach as opposed to the traditional top down method described above )n WPPM the profiles are modelled by convolutions of real physical expression describing e g instrument broadening lattice distortions and crystallite size

49 Chapter Characterization of Nanoparticles by Scattering Techniques but also further complex crystal imperfections such as crystal twinning or antiphase boundaries The full peak profile can be written as follows The integral spans the length L of columns of unit cells in the direction parallel to the scattering vector q hkl k(hkl) contains known geometrical and structural terms and w hkl is a weighting factor is the product of the Fourier components of all possible profile contributions such as the instrumental profile T IP analytical pseudo Voigt approximation size effects A s and dislocations A D The list may also include contributions from faulting anti phase boundaries etc The size contribution from a lognormal distribution of spherical crystallites can be modelled through the parameters 2 variance and mean of the distribution The distribution moments M l,n and the remaining constants are given in the article by Scardi et al From the variance and mean one can calculate the lognormal size distribution For comparison with results obtained from e g Rietveld refinement one may also calculate a volume averaged column size for the size distribution Because of the physical modelling more robust information can be extracted from the diffraction data including e g size distributions This is demonstrated in Chapter in a study of Fe O

50 Chapter Characterization of Nanoparticles by Scattering Techniques 2.5 Total Scattering and Pair Distribution Function Analysis When using conventional crystallographic methods such as Rietveld refinement only the Bragg peaks are used for extracting structural information As was shown in this reflects only the long range global order of the sample )nformation about the short range local order is contained in the diffuse scattering arising from equation away from the Bragg positions which in a Rietveld refinement is seen as a background along with e g incoherent effects Recent years research has shown that many material properties are in fact highly dependent of local structure and being able to characterize this is therefore crucial in order to explain structure property relationships This applies to bulk crystalline materials but also nano and amorphous structures described by Billinge Kanatzidis as crystallographically challenged materials The Bragg law breaks down for very small nanoparticles where there is no long range structural coherence and in amorphous materials where only local order exists )n order to characterize the atomic structure of these materials scattering methods beyond Bragg diffraction are needed Therefore more and more work is done using the total scattering TS approach which treats the Bragg intensities and the diffuse scattering equally thus providing information about both local and global order The total scattering method builds on theory from the early th century and has for many years been applied in studies of glasses and liquids especially after the advent of computers for data analysis in the s and s (owever for crystalline studies the technique is still relatively young with pioneering work done in the and s This development happened as new high energy neutron and synchrotron sources became available as well as the possibility to do fast calculations on computers Since then the method has rapidly developed Today synchrotron beamlines and neutron instruments dedicated to total scattering studies are found at facilities around the world and software for total scattering data analysis are being developed by several groups The method is therefore becoming more and more accessible and new applications of the technique are constantly emerging Total Scattering Experiments Total scattering data are collected in much the same ways as conventional powder diffraction data (owever to analyse the diffuse scattering signal data to high q values Å are needed With a conventional laboratory X ray

51 Chapter Characterization of Nanoparticles by Scattering Techniques diffractometer with a Cu anode the highest obtainable q max is Å and Cu data are thus not suitable for total scattering analysis With Mo or Ag anodes data with q max of Å and Å respectively can be obtained (owever high energy synchrotron radiation is always preferred for X ray total scattering experiments both due to the higher q max accessible and the high X ray flux Good data statistics are essential for total scattering analysis especially at high q values where the scattering signal is weak due to the q dependence of the atomic form factor and Debye Waller factor Today the majority of X ray total scattering experiments are thus done at dedicated beamlines at rd generation synchrotrons as Rapid Acquisition Pair Distribution Function RA PDF experiments using transmission geometry and a large D detector for data collection The X ray energy used is typically kev As is seen in equation the intensity of the scattered beam decreases with higher X ray energy and high flux and or longer acquisition times are therefore required to obtain data quality comparable to conventional PXRD experiments using lower energies For neutrons TS experiments can be done using TOF instruments at pulsed spallation sources The q requirements limit the neutron instruments capable of doing high quality total scattering experiments to just a few facilities The Structure Function S(q) and the PDF G(r) The starting point for analysis of TS data is obtaining the total scattering structure function S(q). This function is acquired by determining the sample coherent scattering intensity I coh (q), and subsequently normalizing the data by the average scattering power of the compound S(q) is thus defined as The determination of I coh (q) is discussed below The term is the Laue monotonic diffuse scattering which arises because of imperfect cancellation of intensity at the destructive interference condition when atomic sites are occupied by atoms of different scattering lengths )t results in an incoherent background even in the case of coherent scattering The reduced total scattering function F(q) is defined as

52 Chapter Characterization of Nanoparticles by Scattering Techniques S(q) and F(q), which contains both the diffuse and Bragg scattering can be treated in q space reciprocal space with appropriate models for both the local and global order (owever most often the total scattering is treated in r space i e real space This is done by taking the sine Fourier transform of the reduced total scattering function over the measured q range to obtain the reduced pair distribution function G(r) which is effectively a weighted histogram of the interatomic distances in the structure sin sin The meaning of G(r) is described in more detail below Two examples of the data reduction process are seen in Figure which shows the raw I(q) S(q) and F(q) and the G(r) for a sample with long range order bulk crystalline LaB and local order amorphous tin oxide nanoparticles nm diameter respectively The data will be discussed further in Chapter )n principle the integration in should be done from zero to infinity This is of course not physically feasible as the experimental configuration dictates both q min and q max. Terminating the integration at finite q value results in oscillations in the Fourier transform known as termination ripples Extending the q range increases the chance of including noise due to statistical errors and determining the optimum q max is therefore often a compromise between termination effects and noise for the specific experiment The amount of structural information that can be extracted from the PDF depends on resolution in r space which is in turn determined by the maximum q max As a rule of thumb the real space resolution is given by For detailed studies of the local order high q values are needed to obtain e g r Å q max should be Å )n practice q max is usually between Å depending on the experimental conditions and the purpose of the study )f using the RA PDF experimental configuration discussed above high r resolution can only be obtained at the expense of q resolution

53 Chapter Characterization of Nanoparticles by Scattering Techniques I(q) (Arb. units) A1: I(q) I(q) (Arb. units) A2: I(q) S(q) (Arb. units) B1: S(q) S(q) (Arb. units) B2: S(q) F(q) (Arb. units) C1: F(q) F(q) (Arb. units) C2: F(q) q (Å 1 ) q (Å 1 ) G(r) (Arb. units) D1: G(r) G(r) (Arb. units) D2: G(r) r(å) r(å) Figure 2.7: Steps in obtaining the reduced pair distribution function G r for crystalline LaB A D and amorphous SnO A D Determining I coh (q) To determine I coh (q), and subsequently obtain S(q) F(q) and G(r), the signal from the sample environment e g air capillary is subtracted from the raw total scattering data Subsequently the data must be corrected for other non coherent effects such as Compton scattering multiple scattering sample self absorption fluorescence detector efficiency etc Due to all these explicit corrections total scattering data reduction has so far been a cumbersome process (owever it has recently been shown that it is possible to use an ad hoc correction procedure to obtain a comparable S(q), making total scattering

54 Chapter Characterization of Nanoparticles by Scattering Techniques analysis much faster and more accessible This approach is used in the new program PDFgetX3 from the Billinge group which has been used for all the total scattering data analysis presented in the dissertation A short description of the data processing is therefore given below Generally the coherent intensity I c (q) can be expressed as a simple function of the measured intensity I m (q), taking into account multiplicative and additive effects (ere a and b are generalized and q dependent correction functions )f doing the data corrections explicitly these functions are calculated from physical models (owever in the ad hoc approach this is not necessary )nstead the knowledge of the behaviour of F(q) and S(q) is exploited From equation it can be shown that a similar relation exist between the measured and corrected F(q): The theory behind the corrections needed is well understood and in particular it is known that the q frequencies of the corrections and the structural signal in the coherent scattering intensity are very different The lowest frequency Fourier component in F(q) coming from a real structural signal is ~2 /r nn where r nn is the nearest neighbour distance This implies that any additive component with frequency lower than this value is due to a non structural contribution to the signal Examples are Compton scattering and multiple scattering which both vary slowly in q By fitting an arbitrary function to I m (q) with no frequencies higher than 2 /r nn and subtracting this function the corrected F(q), and thus S(q) can be obtained )n PDFgetX the error term (q) is modelled as an n th degree polynomial where the value of n is in the order of depending on the experimental q range and the information sought for in the study The multiplicative term is found such that for any q the normalized intensity is close to the normal scattering factor The raw sample intensity is therefore rescaled by a multiplicative function (q) to approach the normalized scattering factor curve prior to the fitting of (q)

55 Chapter Characterization of Nanoparticles by Scattering Techniques Analysis of the Pair Distribution Function The reduced pair distribution function G(r) contains all information about both long and short range order in the sample just as S(q). Since it is now a function in real space the data analysis is very intuitive G(r) is a member of a large family of Pair Distribution Functions PDFs and is specifically closely related to the radial distribution function R(r) which is physically easy to interpret and is illustrated for a simple crystalline single atomic structure in Figure R(r)dr is the weighted number of atoms in a shell of thickness dr a distance r away from another atom This is expressed in where r vu is the distance between the v th and u th atom in the sample and f u and f v are the scattering powers of the specific element The relation between G(r) and R(r) is (ere (r) is the atomic PDF and contains all the interatomic distances in the sample The PDF peaks represent interatomic distances and by simple analysis structural information from the sample can be obtained Firstly the peak positions are directly dependent on the interatomic distances and the atomic positions can therefore be determined directly The peak intensity is dependent on the atom species the coordination and site occupancy while the peak width is determined by the thermal disorder in the structure )f the sample contains nanoparticles with limited structural coherence the extent of correlations is damped at high r values and the particle size and morphology can be determined Figure 2.8: R r for a simple single atomic D crystalline structure The coloured shells show interatomic distances corresponding to the peaks in the PDF

56 Chapter Characterization of Nanoparticles by Scattering Techniques While much information can thus be extracted without applying a structural model to the PDF the G(r) is often treated using Real space Rietveld analysis Conceptually this corresponds to a conventional q space Rietveld refinement A structural model is used to calculate G(r) through and which is then refined to fit an experimentally obtained PDF through the least squares method The program PDFgui from the Billinge group is widely used for this and has also been used in the studies presented in this dissertation PDFgui uses a crystallographic approach where the atomic positions are described in a unit cell and is thus mostly applicable for crystalline materials without siginificant disorder or nanocrystalline materials for which a structural model can easily be constructed (ere simple Gaussian functions are used to describe the PDF peaks and experimental effects such as termination ripples can further be included in the model The fit can be evaluted through the R w factor The summuations are over all points calculated in the G(r) grid determined in the Fourier transform of S(q) w is the weight of a certain point in G(r) and is given be estimated standard deviation of the datapoint such that w r i r i The size and morphology of nanoparticles is in the real space Rietveld approach determined by applying an r dependent particle envelope function (owever before this can be done it is necessary to take the instrumental dampening into account The two contributions correspond to the instrumental and sample broadening in a PXRD pattern Just as for a q space Rietveld refinement the instrumental parameters can be obtained by determining the dampening for a bulk crystalline standard like LaB (ere only the instrument contributes to the dampening of the PDF at high r For extensive disordered or completely amorphous materials real space Rietveld methods are not always applicable For further studies of these structure Reverse Monte Carlo RMC methods are more useful (ere a large box approch is applied describing individual atomic positions of thousands of atoms (owever )t is beyond the scope of the dissertation to go further into this method

57 Chapter Characterization of Nanoparticles by Scattering Techniques 2.6 Small Angle Scattering )n the previous section the emphasis was on the information found at very high scattering vectors q (owever much knowledge about a certain sample can also be extracted from the scattering occurring at very low q values This is exploited in Small Angle Scattering SAS As seen in the scattered amplitude from a sample is the sum of the waves scattered by all electrons present in the X ray or neutron beam When considering only the scattering at very low q values the corresponding r values are on the nanometer scale )t is therefore not possible to separate contributions from electrons from individual atoms and the electron density can be expressed simply as an average electron density (r) in the sample The scattered amplitude therefore becomes This is the Fourier Transform of (r) e g the electron density For a spherical particle it can be shown that the scattering amplitude is given by sin sin cos (ere p is the difference in electron density of the spherical particle and the solvent while R is the particle radius The observed intensity for N non interacting monodisperse particles then becomes sin cos The normalized intensity as function of qr is plotted in Figure A which shows characteristic oscillations in q The scattering signal from particles of different sizes is shown in a linear plot in Figure B which illustrates how small particles give intense scattering at higher q vlues For real polydisperse and anisotropic samples the oscillations in I(q) are smeared out due to the different R values of the particles With careful modelling of the data it is possible to extract this information i e particle size size distributions and particle morphology

58 Chapter Characterization of Nanoparticles by Scattering Techniques Small angle scattering SAS techniques are used widely with both neutrons SANS and X rays SAXS The geometry used for SAXS meaurements is identical to the transmission geometry often used for diffraction experiments and as will be demonstrated later it is possible to measure both SAXS and PXRD data simultaneously Normalized intensity (Arb. units) E 3 1E 4 1E 5 1E 6 A qr Normalized intensity (Arb. units) nm nm 10 nm 5 nm q (Å 1 ) B Figure 2.9: A SAXS intensity plot I(qr) for non interaction monodisperse spherical particles as a semi log plot B SAXS signal for spherical monodisperse and non interacting particles

59 Chapter Characterization of Nanoparticles by Scattering Techniques 2.7 Summary The present chapter has served to show how X ray and neutron scattering techniques can used to characterize several different length scales in powdered and nanostructured samples Small angle scattering probes the nanometer scale and can be used to study size and morphology of both amorphous and crystalline nanoparticles Powder diffraction where Bragg intensities are considered probes the long range atomic order in the sample and gives information about crystal structure as well as crystallite size and shape due to line broadening Total scattering contains information about both local and long range atomic order and can be used for structural studies of molecular or ionic species amorphous particles and crystalline materials as well as crystallite size and morphology Often the q resolution in a total scattering experiment is lower than in powder diffraction whereas the r resolution is higher at least when using the RA PDF method The three techniques small angle scattering powder diffraction and total scattering are thus highly complementary By combing them and adding additional results from e g spectroscopy measurements or electron microscopy very detailed knowledge on materials structure can be obtained With the development of high energy and high flux X ray synchrotron sources and X ray detectors a scattering pattern can be measured extremely fast naturally depending of the desired data quality and the sample This open the possibilities for in situ X ray studies of chemical reactions In situ X ray scattering studies of hydrothermal synthesis are described further in the following chapter

60 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis 3 In situ X ray Scattering Studies of Hydrothermal Synthesis 3.1 Introduction With the growing interest in producing tailor made nanoparticles with well defined properties much research focuses on how nanoparticle characteristics can be precisely controlled during hydrothermal synthesis In situ X ray scattering and spectroscopy studies of the synthesis process are proving useful to obtain the knowledge needed to understand nucleation and growth mechanisms beyond the traditional theories )n this chapter the technique and experimental methods are introduced )n section a short description of the previous approaches to in situ studies of hydrothermal reactions is presented (ere the main focus is on PXRD studies as this has been the primary tool for my own research )n section the capillary reactor used for the studies presented in the dissertation is introduced and finally the significance and limitations of the information that can be extracted from the recorded in situ data are briefly discussed in section 3.2 In situ X ray Powder Diffraction Experiments Before the advent of high intensity X ray sources and fast X ray detectors the scattering experiments described in the previous chapter were limited to static measurements due to the need of long X ray exposures (owever with the developments in X ray science and the broad accessibility of synchrotron radiation time resolved in situ studies of various chemical and physical processes have become possible In situ X ray experiments were initially developed in the s for the studies of solid state reactions such as crystallization and phase transformations but today in situ time resolved studies are widely applied in many disciplines e g catalysis and electrochemistry The first in situ scattering studies of hydrothermal reactions were done using neutron radiation for zeolite studies by Polak et al in Soon after the hydrothermal synthesis of zeolites was studied using synchrotron X ray radiation in pioneering work by Barnes et al, and since then numerous material systems and experimental techniques have been investigated

61 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis Generally different setups for in situ PXRD are used autoclave like cells for energy dispersive diffraction ED XRD or capillary reactors for angular dispersive studies The ED XRD approach has been used extensively for in situ studies by O (are et al, Walton et al, Bensch et al, and Sankar et al, among others A recent example of an ED XRD cell used at the Diamond synchrotron is described in detail by Moorhouse et al. A previous version of this cell from the Daresbury synchrotron is sketched in Figure An autoclave similar to those used for lab scale synthesis is here specifically designed for X ray diffraction experiments The reaction takes place in a small pressure cell which allows X ray beam penetration through windows where the reactor steel wall is very thin The heating is done by a furnace surrounding the cell and as the heating is initiated sequential X ray exposures are started The reaction can now be followed by the X ray beam with second or minute scale time resolution Magnetic stirring is often applied to maintain the sample in the beam position after precipitation and also to probe the average sample composition rather than just the product formed at a specific spot in the autoclave Depending on the design of the experiment data from several different spots in the autoclave can be obtained to study the effect of heating zones etc As the reactor is similar to that used in a real synthesis in the laboratory the results can be directly transferred to ex situ studies Furthermore the product from the in situ reactor can often be recovered for subsequent characterization of the material properties Figure 3.1: The Oxford Daresbusy in situ cell From Norquist and O (are

62 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis (owever the size of the X ray penetrable window limits the angular interval from which the diffracted beam can exit and thus the accessible 2 range The work done with autoclave like cells is therefore restricted to ED XRD where a wide angular range is not necessary because the diffraction pattern is measured as function of X ray energy see section This limits the amount of information that can be extracted from the data compared to angular dispersive experiments where detailed structural and microstructural information is more accessible through e g Rietveld refinement (owever valuable knowledge on crystallization has been obtained through a great number of such studies on e g layered double hydroxides 83 metal organic frameworks and several other material systems The second approach is to use a thin capillary as the hydrothermal reactor The capillary material is chosen such that it can withstand both the pressure and chemicals used in the hydrothermal process while still being relatively transparent to X rays examples are quartz sapphire or thin steel tubes The outgoing beam is thus not limited by a specific window area but can exit from the whole reaction zone The early developments were done in the s by Norby et al and since then several other groups have applied the same approach The precursor for the hydrothermal synthesis is here injected into the capillary which is then sealed and subsequently installed on the diffractometer goniometer as shown in Figure Pressure is then applied often by N gas and simultaneously with initiation of heating X ray exposures are commenced Figure 3.2:. Capillary mounted on goniometer From Norby et al, A Capillary measuring mm B Goniometer head C Swagelok T piece D Pressure tube

63 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis The use of a capillary reactor has some drawbacks compared to autoclave studies As stirring is not feasible in the small volume in the capillary the X ray beam only probes a limited portion of the sample which might not represent the average reaction process Furthermore it is problematic to recover the sample for ex situ characterization since the heating often is inhomogeneous over the length of the capillary and the recovered product will thus represent a mixture of reaction stages Finally the conditions used in a capillary reactor to obtain a certain product cannot be directly transferred to those needed for synthesis on a larger scale On the other hand due to the small volume of the capillary very fast heating rates can be achieved which can mimic the conditions in e g a flow hydrothermal reactor A wide 2 range can be obtained using a capillary reactor and the resulting data can therefore be Rietveld refined or even treated with PDF analysis as shown in the following chapters For detailed studies of the particle growth and structural changes during synthesis capillary reactors are therefore very well suited All the studies presented in the dissertation have been done using this method )t should be noted that several other approaches to in situ studies are emerging accommodating the need for detailed understanding of the processes taking place in more complex hydrothermal synthesis techniques )n the )versen group for example high energy synchrotron X ray in situ studies have been done using the specialized pulse flow reactor mentioned in section Using this we have studied the formation of anatase nanoparticles with further details to be found in the paper appended in Appendix V) 3.3 The Aarhus In Situ Capillary Reactor The capillary setup used by the )versen group for in situ studies of hydrothermal reactions on the second time scale is sketched in Figure and pictured in Figure )nspired by previous capillary reactors the first version was built by Dr Martin Bremholm in and the design has later been further developed and optimized for various beamlines and experiments as described in by Becker et al A reactor capillary discussed further below is mounted using Swagelok fittings and graphite ferrules in a shoe which in the latest version of the setup can be mounted directly on a standard diffractometer goniometer The height of the capillary can then be adjusted to the beam position either using the motorization of the setup at the beamline or by the motor build into the shoe

64 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis The precursor is injected into the capillary from a syringe through a steel string connected with Swagelok fittings to the capillary When the injection is done the string is connected to a commercial (PCL pump which is used to pressurize the sealed capillary with water The capillaries and ferrules can withstand more than bar but usually our hydrothermal studies are done between bar The heating is done by a jet of hot air coming from below the capillary Before the experiment is initiated the air flow is heated up while it is led to an exhaust pointing away from the sample position Sequential X ray exposures are then started and the air flow is led to the sample marking the beginning of the experiment Due to the pre heating of the air flow the set temperature is quickly reached in the capillary Figure shows the temperature profile for an experiment done at o C After just seconds almost of the set temperature is reached After seconds the temperature is at of the set point Figure 3.3: In situ setup The monochromatized synchrotron radiation hits the capillary where the reaction takes place under high pressure and temperature The scattering data are recorded on a D detector o C 245 o C Temperature( o C) Time (seconds) Figure 3.4: Temperature profile for experiment done at o C

65 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis Figure 3.5: In situ setup installed at i MAXlab A )D B APS B and PO PETRA))) C Depending on the specific experiment the precursor can be a solution a gel or a suspension of solid particles Usually we use precursor metal ion concentrations between M which is considerably higher than what is usually seen in a standard laboratory synthesis especially for flow setups (owever to get sufficient intensity in the Bragg peaks compared to the rather large background from the sample environment it has been found that this is necessary for most material systems )f the precursor is inhomogeneous i e a suspension of solid particles we apply magnetic stirring of the reactant during the precursor injection to ensure homogeneity The reactor material of choice for PXRD experiments is single crystal sapphire Al O Specifically we use a thin capillary with inner diameter mm and wall thickness mm This is resistant to even harsh chemical conditions and is relatively transparent to X rays if the wavelength of the incoming beam is Å the transmission through the tube is ca for a capillary with wall thickness mm As the sapphire is a single crystal the scattering from the capillary will be present as discrete diffraction spots on a D detector image This is illustrated in Figure A which shows a frame obtained during the hydrothermal synthesis of CuO at i Before integration

66 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis from D to D the single crystal diffraction spots can be be masked i e excluded from the data The shadow from the sapphire is also masked along with the beamstop arm as illustrated in Figure B Unfortunately sapphire capillaries are not well suited for total scattering because precise subtraction of the background i e the scattering pattern from the sample environment is important for the PDF analysis A direct subtraction of a measurement of the empty sapphire is difficult because the position of the sapphire diffraction peaks depends on the orientation and temperature of the tube With the current setup it is challenging to ensure that this does not change during sample change and experiment preparation Masking is also problematic as it becomes very difficult at high q values where the many sapphire peaks are weak and ill defined Therefore we have used amorphous fused silica tubes for our total scattering experiments The specific tubes are manufactured for use in (PLC analysis and can thus withstand very high pressures bar (owever compared to sapphire tubes they are rather sensitive to harsh chemical environments The tubes burst when increasing the temperature for alkaline samples precursors This limits the reactions that can be studied in fused silica tubes significantly as high p( values are often required to crystallize complex materials Furthermore the scattering from the amorphous silica gives rise to a high background compared to sapphire tubes where the capillary scattering is condensed into well defined diffraction spots )t is therefore of great interest to find a way to treat the sapphire diffraction spots in the data analysis to make it feasible to use sapphire capillaries for total scattering measurements Figure 3.6: A Raw data recorded in sapphire capillary B Masked image ready for integration

67 Chapter In Situ X ray Scattering Studies of (ydrothermal Synthesis During the past years we have used this setup for in situ PXRD SAXS EXAFS and TS PDF experiments The reactor has thus been used at several different beamlines at synchrotrons around the world and has been designed such that it can rather easily be installed in the often small space available The flexibility of the setup is illustrated in Figure which shows the setup installed at i MAX lab at )D B APS and at P PETRA ))) Further details on the beamlines are found in Appendix ) as well as the research chapters 3.4 What can be Learned from In Situ X Ray Studies? )n section the various setups for in situ studies were introduced and the limitations using a capillary reactor were discussed When interpreting results regarding particle formation and growth from our in situ setup it is important to keep these limitations in mind the results obtained for a synthesis in small capillary cannot be directly transferred to the processes happening in a real synthesis on a large scale and the synthesis conditions have to be re explored to fully map the parameter space for a certain reactor (owever in situ studies can make this process easier even though the exact synthesis conditions temperature precursor concentration etc required to obtain certain particle characteristics may not be equal for different reactors the mechanisms dictating particle formation and growth are most likely the same A thorough understanding of the influence of various parameters on crystallization particle growth and crystalline structure can therefore limit the time needed in the lab for parameter exploration Furthermore with our in situ studies we want to address broader questions than those regarding optimal parameters for a certain synthesis By investigating the particle formation and growth mechanisms for a range of different material systems on a second or sub second time scale the goal is to get a much deeper understanding of fundamental inorganic reactions As discussed in Chapter the classical theories regarding particle nucleation and growth do not account for the complex processes in a hydrothermal synthesis )f we can start to understand the behaviour of various precursor complexes anions and cations in a hydrothermal synthesis during crystallization it may become possible to limit the trial and error processes when designing new synthesis pathways

68

69 PART II Research Projects The following chapters present the main research projects ) have conducted during my PhD studies By means of in situ powder diffraction and total scattering coupled with detailed ex situ characterization ) have investigated the synthesis of LiCoO LiFePO SnO and finally Fe O The chapters are presented more or less chronologically and thus also illustrate the advancement of our abilities in measurements and data analysis

70 Chapter Formation and Growth of Nanocrystalline LiCoO 4 Formation and Growth of Nanocrystalline LiCoO2 4.1 Introduction When Sony first commercialized Li ion batteries in their cam corders in the active material in the cathode was LiCoO This development build on groundbreaking research on Li intercalation in LiCoO by Goodenough et al. who had first reported its potential use in Li ion batteries in LiCoO has since then proven its strength and is to this day the most widely used cathode material in Li ion batteries for portable electronics )t has a high voltage V open circuit voltage high theoretical capacity mah g for full Li delithiation and good cyclability and has for this reason been studied extensively for the past two decades Although it is not well suited for large scale applications in e g electric cars due to price toxicity and safety LiCoO continues to attract attention for small battery applications More recently isostructural mixed layered oxides where part or all of the cobalt has been replaced by cheaper materials e g LiCo Mn Ni O have also been widely studied )n early structural studies of stoichiometric LiCoO cathode materials two different polymorphs were reported named LT and (T LiCoO for high and low temperatures respectively The two phases were originally synthesized by solid state reactions from Li CO and CoCO at o C and o C As will be seen below the names are quite misleading as (T LiCoO can also be synthesized at rather low temperatures by other methods (T LiCoO is a layered structure with a hexagonal cell described in space group R 3m The structure is shown in Figure A )t consists of cubic closed packed oxygen surrounding layers of cobalt and lithium where both cation sites are octahedrally coordinated to oxygen The Li ions can diffuse freely in dimensions in the Li layers which combined with the high voltage of the Co Co redox couple makes the structure ideal for Li ion batteries When the compound is delithiated the oxygen layers rearrange themselves to hexagonal close packing in CoO (owever when cycling in a real battery the delithiation is restricted to Li CoO to avoid irreversible structural changes The low temperature version LT LiCoO was initially reported to take the same structure but with cation mixing such that some of the cobalt ions reside in the Li layers This heavily affected the electrochemical properties The ratio of the unit cell dimensions i e c a provided a way of discriminating between the LT and (T phases the c/a ratio was found to be about for the LT form and for the ordered layered structure

71 Chapter Formation and Growth of Nanocrystalline LiCoO Figure 4.1: A Layered hexagonal (T LiCoO with pink LiO and blue CoO polyedra B )dealized spinel structure for LT LiCoO with pink LiO and blue CoO polyhedral Later the LT structure was reported in the Fd 3m space group as a spinel like phase shown in Figure B Li was said to reside in the tetrahedral sites whereas the octahedrally coordinated sites were occupied by Co Again cation mixing was observed suggesting that ca of the Co actually occupied the Li sites No final conclusions regarding the exact structure of LT LiCoO were reached from the work done in the s and often LT LiCoO is now referred to as a quasi spinel structure Recently LT LiCoO has only received limited attention as its electrochemical properties are inferior to (T LiCoO When designing new synthesis pathways of LiCoO it is however important to structurally validate that (T LiCoO actually forms )n the following LiCoO will refer to the ordered layered phase Since the first introduction of commercial LiCoO batteries the cathode performance has been improved through e g coating doping and mixing with other phases )n recent years much work in layered oxide synthesis has concerned nanostructuring for rate improvements (owever nanosizing LiCoO particles can influence both the stability of the phase and the electrochemical properties and extreme size reduction is therefore not always favourable For this reason size and morphology control of LiCoO is crucial during synthesis Many different synthesis methods have over the years been used to produce nanocrystalline LiCoO including post templating methods sol gel methods coprecipitation methods as well as both batch and flow hydrothermal methods )n this study we used in situ PXRD to follow the hydrothermal formation of LiCoO from CoOO( suspended in an aqueous solution of LiO( The structure of CoOO( is similar to that of

72 Chapter Formation and Growth of Nanocrystalline LiCoO LiCoO except with ( residing on the Li site Studies of this reaction pathway goes back to where it was first discussed by Fernandez Rodriguez et al They showed that in the presence of (Cl LiCoO underwent ion exchange and transformed to CoOO( (owever by hydrothermal treatment of CoOO( in LiNO solutions they obtained Co O instead of LiCoO Later several groups showed that LiCoO could be synthesized using aqueous LiO( instead of LiNO )n Okubo used a similar route in a study of the nanosize effect on electrochemical properties and showed that by varying temperature and or LiO( concentration various particle sizes could be obtained The aim of our in situ study was to understand the particle formation and growth mechanisms in further detail The main results were published in Crystal Growth and Design in 4.2 Experimental Methods Precursor Preparation The CoOO( particles were synthesized prior to the synchrotron experiments by the method reported by Okubo et al An aqueous solution of Co NO ml M was slowly added to a solution of NaO( ml M resulting in a pink suspension of crystalline Co O( particles This was then diluted to L and after hours of stirring in air the colour of the particles had changed to dark brown and the particles had gone amorphous The suspension was then centrifuged whereupon the product was washed with water twice and subsequently dried at o C for hours PXRD data showed weak peaks from nanocrystalline CoOO( but most probably a large fraction of the CoOO( was still amorphous The precursor suspension was then prepared by adding g CoOO( to a syringe containing ml of LiO( solution Two different LiO( solutions with concentrations of M and M respectively were used in order to obtain Li Co molar ratios of and A small magnet was introduced into the syringe and the precursor suspension was injected in the sapphire capillary in the in situ setup under constant stirring The magnetic stirring of the suspension in the syringe during injection ensured that the Li Co ratio in the capillary could be assumed equal to that in the syringe In Situ Experiments The in situ X ray measurements were carried out at beamline ) MAXlab Sweden during two different beamtime periods Experiments were done at o C o C and o C all at p bar Experiments at higher temperatures were also attempted but when going above o C the particles started

73 Chapter Formation and Growth of Nanocrystalline LiCoO moving inside the capillary thus diffusing out of the X ray exposed region The X ray wavelength was Å during the first beam time and Å during the second The CCD detector MAR was placed cm from the capillary during the first beamtime and cm during the second giving slightly different accessible q ranges of Å and Å The detector readout time in all experiments was about seconds and with an exposure time of seconds the time resolution was seconds The beam size was mm by mm 4.3 Data Analysis The raw time resolved D data frames were integrated in Fit2D, and subsequently analysed by Rietveld refinement using the sequential feature in FullProf suite Both phases LiCoO and CoOO( were included in the Rietveld model The refinements employed the range from o to o where the background was modelled using linear interpolation The scale factors for the two phases the unit cell parameters and particle size parameters were refined but due to the limited q range the atomic positions and thermal parameters of both phases were held fixed The refinements were done based on the structure of (T LiCoO space group R 3m) although modelling using the LT LiCoO structure space group Fd 3m) gave comparable R values The Thompson Cox (asting formulation of the pseudo Voigt function was applied to describe peak profiles Corrections for instrument broadening were done by characterizing a N)ST LaB standard sample by profile Le Bail refinement thus determining the profile parameters for calculations of the instrumental ( G and ( L This was implemented in the sample Rietveld refinement by using a Fullprof format instrument resolution file )RF Due to the small size of the particles the sample peak broadening was assumed to arise purely from particle size and strain contributions were neglected This assumption was supported by the data as the peak broadening could be described using only profile parameters with cos 1 ( ) angular dependency (owever to fit the model to the data it was necessary to include hkl dependent broadening due to particle anisotropy This was expected as previous work on the hydrothermal synthesis of LiCoO as well as preliminary home lab syntheses had given disk shaped nanoparticles The peak broadening modelling was therefore done using a linear combination of the spherical harmonic functions of the same symmetry as the crystal structure and refining the coefficients determining the shape of the particles )t was found that three

74 Chapter Formation and Growth of Nanocrystalline LiCoO normalized spherical harmonic functions were necessary to describe the hkl dependence of the peak broadening cos cos cos As described in the arguments to the spherical harmonic functions are the polar angles of the vector [hkl] with respect to the crystal coordinate system is the inclination angle defined to go from the z axis to the vector towards the xy plane Since no Gaussian contribution was needed in the refinement the particle size could be calculated directly from the refined coefficients A 00, A 20 and A 40, according to equation cos cos cos For the calculation of the particle size in the a and b direction [100] and [010], is in both cases For the c direction [001] is The volume weighted crystallite sizes are thus calculated as For all the diffraction patterns the scale factors for both phases were refined (owever the peak shape and the unit cell parameters were only refined for one phase at a time Thus when more than of LiCoO was present the peak shape and the unit cell parameters for LiCoO were refined whereas only the scale factor for CoOO( was refined This rather strict constraint was necessary because the two structures CoOO( and LiCoO have quite similar powder diffraction patterns and therefore many overlapping peaks within the observed q range Examples of fits to the data are shown in Further examples as well as the refined parameters are found in Appendix ))

75 Chapter Formation and Growth of Nanocrystalline LiCoO A B Intensity (Arbitrary Units) C D (degrees) 2 (degrees) Figure 4.2: Data red calculated diffraction pattern black and diffrence blue A T o C p bar Li Co t min Only CoOO( B T o C p bar Li Co t min Both LiCoO and CoOO( are present C T o C p bar Li Co t h min Only LiCoO D T o C p bar Li Co t min Only LiCoO 4.4 Results and Discussion Formation of LiCoO 2 Time resolved powder diffraction data obtained from the experiment done at o C with Li Co are shown as a contour plot in Figure )nitially diffraction peaks from the crystalline precursor CoOO( are present but after approximately minutes the reaction starts and peaks from LiCoO appear Clearly the main peaks from the two phases overlap and care should thus be taken when interpreting detailed results from the two phase refinements (owever trends can be extracted Figure A shows the refined weight fractions of LiCoO as function of time for both experiments done at T o C i e with Li Co and The LiO( concentration has very large impact on the reaction rate For the low LiO( concentration the reaction takes more than minutes while the transformation is complete in less than two minutes when using the high LiO( concentration

76 Chapter Formation and Growth of Nanocrystalline LiCoO Figure 4.3: Time resolved PXRD data from the experiment done at o C and Li Co Phase fraction LiCoO 2 (%) A Li/Co=10 Li/Co= Time (minutes) Phase fraction (%) Particle size [nm] B CoOOH LiCoO Time (minutes) Phase fraction LiCoO 2 (%) C 250 o C 200 o C 160 o C Time (minutes) Figure 4.4: A Weight percentage of LiCoO as function of time for experiments at T o C B Top Weight percent of LiCoO and CoOO( Bottom Size of CoOO( particles along c C Weight percentage of LiCoO as function of time Li Co The lines are guides for the eye Further understanding of the LiO( dependency can be obtained by considering the evolution of the CoOO( particles Figure B shows the CoOO( particle size in the c direction <D c >, along with the weight percentage of CoOO( and LiCoO as function of time )nitially the apparent CoOO( particle size increases but it subsequently decreases simultaneous with the formation of LiCoO The evolution of the CoOO( particles gives an indication the reaction mechanism After an initial crystallisation period the CoOO( particles starts dissolving in the alkaline solution and provides material for crystallization of the more stable LiCoO phase This mechanism dissolution recrystallization has previously been suggested as well as a solid state transformation but

77 Chapter Formation and Growth of Nanocrystalline LiCoO our current results support the former explanation (owever it should be noted that the size determination in the two phase refinement is associated with rather large uncertainties due to the peak overlap Furthermore the refinements only take size broadening into account The cosine dependency of the peak width indicate that the sample broadening is in fact mainly due to size but to fully characterize this more advanced models such as the WPPM approach could be applied The dissolution of the CoOO( particles seems to control the rate of the reaction as the LiCoO particles form simultaneously with the decrease in precursor particle size A high solubility of CoOO( therefore increases the reaction rate The solubility of CoOO( also termed cobaltic acid (CoO increases with p( value and consequently the dissolution is faster for the experiments done with high LiO( concentration This explains the large difference in reaction rate between the experiments done with low and high LiO( concentration as well as the failure in synthesizing LiCoO from LiNO and CoOO( As would be expected the reaction kinetics is also increased by raising the temperature The effect of this is shown in Figure C where the weight percentage of LiCoO is plotted as function of time for three different temperatures The time before the reaction starts is highly temperature dependent whereas the rate of the reaction seems almost constant Crystallite Growth Crystallite growth curves are shown in Figure A B Particles start growing immediately after nucleation from the dissolved precursor but after a short time period the growth nearly stops and a stabilized particle size is reached The growth rate and the final particle size are highly temperature dependent As expected the particles are disk shaped i e elongated in the a and b direction compared to the c direction Figure C clearly illustrates that the thickness to diameter ratio of the disk shaped particles is temperature dependent The growth curves show that the crystallite size can be precisely controlled within few nanometers by adjusting the temperature )n addition the data show that the crystallite morphology i e the aspect ratio of the anisotropic disk shaped particle can also be changed This is interesting in terms of battery properties as the Li diffusion is anisotropic and only takes place in the ab plane The morphology of the disk shaped particles that form during hydrothermal synthesis is therefore not optimal for the application of LiCoO in cathodes but if the particles can be elongated in the c direction

78 Chapter Formation and Growth of Nanocrystalline LiCoO better performance is expected as this increases the number of layers for Li diffusion Our results indicate that this can be achieved by increasing the synthesis temperature An interesting next step in the study could thus be to transfer the results to synthesis on a larger scale and characterize the electrochemical properties The nature of the crystallite growth was attempted analysed with kinetic models as described in section The expression D t D k t t N was thus fitted to the curves here D is the size of the particle t is time D 0 is the particle size at time t 0 and k a constant dependent on the probed microenvironment )f the surface reaction between the precursor and growing particles is fast the growth is usually diffusion limited )n this case the LSW theory states that the volume of the particles should increase linearly with time and consequently N should be close to )f the surface reaction kinetics is the limiting factor then the surface of the particles increases linearly with time and N is close to The fitted parameters obtained from the growth curves are listed in Table and the curves plotted along with the data in Figure For the highest temperatures the growth is too fast to obtain reliable fitting results Furthermore only the initial growth before stagnation of the crystallite size could be fitted within the current growth model A B C Particle size along a (nm) o C 200 o C 160 o C Time (minutes) Particle size along c (nm) o C 200 o C 160 o C Time (minutes) Size along c / Size along a 250 o C o C o C Time (minutes) Figure 4.5: A Volume weighted particles size along a for the experiments done at different temperatures with Li Co B Volume weighted particle size along c The red lines in A and B show the fitted kinetic models from LSW theory C Ratio between the two sizes expressing the morphology of the particles

79 Chapter Formation and Growth of Nanocrystalline LiCoO Growth T ( o C) Time interval N direction (min) a c a c Table 4.1: Parameters obtained by from kinetic modelling D t D k t t N For the low temperature experiment T cap o C the N parameter is very close to for both growth directions and the growth therefore appears to be limited by diffusion (owever as the temperature is increased to o C N increases to and in the a and c directions respectively The results thus indicate that surface reaction effects start to be important for the initial growth processes The difference between the growth mechanisms may be related to the dissolution recrystallisation process When the temperature is low the dissolution proceeds slowly and the amount of precursor for the formation of the LiCoO particles is therefore limited At higher temperatures the dissolution can proceed much faster and therefore the diffusion of precursor no longer limits the formation of the LiCoO particles (owever as discussed in section the kinetic analyses are only simplified models describing complex phenomena and can in the present case only describe parts of the growth curves The results should therefore merely be taken as an indication of the growth mechanism being temperature dependent Structure and Unit Cell Parameters The unit cell parameters change during the growth of the particles )n Figure A the development of the a axis is plotted as function of particle volume The volume of the particles has been calculated assuming a cylindrical shape using <D c > the size along c as the height and <D a > the size along ab as the diameter Clearly the a axis decreases with increasing particle size This behaviour was also reported by Okubo et al based on a limited number of data points from ex situ experiments The effect was explained to be due to Co residing on the surface of the particles which increased the Co O bond length and thus the average unit cell parameters for the small nanoparticles (owever a completely different trend is observed for the c axis As seen in Figure B the development of the c parameter for experiments done at high LiO( concentration agree with the surface theory described by Okubo et al but the opposite effect is observed for the experiments done at low LiO(

80 Chapter Formation and Growth of Nanocrystalline LiCoO concentration The latter development in the c axis length may not be related to particle size Since it is only observed for the particles synthesised using low LiO( concentrations it is likely to be linked to the Li content in the structure (owever it is well known that a lower Li content gives a longer c axis due to repulsion between the oxygen layers Therefore the behaviour of the c axis cannot be explained by a non stoichiometric LiCoO phase with Li deficiency Although Li deficiency has been shown to be the defect of the lowest energy other defects have also been reported in the literature These include oxygen dislocations and deficiency (owever we are not able to determine if these defects are responsible for the structural changes observed as the in situ X ray data do not allow us to refine the occupancies of Li and O A a a final (Å) c c final (Å) Particle volume (nm 3 ) Particle volume (nm 3 ) B c/a C Time (minutes) Li/Co=1.3, T=160 o C Li/Co=1.3, T=250 o C Li/Co=10, T=160 o C Li/Co=10, T=200 o C Li/Co=10, T=250 o C Figure 4.6 A Deviation from initial a value B Deviation from initial c value C Unit cell ratio

81 Chapter Formation and Growth of Nanocrystalline LiCoO As described above LT LiCoO can be distinguished from the (T modification by determining the c a ratio )n Figure C this ratio is plotted versus time For the experiment done at o C with Li Co the c a ratio is initially close to but with time it increases to The behaviour indicates that LT LiCoO forms and subsequently transforms into (T LiCoO This can be understood as a disorder order transformation )n the initially formed particles the Li and Co ions are disordered but as the reaction proceeds the ordered layers of Li and Co in the (T structure form This transition is only observed for the experiment conducted at low temperature with low LiO( concentration All other experiments have c a ratios close to i e we do not observe the disordered LT structure within the time resolution of the experiment (owever it is likely that the peculiar cell dependencies of both experiments performed with low Li Co ratios is indeed related to this Other characterisation methods e g neutron diffraction are needed to fully understand the structural changes taking place 4.5 Conclusions The LiCoO study has shown how in situ PXRD combined with Rietveld refinement can be used to follow complex chemical reactions and extract information about phase evolution and particle growth Based on studies of reaction rates and changes in the precursor particle size our results confirm that the reaction from CoOO( to LiCoO happens as a dissolution recrystallization The rate of the reaction can be controlled by adjusting either the LiO( concentration or the temperature in order to increase the solubility of CoOO( From size analysis we were furthermore able to show that the particle growth is highly temperature dependent After an initial fast growth the particle size stagnates at a stable temperature dependent size showing that the final particle size can be controlled within few nanometers The morphology of the particles is also temperature dependent and can be adjusted to be either thin disks or almost spherical particles Both size and morphology of the particles are expected to be important for the cathode properties Plots of the unit cell c/a ratio indicate that at low temperature and low LiO( concentrations disordered LiCoO initially form but sustained reaction lead to ordering to the layered (T structure At other conditions the ordered structure is seen immediately within the time resolution of the experiment The unit cell a axis is observed to decrease with increasing particle volume and at higher Li Co ratios this is also observed for the c axis (owever at low

82 Chapter Formation and Growth of Nanocrystalline LiCoO Li Co ratios the c axis increases with increasing particle size leading to highly anisotropic crystal structure changes with particle size This peculiar effect cannot be explained by Li deficiency in the crystal structure and other characterization methods e g neutron diffraction are required to address this question )t may be related to the formation of the disordered LiCoO structure The chapter also serves to illustrate some of the challenges related to both data acquisition and data analysis when doing in situ X ray diffraction experiments )nitially we wanted to study a much wider temperature range including supercritical synthesis but movement of the particles at elevated temperatures made it impossible to keep the particles in the X ray beam so that the reaction could be followed Furthermore using a suspension with reactants in both the liquid and solid phase as a precursor proved challenging as it was necessary to ensure that the Li Co ratio in the capillary was the same as in the prepared syringe )nitially we thus had problems reproducing our results especially for experiments conducted with low Li Co ratios (owever the development of simultaneous stirring and injection eliminated this problem and has since then been used for many other systems The data obtained also demonstrates the limitations of our in situ PXRD experiments Combined with the large background from the sample environment and the small amount of nanoparticles in the beam the fast time resolution in the data acquisition makes it difficult to obtain high quality diffraction data Furthermore using the specific setup at MAX lab only a limited q range could be reached This meant that structural parameters such as Debye Waller factors and site occupancies could not be robustly refined As discussed in section the large overlap of peaks in the specific example of CoOO( and LiCoO made it difficult to extract detailed information about the phase transformation The LiCoO study was among the first in situ PXRD studies done using the Aarhus capillary reactor together with synthesis of ZrO and Ce x Zr x O These studies thus taught us how to optimize the experimental conditions as well as the data acquisition and analysis Since then we have used PXRD and later SAXS and total scattering to study particle formation phase transformations and particle growth in several other systems This is illustrated in the following chapters

83 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo 5 Defect Formation during Hydrothermal Synthesis of LiFexMn1 xpo4 5.1 Introduction After the development of LiCoO batteries for portable electronics in the early s it soon became clear that in order to use Li ion batteries on larger scales in e g electric cars it was necessary to develop alternative cathode materials LiCoO is both expensive and toxic and the Li x CoO layered structure is not stable and may undergo structural degradation if Li is extracted to x The degradation of the structure can generate O which reacts exothermically with the organic electrolyte resulting in thermal runaway where the battery is overheated and possibly ignited )n the s much research was put into the development of new safer cheaper and environmentally benign cathodes The early work mainly focused on layered LiNiO and spinel LiMn O which both became applied in commercial small scale batteries (owever there was a general interest in further lowering the cost of the cathode by using cheaper materials This lead to intense research in the use of iron based compounds as iron is abundant non toxic and cheap (owever attempts to use e g LiFeO and LiFe O cathodes showed that the phases were only metastable and did not perform well in electrochemical studies )n Goodenough s group proposed LiFePO as a cathode candidate This revolutionized the cathode field as focus was moved from oxide materials to polyanionic compounds Since then LiFePO has received immense interest )ts merits are plentiful )t is cheap non toxic and it shows good electrochemical properties such as high voltage V high gravimetric capacity mah g good cyclability and very high stability )t can thus be delithiated lithiated fast without any irreversible capacity loss and is well suited for high rate applications A drawback for LiFePO is low ionic and electronic conductivity and enhancing this has been the biggest challenge to overcome for application of LiFePO in Li ion batteries (owever the problem can be reduced by downsizing the LiFePO particles and by coating them with an electronically conducting carbon layer Today the compound is widely used in commercial batteries

84 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Figure 5.1 a LiFePO structure where pink octahedra show LiO red octahedral show FeO and blue dots are the P atoms b )llustration of the D Li channels along b The red octahedra are FeO and the blue tetrahedra PO As shown in Figure A LiFePO and isostructural LiFe x Mn x PO x crystallize in the olivine structure and has an orthorhombic unit cell space group Pnma where edge sharing LiO octahedra M site purple form chains along b while corner sharing FeO octahedra M site red form a zigzag pattern in the b/c plane During charge and discharge the D Li ion diffusion takes place along the b direction as illustrated in Figure B During delithiation iron is oxidized to yield FePO through a phase reaction for bulk material and as a single phase reaction for small nanoparticles LiFePO is now used extensively in commercial Li ion batteries but comprehensive research is still done to improve the cathode material The work done today is directs several different issues e g enhancing the conductive properties by nanostructuring doping coating carbon addition or surface structuring etc or obtaining a deeper understanding of the electrochemical processes by theoretical and experimental studies My research in LiFePO has concerned the synthesis structure relation in hydrothermally synthesized samples While the raw materials used in the synthesis of LiFePO are abundant and cheap the main synthesis methods currently applied in industrial processes require high temperature sintering before the end product is obtained Much effort thus goes towards developing new synthesis methods to reduce the cost of the batteries )n Whittingham et al 8, were the first to hydrothermally prepare LiFePO and many studies have since been published for both LiFePO and LiFe x Mn x PO (owever when synthesized hydrothermally at low

85 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo temperatures the material shows disappointing electro chemical properties due to defects in the crystal structure This is believed to be due to partial occupancy of the M Li sites of the transition metal which thereby blocks the Li diffusion pathway The exact nature of the defect has been discussed in the literature using several approaches )slam et al have shown by theoretical calculations that Fe Li interchange is the defect of lowest energy and this anti site defect has also been studied experimentally using both diffraction and microscopy methods Further theoretical studies of anti site defects have also been done (owever other studies report defects due to non stoichiometry with Li deficiency resulting in Fe on the M sites Masquelier et al. have studied the structure of LiFePO nanoparticles synthesized by precipitation and they observed Fe on the M site and Fe deficiency on the M site )n this chapter ) will present my research on the defect formation during hydrothermal synthesis of LiFe x Mn x PO x and ) have done both in situ and ex situ studies using various characterization techniques to understand how defects form The in situ PXRD study was published in Journal of Applied Crystallography in 186 while the ex situ results were published in Chemistry of Materials in The in situ SAXS and PDF studies are still to be published The in situ study is presented first section followed by the extensive ex situ characterization section of samples also synthesized using the hydrothermal method Although the synthesis conditions for the two studies were quite different the studies complement each other and a common conclusion is given in section 5.2 In Situ Experiments X ray Powder Diffraction at MAX lab In situ PXRD experiments were carried out at beamline ) at MAX )) MAX lab Sweden using the experimental setup described in Chapter Two different synthesis routes of LiFePO were studied For route A the precursor was prepared by mixing ml M o ( PO Riedel de (aen with ml M FeSO Sigma Aldrich in a syringe Then ml M LiO( Sigma Aldrich was slowly added resulting in a thick green gel This gel was thoroughly mixed and injected in the sapphire capillary outer diameter mm inner diameter mm For route B the experiments were done in exactly the same way except that the FeSO solution was replaced by a solution of N( Fe SO Sigma Aldrich of the same concentration

86 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo The precursor for the LiFe x Mn x PO x and experiments was prepared by mixing x ml M FeSO with x ml M MnSO Sigma Aldrich and ml M o ( PO ml M LiO( was slowly added just as for the LiFePO A experiments The pure LiMnPO were synthesized by mixing ml M o ( PO ml M MnSO and ml M LiO( ml M N( O( was then added The base was added as preliminary home laboratory experiments had shown that phase pure LiMnPO could only be obtained under alkaline conditions Unfortunately the different synthesis conditions and p( value mean that the LiMnPO results regarding defect formation and concentrations cannot be directly compared to the results on LiFe x Mn x PO All experiments were done at p bar while the temperature was varied from o C to o C The experiments were allowed to run for minutes For the experiments using precursor A the X ray wavelength was Å while the experiments using precursor B and studies of the manganese substituted compounds which were performed during another beam time were done with a wavelength of Å The detector was a MAR CCD camera For all experiments the frame exposure time was seconds The time resolution for the precursor A experiments was seconds while all other experiments were done with a time resolution of seconds due to a different readout mode of the detector The resulting D data were integrated in Fit2D 146 and subsequently treated by Rietveld refinement in FullProf suite. 59 The refinements included the region from o to o The background was modelled by linear interpolation between points with refinable intensities while the peak shape was described using the Thompson Cox (asting TC( Pseudo Voigt model The peak broadening was corrected for the instrumental contribution by means of peak shape analysis on a diffraction pattern of a N)ST standard LaB sample just as in the LiCoO study The olivine structure was refined in the Pnma space group )n each series the last recorded frame was the first to be refined The scale factor was refined along with the unit cell parameters the peak shape parameters and the overall temperature factor The zero point and atomic positions were also refined in the treatment of the last recorded frame but these were then kept fixed in the sequential refinement The Fe Mn M defect was introduced in the model by allowing Fe Mn to occupy the M site and Li to occupy the M site The overall stoichiometry was constrained so that the ratio between Li and Fe Li and Fe Mn for the manganese substituted

87 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo compounds was always unity This follow the anti site model suggested by Chen Whittingham and )slam et al. Figure shows a representative refinement and as can be seen the model gives a good description of the data Further examples can be found in Appendix ))) Intensity (arb. units) R Bragg =2.74% (degrees) Figure 5.2: Example of the results of Rietveld refinement the frame is recorded after minutes at o C from precursor A The resulting parameters are shown in the table In Situ SAXS Experiments In situ SAXS WAXS experiments were done at )D C at the APS Argonne National Laboratory USA The synthesis of LiFePO from precursor A was studied using the same synthesis method and the same experimental setup as the PXRD measurements The X ray wavelength was Å and the distance between the sample and detector m The detector was a by cm General Electric Si detector The large detector area and the long sample to detector distance allowed for a significant part of the SAXS and WAXS regions to be measured on the same detector A cone shaped Cu attenuator was placed over the beam stop to prevent exceeding the detector counting threshold with the strong SAXS signal Only one experiment done at o C and bar is presented in the dissertation The time resolution was sec per frame The SAXS WAXS data were integrated using Fit2D. The WAXS part of the data the region from to C from the SAXS WAXS experiments were then treated with Rietveld refinement but the data were of much poorer quality than what was obtained at MAX lab Therefore the defect was not introduced in the Rietveld model and the only relevant information that could be extracted was the time of formation of the phase and the evolution of the unit cell parameters The SAXS part of the data were corrected for the cone

88 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo attenuation background subtracted and subsequently analysed by fitting a Debye Bueche function to extract the Debye correlation length and an intensity scaling factor The SAXS data treatment was done by Dr Brian Pauw and no detailed description will therefore be given in the dissertation (owever some of the results will be presented as these provide interesting insight in the formation of LiFePO In situ Total Scattering Experiments In situ total scattering experiments were performed at beamline P at PETRA))) (amburg Germany For these experiments the same experimental setup as for the PXRD and SAXS WAXS experiment were used however the reactor was a thin fused silica tube measuring mm in inner diameter and mm in wall thickness The detector was a PerkinElmer XRD amorphous silicon detector With an X ray wavelength of Å and a detector distance of cm the q max available was Å The time resolution was s The recorded total scattering data were treated by PDF analysis First the raw D images were integrated in Fit2D and the PDFs were subsequently obtained using PDFgetX3 Scattering from the capillary with deionized water at the appropriate conditions was subtracted from the integrated pattern before the Fourier transform Due to low signal to noise levels at high q values the q range used in the Fourier transform was limited to Å Å The PDFs were modeled using PDFgui In Situ Results and Discussion Crystallization of the Olivine Phase PXRD data Figure shows the very first frames from the PXRD experiments done at MAX lab for synthesis of LiFePO from precursor A FeSO iron source and B N( Fe SO iron source at o C )f considering first Figure A the precursor is almost amorphous and subsequently turns into a slightly crystalline intermediate phase characterized by the strong broad peak at q Å This phase then transforms to phase pure LiFePO and after about three minutes all diffraction peaks can be ascribed to the LiFePO structure Figure B shows the first frames from the experiment done at o C with precursor B This precursor is more crystalline than that seen in Figure A but the positions of the most intense peaks compared to e g the very weak peak at Å in precursor A indicate that the two phases are similar During the various experiments and beamtimes we saw that

89 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo the precursor aging time prior to the measurements can affect the intensities of the diffraction peaks from the two precursors i e the higher crystallinity of the precursor B experiment shown in the figure is not necessarily related to the presence of ammonia This is illustrated in Appendix ))) Under the experimental conditions at the beamtimes it was very difficult to control the crystallinity of the precursor phase and the influence of this on the olivine phase formation is thus not clear at this point With precursor B phase pure lithium iron phosphate forms already within the first minute indicating that the presence of ammonium ions from N( Fe SO enhances the formation of LiFePO Unfortunately the beamstop covered the low q region during the beamtime of the precursor B measurements hindering observation of the intermediate phase peak at q= Å A shoulder from it may be visible and the two reactions are believed to happen though the same mechanism The formation times i e the time before phase pure LiFePO or phase pure Li Fe x Mn x PO is achieved are plotted in Figure The effect of ammonia is seen at all temperatures When using precursor B LiFePO forms after only minutes at o C whereas the phase did not form within minutes in the experiment using precursor A at the same temperature Furthermore the mixed Mn Fe phases form faster than pure LiFePO A B Intensity (Arb. units) Intensity (Arb. units) q ( Å 1 ) q (Å 1 ) Figure 5.3: A )nitial PXRD frames obtained in experiment with precursor A and T o C Only every second frames are shown i e the time between the frames is seconds B )nitial data frames obtained in experiment with precursor B and T o C The time between the frames is seconds

90 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo LiFePO 4 Precursor B Formation time (s) LiFePO 4 Precursor A LiFe Mn 0.25 PO Temperature ( o C) Figure 5.4 Time of formation of LiFePO from the PXRD measurements Green Precursor A Red Precursor B Blue LiFe Mn PO The lines are guides to the eye Note the broken y axis for the lowest temperature data point The precursor and intermediate phases have not been fully identified but other papers on ex situ studies report that the green gel that forms in precursor A is vivianite Fe PO ( O This is not the phase seen in our in situ experiments Ellis et al reported N( FePO ( O as an intermediate phase in the formation of LiFePO from precursor B but again this is not the phase that we observe in situ (owever it is very likely that the precursor and intermediate are closely related to these phases and are thus hydrated forms of iron )) phosphates The exact structure and crystallinity are most probably highly dependent on the mixing local p( value and iron lithium concentration The total scattering experiment described in section gives more insight into the local atomic structure of the precursors and intermediates The LiFePO peak broadening can throughout the synthesis be described by applying solely the U parameter in the TC( Pseudo Voigt function This parameter is related to lattice strain as will be discussed further in section Even the initially formed crystallites are thus not small enough to give significant size broadening of the peak profiles and growth can therefore not be studied with our PXRD studies The fact that the newly formed crystallites are relatively large above nm indicates that the size of the particles is determined already before the crystallization i e from the intermediate phase as confirmed by SAXS data below

91 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Insight from SAXS/WAXS By means of the SAXS data from the simultaneous SAXS WAXS experiments we were able to study the formation of particles before the crystallization of LiFePO from precursor A Figure A shows the background corrected SAXS data from the experiment done at C The data are presented in a false colour plot where the SAXS intensity is plotted as function of q and time At the very early stages of the reaction high intensity scattering is seen at rather high q values indicating small particles After a short while the high q scattering disappears The red line in the false colour plot represents t s which is the time for formation of phasepure LiFePO as observed in the corresponding WAXS data in Figure B The large change in the SAXS region is seen at exactly this point Similar data were obtained for precursor B Figure C shows the Debye correlation length expressing the size of the particles seen by SAXS Growth appears to occur in two stages with the first stage ending at ca nm around seconds into the experiment A second growth stage is then initiated with no clear sign of levelling off the final size of about nm after seconds indicate reaching the size limit observable in the experimental configuration Figure 5.5: A SAXS data and B WAXS data from the simultaneous SAXS WAXS experiment precursor A o C C Results from the analysis of the SAXS data The black line shows the Debye correlation length while the blue line is the scale factor

92 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo The scale factor has a maximum at the end of the first growth stage This confirms that after this point the particles grow beyond the detectable limit The initial behaviour shows that the formation of the nanoclusters happens quickly after the heating has been initiated The SAXS results confirm that the large crystallite size of the LiFePO is determined from the precursor phase as it is while this phase is still present that the initial growth happens This makes it challenging to control the size of the LiFePO particles during hydrothermal synthesis at least without e g surfactants present Total Scattering Studies of LiFePO 4 Formation While the SAXS data reveal the formation of small almost amorphous particles prior to the crystallization of LiFePO small angle scattering does not say anything about the atomic structure of these particles (owever this information can be obtained from total scattering and PDF analysis Figure A shows the low q range of the total scattering data while PDFs plotted as function of time in a contour plot are seen in Figure B The experiment was done using precursor A at o C and bar The data quality is quite low and detailed structural information cannot be extracted from the PDFs (owever after ca. minutes it is clear that all peaks in the r range Å can be assigned to the LiFePO structure as shown by the fit to the experimental PDF in Figure C The local structure is not well fitted i e the crystalline phase coexists with phases with only local order This can arise from unreacted precursor as will be described in section and from sulphate also present in the solution from the iron source For both PO and SO the semimetal oxygen distance is ca Å thus overlapping in the PDFs Selected PDFs are shown in Figure from the precursor the nano intermediate phase initially crystallized LiFePO and the final product after minutes of synthesis The local order i e the range from Å only changes very little during the synthesis This range contains the first coordination of phosphate and iron and the data thus show that for all the different stages the iron phosphate coordination is kept throughout the synthesis The largest change is seen for the nd Fe P distance which moves towards higher r values as the synthesis proceeds The iron iron peaks arising in the LiFePO structure at Å and Å are not seen in the precursor or intermediate structure and the structure beyond Å generally changes during the crystallization )nstead an intense peak is seen at ca Å most probably arising from Fe Fe distances As the Fe O bond distance is ca. Å this could correspond to a structure containing aligned cornersharing FeO units (owever this is still very speculative and much more modelling is

93 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo required to understand the precursor structure and the formation of the olivine phase The local atomic structure seems to change only very little when the heating is initiated i e from the precursor to the intermediate This might be due to the rather low data quality as subtle differences cannot be observed (owever the results indicate that the nanoparticles seen by SAXS have very similar atomic structure to the precursor gel and that the largest change during this transformation is in the nanostructure Figure 5.6: A Low q range of the in situ total scattering data synthesis of LiFePO at o C bar from precursor A B Corresponding PDFs C Fit of the LiFePO structure to the PDF obtained after minutes Black experimental PDF Red PDF calculated from the model Blue Difference curve

94 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Figure 5.7: PDFs obtained for different stages in the LiFePO synthesis Structural Changes in LiFePO 4 after Crystallization Lithium Iron Phosphate Precursor A After crystallization of LiFePO significant structural rearrangements take place Since no internal standard can be used in the present experiments absolute unit cell parameters are not known and only the relative values are discussed Figure A C thus show the relative deviations from the final values of the unit cell parameters as function of time Results from the precursor A experiments done at o C o C and o C are plotted )n all cases a large decrease in the a and c parameters is observed for the whole duration of the experiments At o C the b parameter is almost constant throughout the experiment while a decrease similar in size to that of a and c is seen at higher synthesis temperatures after the initial stage of the synthesis This divides the unit cell evolution into two parts anisotropic throughout the synthesis at o C and the first minutes at higher temperatures and isotropic the remainder of the synthesis at o C and o C For the high temperature experiments thermal expansion is observed in the beginning of the experiments when the set temperatures are still not reached This is mostly evident in the b parameter which is not affected by the competing anisotropic changes

95 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Deviation from final value (%) A: 170 o C c a b a c b B: 270 o C a c C: 345 o C b Deviation from final value (%) Synthesis time (minutes) Figure 5.8 Changes in unit cell parameters for LiFePO precursor A relative to the final value a is black b is blue and c is red The refined occupancy of Fe on the M site is shown in Figure A The introduction of the defect in the model improves the fit and the data convincingly show that the higher the temperature the faster the ordering of the structure While interpretation of defect concentrations of less than should be done with care the trends are very clear Although higher temperature leads to faster ordering it still takes several minutes before the structure is ordered even at o C i e above the critical point of water The difference between the ordering rates for o C and o C is almost negligible showing that no matter what temperature the synthesis is done at the initial formed particles contain a certain amount of defects The relation between the unit cell contraction and defect concentration is seen in Figure B which shows the Fe M occupancy versus the relative change in the a parameter for the precursor A experiments At o C the changes in lattice parameter and the concentration of M defects are almost linearly dependent This behaviour was also seen by Chen Whittingham and Axmann et al based on ex situ data of particles synthesised at different temperatures The results show that the anisotropic unit cell changes seen in Figure are due to Fe occupancy on the M site The lattice expansion for the initially formed disordered structures is caused by the slight size difference of Li and Fe Shannon ionic radii of pm and pm respectively The presence of Fe on the M site will thus expand the unit cell slightly along a and c, while it is almost unaffected along b where there is more space for the Fe ion in the Li diffusion channels as seen in Figure

96 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo o C A 8 B 170 o C % Fe on M1 site o C 270 o C % Fe on M1 sites o C 345 o C o C Time (minutes) o C Deviation from final a (%) Figure 5.9: A Refined concentration of Fe on the M site B Defect concentration plotted as function of unit cell change Black o C Blue o C Green o C Red o C At higher synthesis temperatures other factors than the Fe defect affect the unit cell For the highest temperatures the unit cell volume continues to decrease even after the Fe ions have completely ordered in the crystal structure As was seen in Figure this happens isotropically in the unit cell The reasons for the isotropic changes in the unit cells are not clear (owever as the precursor preparation and syntheses were done in air oxidation of Fe to Fe may take place )f the LiFePO structure is retained during the oxidation the smaller size of Fe may lead to a decrease of the unit cell volume as seen by (amelet et al The reason for the change in unit cell volume could also be other structural defects According to the calculations done by )slam et al. the defect with the second lowest energy is a Li Frenkel defect i e a Li moved from the lattice site to an interstitial site The presence of such defects in the structure may increase the unit cell volume and the continuous decrease of the unit cell after removal of the Fe M anti site defect could be due to an ordering of the Frenkel defects (owever it is unclear whether this ordering would affect the unit cell parameters to such a high degree The Li Frenkel defects cannot be observed directly in the X ray diffraction data but can be investigated by neutron diffraction This is discussed further in section Although our in situ data clearly show Fe on the Li sites the precise nature of the defects is not clear Axmann et al discussed whether the defect observed by Chen Whittingham is a true anti site defect or rather a Li deficiency leading to Fe occupancy on the Li sites )n the in situ study we have used the model suggested by Chen Whittingham and our data were not of

97 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo sufficient quality to distinguish between the different models (owever the defect chemistry will be discussed in more detail in section concerning the ex situ studies Lithium Iron Phosphate Precursor B Figure A C show the unit cell changes for the precursor B experiments while the Fe M concentrations are shown in Figure D Just as for precursor A the defect ordering time is temperature dependent The same amount of defects as for precursor A initially form but the ordering occurs faster for precursor B Above o C the temperature dependence is almost negligible The presence of ammonia therefore not only enhances the formation rate of the compound but also the ordering of the structure This is consistent with the work done by Liu et al who have studied the influence of p( on the defect concentration and observed that LiFePO synthesized at slightly alkaline conditions show fewer defects than material synthesized at neutral p( Deviation from final value (%) c a b A: 170 o C a c b B: 270 o C a b c C: 345 o C Deviation from final value (%) Time (minutes) % Fe on M1 site Time (minutes) D % Fe on M1 sites 8 E Deviation from initial a (%) Figure 5.10: A C Changes in unit cell parameters for LiFePO precursor B relative to the final value a is black b is blue and c is red D Refined concentration of Fe on the M site E Defect concentration plotted as function of unit cell change Black o C Blue o C Green o C Red o C

98 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo The experiment done at o C shows similar unit cell behaviour to the precursor A experiment whereas the trends at higher temperatures are quite different as the unit cell parameters quickly become constant When plotting the defect concentration as function of a as seen in Figure E a linear dependency is seen for high defect concentrations while a is almost constant when the structure is ordered The results indicate that the additional structural changes possibly due to oxidation seen for precursor A do not happen when using precursor B Lithium Iron Manganese Phosphate Figure A C show the Fe Mn M concentration for the manganese substituted compounds as function of time When comparing this to the results from LiFePO it is clear that for T o C the concentration of defects is higher when manganese is present After minutes the defect concentration is ca. regardless if the manganese content is or while this value was ca for LiFePO The retained defect concentration is consistent with the theoretical work done by Gardiner )slam who showed that the energy for the Fe Mn Li antisite defect is lower for LiFe Mn PO than for LiFePO i e the presence of the defect is more favourable in the manganese substituted compounds Above o C the energy difference for the formation of the defect in the non manganese and manganese substituted compound no longer plays a role compared to the thermal energy and the M defect concentrations observed are comparable to the results obtained for pure LiFePO At these temperatures the ordering of the structure happens faster than for LiFePO with precursor A The reason for this is discussed in section concerning the ex situ study Figure D F show the cation disorder versus the change in lattice parameter a for LiFe x Mn x PO The data show that the structural changes observed for LiFePO with precursor A after ordering of the cations do not appear for the manganese substituted samples Only very small deviations in the unit cell parameters are thus observed after ordering of the M defect This is rather surprising if the reason for the structural changes in LiFePO is in fact oxidation the same effect would be observed for LiFe x Mn x PO just to a lesser degree due to the smaller amount of Fe present

99 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Fe/Mn on M1 site (%) A: LiFe 0.75 Mn 0.25 PO o C 270 o C B: LiFe 0.50 Mn 0.50 PO o C 270 o C C: LiFe 0.25 Mn 0.75 PO o C 270 o C Fe/Mn on M1 site (%) o C o C Time (minutes) 345 o C Fe/Mn on Li site (%) D: LiFe 0.75 Mn 0.25 PO o C 270 o C 345 o C E: LiFe 0.50 Mn 0.50 PO 4 F: LiFe 0.25 Mn 0.75 PO o C 170 o C 270 o C 270 o C 345 o C 345 o C Deviation from final a (%) Fe/Mn on Li site (%) Figure 5.11: A C Refined defect concentration of LiFe xmnxpo as function of time Black o C Blue o C Green o C D E Refined defect concentration as function of change in unit cell parameter a Lithium Manganese Phosphate Figure A shows the changes in unit cell observed for the LiMnPO experiment done at o C The unit cell changes have been plotted on the same scale as those for LiFePO in Figure to facilitate comparison For LiMnPO the unit cell size is almost constant with synthesis time indicating that the defect concentration does not change This is confirmed in Figure B where the Mn M concentration is plotted for o C o C and o C )f first considering the experiment done at o C ca Mn defects is initially seen and the structures orders much slower than in LiFePO the defects seem to get locked in just as for LiFe x Mn x PO The initial structure seen within the time resolution of the experiment at o C contain only few defects but again the final ordering seem to happen slower than for LiFePO and LiFe x Mn x PO (owever it should be noted that these results cannot be directly compared with those of LiFePO and LiFe x Mn x PO due to the different p( value required in the synthesis

100 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Change in unit cell (Å) A Time (minutes) Mn on M1 site (%) 8 B o C o C o C Time (minutes) Figure 5.12 A Change in unit cell parameters for LiMnPO synthesized at o C The change from the initial a value is plotted in red b in black and c in red B Refined defect concentration of LiMnPO Black o C Blue o C Green o C 5.4 Questions Raised in the In Situ Study )n the first part of this chapter it has been described how in situ synchrotron data have been used to study the formation of LiFe x Mn x PO under sub and supercritical conditions A combination of in situ techniques allowed us to study the crystallization of LiFePO from a semi crystalline phosphate precursor through a similar intermediate phase consisting of small nanoparticles PXRD data revealed that when LiFePO initially forms the structure is highly defective as Fe is observed on the M Li site With time and temperature the structure orders )n the presence of ammonia both the crystallization and the ordering happen faster (owever the in situ studies also raised several questions The data quality the low scattering power of Li and q range available in the PXRD studies did not allow for a determination of the exact defect chemistry of the synthesized particles Different defect models anti site defects and non stoichiometric compounds gave comparable fits to the data and further analyses were therefore needed to fully understand the defect formation Furthermore additional experiments were needed to comprehend the differences in the defect concentrations in the pure LiFePO and manganese substituted compounds The structural changes not related to the Fe M occupancy could not be explained based on the defect model employed in the in situ studies These issues lead to further investigations of the defects in LiFePO as presented in the remainder of the chapter

101 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo 5.5 Ex situ Characterization Synthesis All samples for the ex situ study were synthesized hydrothermally in ml steel autoclaves with Teflon linings The precursors were prepared just as in the in situ experiments For the LiFePO synthesis ml M ( PO Riedel de (aen were mixed with ml M FeSO Sigma Aldrich Then ml M LiO( Sigma Aldrich Li was added forming a thick green precursor gel LiO( was used because of the lower neutron absorption cross section of Li The LiFe x Mn x PO x and samples were prepared in the same way by replacing the appropriate amount of FeSO with MnSO Sigma Aldrich of the same concentration All syntheses were performed at o C The reaction time was varied in order to obtain different defect concentrations with synthesis durations of min hours and hours For all syntheses g of ascorbic acid Sigma Aldrich was added to act as a reducing agent to avoid the formation of iron ))) compounds The pressure was autogenously generated in the autoclaves which were filled )n summary the following samples were prepared 1 LiFePO o C min 2 LiFePO o C h 3 LiFePO o C h 4 LiFe Mn PO o C min 5 LiFe Mn PO o C h 6 LiFe Mn PO o C min 7 LiFe Mn PO o C h For each sample four identical syntheses using identical autoclaves in the same position in the oven were performed to obtain enough material for neutron experiments Note that the heating rates in the autoclaves are much slower than those achieved in the capillary used for the in situ measurements The synthesis conditions can thus not be directly compared between the two studies X ray and Neutron Scattering Experiments (igh resolution powder X ray diffraction PXRD data for Rietveld refinement were measured at beamline BL B at Spring Japan using a large Debye Scherrer camera The X ray wavelength was determined to be Å by Rietveld refinement of a CeO standard a Å The samples were loaded into mm glass capillaries and the measurements were done at room temperature For the LiFePO samples data for crystallinity determination were measured by mixing a small amount of LiFePO with crystalline diamond powder X ray total scattering data were obtained at beamline )D B Advanced Photon Source USA using an X ray wavelength of Å and a

102 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Perkin Elmer amorphous silicon detector The samples were loaded in mm kapton capillaries and the measurements were done at room temperature Neutron powder diffraction and total scattering data were measured at room temperature at the time of flight diffractometer NPDF Los Alamos National Laboratory USA The samples of ca g were loaded into vanadium cans mm in diameter Background corrections were determined by measurements on the empty sample chamber and the empty vanadium sample can The detector efficiency was normalized by measuring data on a vanadium rod Each data collection took h Rietveld Refinement The X ray and neutron diffraction data were analysed by simultaneous Rietveld refinement in GSAS using the EXPgui interface For the Spring X ray data the range from to i e q max Å was included in the refinement The background was modelled by interpolation between points with refinable intensity values The scale factor and the zero point were refined as well as the peak shape which was described by the Thompson Cox (asting pseudo Voigt function using U V W X and Y Corrections for X ray absorption were done by GSAS For the neutron data measurements from all detector banks at the NPDF instrument were included in the fit covering q space to Å For all banks the background was described by GSAS model sum of exponential functions where parameters were refined Furthermore for each bank a scale factor was refined along with the zero point and the profile parameters were refined in profile function in GSAS which is a convolution of back to back exponential functions and a Pseudo Voigt function Corrections for neutron absorption were done by GSAS The X ray and neutron data were weighted equally in the refinement as the counting statistics are similar No correlation between refined parameters larger than were seen The structure was described in the Pnma space group and unit cell atomic positions and isotropic Debye Waller factors were refined for each site An average of the neutron scattering length of Li and Li was used in accordance with their abundance in the samples Fe was allowed on the Li site and Li on the Fe site independently without constraints For the Mn containing samples two models were refined Both Mn and Fe on the M defect site and Only Fe on the M defect site For the crystallinity determination the weight fractions of crystalline LiFePO and diamond in the mixed samples were found by Rietveld refinement using

103 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo the FullProf Suite program package The crystallinity of the samples was then obtained from the amounts of sample according to Further details on the crystallinity determination are given in Appendix ))) PDF Analysis PDF analysis was done for the LiFePO and LiFe Mn PO samples Neutron PDFs were calculated from the TOF data using PDFgetN All detector banks were included to obtain the total scattering function S q which was Fourier transformed using q max Å X ray PDFs were obtained in PDFgetX using q max Å Both the neutron and X ray PDFs were modelled individually in PDFgui The structure was described as for the Rietveld refinements however with the difference that the metal occupancies were not refined but kept fixed at the values obtained from the Rietveld refinements The pair distribution r ranges from Å and Å were used in the analysis Apart from the structural parameters the scale factor and the quadratic dynamic correlation factor were refined For the X ray measurements the q damp value was obtained from refinement of a LaB standard For the neutron data q damp and q broad were provided for the instrument ICP Analysis The elemental composition of the samples was analysed by )CP analysis using a Spectro Arcos )CP spectrometer Prior to the analysis the samples were dissolved in an aqueous (NO solution Scanning Electron Microscopy Scanning electron microscopy SEM images were recorded using a Nova Nano SEM from FE) A Low Vacuum Detector was used due to the insulating nature of the particles and a water atmosphere Pa was applied Mössbauer Spectroscopy The Mössbauer data collection and analysis were done by Dr (araldur P Gunlaugssen at Department for Physics and Astronomy at Aarhus University Only the most important results will thus be presented in the dissertation The Mössbauer spectra were obtained for the LiFePO samples at room

104 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo temperature in transmission geometry using a Co Rh source of mci mounted on a conventional drive system Velocities and isomer shifts are given relative to the centre of the spectrum of 57 Fe The spectra were analysed with one component due to Fe and one component due to Fe which was simulated using a quadrupole splitting distribution based on linear segments in the distribution function The coupling between the quadrupole splitting and isomer shift was assumed to be the same in all cases 5.6 Ex situ Results and Discussion Crystal Structure of LiFePO 4 Dependence on Synthesis Time Figure A E page show examples of the Rietveld fits to both neutron and X ray data As seen from the difference curves good fits with R F values around were obtained for all the data sets Generally the quality of the fit decreased slightly with shorter synthesis time indicating some structural disorder not included in the model The refined parameters and R values for all samples can be found in Appendix ))) Just as was seen in the in situ PXRD and SAXS WAXS study the refined unit cell size is dependent on the synthesis time This is clear in Figure A where the changes in the unit cell parameters are plotted relative to the final values h data as function of synthesis time Again the unit cell size decreases along a and c with synthesis time while b increases slightly The change in cell volume is thus again related to the defects in the sample which is apparent from the occupancy of the Fe M site shown as the black line in Figure B Deviation from final value (%) 0.24 A Synthesis time (hours) Occupancy on M1 site (%) Fe Vacancies B Synthesis time (hours) Strain (%) Synthesis time (hours) C Figure 5.13: A Change in unit cell parameter for LiFePO relative to the value obtained after h B Refined concentration of Fe black and vacancies red on the M Li site red C Microstrain plotted as function of Fe occupancy on M Li sites

105 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo The refinements confirm that short syntheses times produce disordered samples with a high concentration of Fe on the Li site Moreover it is now possible to characterize this in more detail While the Rietveld refinements show that after short syntheses large amounts of Fe is present on the M site there is no Li on the M site which is always fully occupied with Fe The results thereby confirm earlier studies stating that the crystallographic disorder present in hydrothermally synthesized LiFePO samples is not an anti site defect but rather Fe excess The results suggest that this deviation from ideal LiFePO stoichiometry is caused by reaction kinetics and is directly linked to the crystallinity of the samples as will be discussed further below The simultaneous treatment of the X ray and neutron data allows refinement of the full site occupancy of Li and Fe on the two metal sites This provides a determination of the metal site vacancy concentration which for the M site is calculated as occ vac M occ Li M occ Fe M The M vacancy concentration is plotted as the red curve in Figure B The vacancy and Fe concentration on M sites follow the same trend and fewer vacancies are seen with longer synthesis time (owever the vacancy concentration is always slightly higher than the Fe occupancy and for charge balance conservation substitution of a Li ion with Fe requires the formation of only one single Li site vacancy The additional M vacancies in the refined model are believed to be due to presence of Fe on the M sites as is corroborated by the Mössbauer measurements discussed below Just as for the in situ PXRD data the U parameter describes the largest contribution to the peak width indicating broadening caused by crystal lattice strain The strain parameter S calculated from the instrument corrected profile parameters is plotted as function of synthesis time in Figure C The plot suggests that the strain arises from the differences in unit cell sizes due to Fe occupancies on the M site To account for the structural changes in the in situ PXRD studies after ordering of the Fe M occupancy different models with Li Frenkel defects suggested by )slam et al 176 were tested (owever neither of the refinements gave any physical results as the scattering density on the interstitial sites for example the interstitial positions and around the Li site was moved towards the corresponding Li site in the refinement Thus Frenkel defects are not observed in the hydrothermally synthesized samples and ordering of these cannot explain the unit cell decrease seen at high synthesis temperatures Oxidation of Fe is therefore a more probable explanation for the observations in the in situ study

106 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Normalized int. (Arb. units) A: Neutron bank d spacing (Å) B: Neutron bank d spacing (Å) Normalized int. (Arb. units) Normalized int. (Arb. units) C: Neutron bank 3 D: Neutron bank d spacing (Å) d spacing (Å) E: X ray (degrees) Figure 5.14 Rietveld fits The black line shows the powder diffraction data the red the fitted model and the blue line the difference between the two

107 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Relation Between Crystallinity and Defects The in situ data showed that when using precursor A LiFePO formed from an almost amorphous precursor gel through a slightly crystalline intermediate consisting of small nanoparticles From the present diffraction data there are no clear observations of any remaining crystalline precursor or intermediate phases and good Rietveld fits using a single phase model are obtained for all data sets (owever from the crystallinity measurements of the LiFePO samples shown in Figure it is clear that a considerable fraction of the samples synthesized for min and hours is not crystalline LiFePO Although the absolute crystallinity values are associated with rather large uncertainties arising from the sample preparation and data analysis it is clearly seen that the mass fraction of crystalline LiFePO increases with increasing synthesis time The atomic structure of the amorphous material can be characterized by PDF analysis Neutron and X ray PDF fits for the three LiFePO samples are shown in Figure page The fitted paramters are given in Appendix ))) (ere the data are fitted in the r range from Å and in this region the crystallographic model fits well with the experimental PDFs (owever when extending the same model to r values below Å a large fraction of the peak intensities in the experimental PDF are not well described showing that amorphous lithium and iron phosphates nanoclusters with only local order coexist with the crystalline LiFePO The peak seen at Å originates from the P O bond while the range from Å covers the first Li O and Fe O distances The first metal P distance is seen around Å and this peak is particularly poorly described in the X ray data from the shorter syntheses time Crystallinity (%) Synthesis time (hours) Figure 5.15: Crystallinity of the LiFePO samples as a function of synthesis

108 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo To quantify the difference in intensity in the different r regions fits based on the LiFePO structure were also made individually from Å The low r region fits are plotted in Figure (ere it is seen that the region from Å can in fact be fitted well with the crystalline LiFePO structural model for both X ray and neutron PDFs when only this region is included This shows that the atomic structure of the amorphous nanoclusters is very closely related to the bulk phase The ratio between the scale factors obtained for the Å and Å fits are plotted in Figure A which clearly shows that the shorter the synthesis time the larger the amount of amorphous LiFePO with only short range order )t should be noted that an additional origin of the poor fit at low r for the defective phase could be local structural disorder induced by the presence of Li at the Fe sites leading to a split metal site When using our small box structural models this is not observed (owever to fully characterize whether the cation disorder changes the local structure of the metal sites large box modelling e g by the Reverse Monte Carlo technique may be applied A: X ray, 40 min D: Neutrons, 40 min G(r) (arb. units) B: X ray, 2 h G(r) (arb. units) E: Neutrons 2 h C: X ray, 7 h F: Neutrons, 7 h r (Å) r (Å) Figure 5.16 Modelling of the neutron and X ray PDF data fitted in the range Å

109 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Fitted region A: X ray, 40 min G(r) (Arb. units) G(r) (Arb. units) B: X ray, 2 h C: X ray, 7 h r (Å) Fitted region D: Neutrons, 40 min E: Neutrons, 2 h F: Neutrons, 7 h r (Å) Figure 5.17: Modelling of the neutron and X ray PDF data fitted in the range Å

110 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Low r scale / High r scale 1.3 A 1.2 X ray Neutron Fe/ Li ratio 1.3 B 1.2 Rietveld 1.1 ICP Synthesis time (hours) Synthesis time (hours) Figure 5.18: A Scale factor obtained from refinement of the low r range of neutron black and X ray red PDFs B Fe Li ratio from Rietveld analysis black and )CP red The Fe Li ratios obtained from the crystallographic analysis as well as )CP are plotted in Figure B The stoichiometry of the crystalline LiFePO changes as function of synthesis time and for all samples the Fe Li ratio is higher than The )CP results show similar trends although here the ratio between Fe and Li is much closer to that of stoichiometric LiFePO The diffraction results express the stoichiometry of the crystalline part of the sample while the )CP analysis gives the composition of the entire sample including the amorphous part The discrepancy between the results from the two techniques therefore indicates that there are differences in the way that Li and Fe are incorporated into the crystal structure during the synthesis Thus Fe is included relatively faster into both the M and M sites of the crystal structure than Li leading to the Fe excess SEM images of the three LiFePO samples are shown in Figure All the samples are very heterogeneous and consist of particles of several different sizes and shapes After minutes at o C large rhombus shaped particles coexist with smaller spherical like particles The smallest particles are most likely amorphous while the rhombuses are crystalline After hours the rhombic particles have grown bigger and the size distribution has broadened The largest particles are more irregular but still keep the basic rhombic shape Again smaller particles without the rhombic morphology are also observed After hours of synthesis some of the particles have grown significantly to rhombes m (owever much smaller rhombic and some irregular particles are also observed

111 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Figure 5.19 SEM images of LiFePO particles synthesized at and hours C C for o minutes A hours B

112 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Formation Mechanism By combining the results from the various in situ studies as well as ex situ Rietveld analysis PDF analysis )CP and SEM a picture of the formation mechanism from precursor A emerges as illustrated in Figure The precursor is almost completely amorphous and consists of lithium and iron phosphates )n the initial stage of the synthesis these form nanoparticles smaller than nm As LiFePO starts crystallizing an amorphous fraction remains which surround the crystalline defective particles Furthermore additional lithium phosphates may be found in solution The amorphous particles and dissolved Li phosphates then act as ion donors to the growing crystallites Fe PO structures are incorporated in the crystalline particles faster than Li leading to defects in the structure (owever as the synthesis proceed more LiFePO crystallize and the remaining amorphous and dissolved lithium phosphate is included in the crystalline particles As this happens the structure orders and Fe is moved from the M site to the M site Thus only when full crystallinity is obtained defect free LiFePO can be achieved The presence of defects is therefore directly related to the crystallinity of the particles With our novel understanding of defects and crystallinity of hydrothermally synthesized LiFePO a new interpretation of the poor electrochemical properties of samples synthesized using this method can be given Firstly we have confirmed that the defects present are not anti site defects but in fact excess Fe and vacancies occupying the M sites Although Li vacancies have previously been suggested to increase the performance of the cathode material there is no doubt that the presence of Fe in the Li channels blocking the diffusion pathway will reduce the electrochemical capacity significantly (owever the main reason for the low capacity of hydrothermally synthesized samples might very well be the presence of a large amorphous fraction The lithium and iron phosphate nanoclusters do not contribute to the electrochemical capacity or the electronic or ionic conductivity of the samples Figure 5.20: Formation mechanism for LiFePO

113 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Furthermore as the amorphous clusters seem to reside on the surface of the crystalline particles their presence could hinder the diffusion of Li into the crystalline particles Only by ensuring crystallinity high quality materials can thus be obtained This can be done by high synthesis temperatures longer synthesis times and or post synthesis high temperature treatment Mössbauer Analysis of the LiFePO 4 Samples Figure shows the Mössbauer spectra obtained from the LiFePO samples The overall shape of the spectra is due to a dominating Fe component but close inspection shows two distinct features in the samples compared with a single phase Fe compound First there is a feature at v mm s most clearly seen in the sample from the shortest synthesis Most likely this is due to the right leg of a Fe component where the left leg overlaps with the left leg of the dominating peak due to Fe Secondly there is an asymmetry in the line shape of the Fe component suggesting the presence of additional components with lower quadrupole splitting than the dominating component The results of the modelling are summarized in Table The Fe content is highest for the shortest syntheses and after hours only very small amounts of Fe is observed The results agree with the trends from Rietveld analysis which indirectly showed the Fe as additional vacancies (owever the Mössbauer results show Fe in the sample synthesised for min which is much higher than the extra vacancies seen by Rietveld refinement Furthermore if Fe was present in the crystal structure the unit cell size should be reduced due to the smaller ionic radii of Fe pm as reported by (amelet et al We see the opposite effect the unit cell is largest for the samples with the highest Fe content The results indicate that a large fraction of the Fe ions are present in the amorphous part of the sample As the amount of Fe decreases with synthesis time the results propose that Fe does not get oxidized during the low temperature synthesis The Fe fraction most probably originates from Fe in the amorphous phase that gets oxidized during handling of the samples after the synthesis when the reducing ascorbic acid is no longer present

114 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo A: 40 min Fe III Fe II Relative transmission (arb. units) B: 2 hours C: 7 hours P( E Q ) (arb. units) D: Quadrupole splitting E Q (mm/s) Velocity (mm/s) Figure 5.21: A C Room temperature Mössabauer spectra of the three LiFePO samples The experimental data are shown as black dots while the solid lines shows the fitting components from Fe green Fe blue and their sum red D Quadrupole splitting distribution determined for the LiFePO sample synthesized for min FeII Sample mm s EQ mm s Area mm s EQ mm s mm s Area LiFePO4, 40min LiFePO4, 2 h LiFePO4, 7 h FeIII Table 5.1: (yperfine parameters and spectral areas found from simultaneous analysis of the Mössbauer spectra The table lists the values of average isomer shift quadrupole splitting EQ and FW(M line width

115 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo The hyperfine parameters for Fe in the peak of the quadrupole splitting distribution mm s E Q mm s are in a reasonable agreement with parameters obtained on natural LiFePO i e triphylite The lower average quadrupole splitting for the sample synthesized for min and hours cf Table are due to the quadrupole splitting distribution as shown in Figure D The Mössbauer results show that several different Fe environments exist in agreement with the diffraction and total scattering results where Fe was observed at M M and in the amorphous Fe PO structure Bini et al saw a similar asymmetry of the Fe component in samples produced by microwave assisted hydrothermal synthesis route Metal Disorder in LiFe 1 x Mn x PO 4 The refined unit cell parameters for the manganese substituted compounds are plotted in Figure As Mn has a larger ionic radius than Fe substitution of Fe for Mn increases the unit cell volume Just as for the LiFePO samples the unit cell also increases for short synthesis time due to disorder on the metal sites The results from refinements using the two different disorder models are shown in Table When both Mn and Fe are allowed on the M site Model the refinement increases the vacancy concentration significantly for LiFe Mn PO min which does not seem reasonable and does not agree with the )CP results Model where only Fe is allowed on the M site gives a comparatively better and more physical result This indicates that in LiFe x Mn x PO only Fe defects and not Mn defects are present The Shannon ionic radii of Mn and Fe are pm and pm respectively compared with pm for Li and therefore the manganese ion may be too large to be incorporated on the M site a (Å) % Fe 75% Fe 100% Fe b (Å) % Fe 75% Fe 100% Fe c (Å) % Fe 75% Fe 100% Fe Synthesis time (hours) Synthesis time (hours) Synthesis time (hours) Figure 5.22: Unit cell parameters for all samples as a function of synthesis time

116 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo Sample Total Fe and Mn occupancy on M1 (%) Vacancy concentration on M1 (%) Model 1 Model 2 Model 1 Model 2 LiFe0.75Mn0.25PO4 40min LiFe0.75Mn0.25PO4 7h LiFe0.50Mn0.50PO4 40min LiFe0.50Mn0.50PO4 7h Table 5.2: Defect concentration and sample compositions in LiFe xmnxpo )n model both Mn and Fe were allowed on the M site whereas for model only Fe was allowed on the M site Fe occupancy on M1 site (%) % Fe 75% Fe 50% Fe Synthesis time (hours) Figure 5.23: Fe occupancy on the M site in LiFe xmnxpo as a function of synthesis time The defect concentrations from Model are plotted in Figure which includes a comparison with LiFePO For short syntheses min less Fe occupancy is seen on M with increasing Mn content (owever after long synthesis times h where the disorder is almost completely suppressed in LiFePO there are still significant amounts of Fe on the Li site when Mn is present in the structure Thus Mn seems to lock the defective structure making it challenging to synthesize defect free LiFe x Mn x PO nanoparticles hydrothermally This agrees with the theoretical calculations by Gardinier )slam The PDF results for LiFe Mn PO are similar to those of LiFePO as seen in Figure page The fitted parameters are given in Appendix ))) When using the model obtained for Å poor fits to the low r region is seen which is again believed to be due to the presence of amorphous content Again local disorder induced by the split cation site now from both Fe Mn and Li is not apparent in our small box refinements (owever to fully characterize this in detail RMC modelling may be done

117 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo When comparing the Rietveld and )CP stoichiometry results in Table the Fe Li ratio is higher in the crystalline part of the sample than in the whole sample just as for pure LiFePO This again shows that Fe is incorporated faster into the crystal structure than Li (owever the Mn Li ratios found from the two methods are almost the same even after short synthesis times This indicates that Mn is immediately incorporated in the crystal structure when the synthesis is initiated This agrees well with our previous in situ study showing that Mn substituted samples form faster than LiFePO Fe:Mn:Li Rietveld Crystalline stoichiometry Fe:Mn:Li ICP Total sample stoichiometry Model 1 Model :0.38:1 0.85:0.33:1 0.72:0.82:1 0.66:0.74:1 Table 5.3 Sample stoichiometry obtained by Rietveld and )CP analysis

118 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo High r fits G(r) (Arb. units) Fitted region A: X ray, 40 min B: X ray, 7 h r (Å) G(r) (Arb. units) Fitted region C: Neutron, 40 min D: Neutron, 7 h r (Å) Low r fits G(r) (arb. units) E: X ray, 40 min F: X ray, 7 h r (Å) 4 2 G: Neutron, 40 min H: Neutron, 7 h r (Å) Figure 5.24: A D Modelling of LiFeMnPO PDFs in the range Å E ( Modelling of LiFeMnPO PDFs in the range Å

119 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo 5.7 Conclusions By a combination of extensive in situ and ex situ characterization techniques the crystallization and formation of defects in hydrothermally LiFe x Mn x PO have been elucidated From in situ PXRD studies the crystallization of the olivine phase from various precursors and intermediates was followed We saw that the presence of ammonia from N( Fe SO enhances the crystallization of LiFePO Combined SAXS WAXS studies showed that the large LiFePO crystallites form through amorphous nano sized particles and the growth of these dictate the crystallite size of LiFePO Total scattering studies were used to investigate the atomic structure of the almost amorphous precursor and intermediate which showed that the local structure the r range from Å is retained throughout the synthesis (owever the assembly of the various FeO and PO units changes as the olivine phase crystallizes Further modelling of the PDFs is needed to fully understand this process Sequential Rietveld refinement of the PXRD data provided information about the structural changes during the hydrothermal process )t was shown that at all temperatures the initial formed particles always contain a certain amount of Fe on the M Li site The concentration of these defects decreases with increasing synthesis time and the rate of ordering of the structure is temperature dependent A structure free of Fe on the M site is obtained only after several minutes of reaction even in supercritical water This is an important point when considering the possibilities for hydrothermal synthesis of commercial LiFePO From a commercial point of view continuous hydrothermal synthesis in a flow reactor is preferred (owever in typical continuous reactors the residence times are below one minute The present data show that this is insufficient time to remove the M defects even at supercritical conditions (anwha Chemical in South Korea produces ton scale LiFePO from supercritical flow synthesis each year While their synthesis conditions and post synthesis treatments are not known to the public several studies of supercritical synthesis have shown the need for sintering after the hydrothermal treatment to obtain good electrochemical properties The defective structure explains this need The precursor study showed that the presence of ammonia in the synthesis not only enhances the crystallization of the phase but also the ordering of the structure Furthermore when synthesizing the manganese containing compounds at low temperatures a higher equilibrium defect concentration is seen compared to pure LiFePO

120 Chapter Defect Formation during (ydrothermal Synthesis of LiFexMn xpo To explain the observations done in the in situ studies regarding defect formation extensive ex situ studies were done Simultaneous Rietveld refinement of high quality neutron and X ray powder diffraction data was used to obtain detailed information about the structure of hydrothermally synthesized LiFe x Mn x PO particles The data clearly showed that the defect seen is not an anti site defect as first proposed but excess Fe residing on the M Li site The defects arise due to differences in the rate with which Li and Fe are introduced in the crystalline LiFePO structure as shown by the fact that Li x Fe y PO coexists with amorphous Li Fe PO units For the crystalline particles the defects are suppressed and thus high quality battery materials are obtained either from extended synthesis time or from higher synthesis temperature LiFe x Mn x PO is also disordered on M but the refinements show that only Fe occupies the Li site The presence of Mn in the structure locks the Fe disorder even for long synthesis times and suppression of the defect formation is challenging for hydrothermal synthesis The present study underpins the need for thorough structural investigations of cathode materials synthesized by low temperature methods The disappointing electrochemical properties of hydrothermally synthesized LiFePO have so far been explained by the presence of Fe in the Li channels Although there is no doubt that this will influence the capacity of the resulting cathode the low crystallinity of defective samples might have an even larger effect Low crystallinity is generally a problem for samples synthesized at low temperatures and affects the properties of almost all functional materials Although PXRD is a standard characterization technique simple crystallinity measurements using a crystalline standard are rarely done By measuring this and characterizing any amorphous part of the sample as well as the crystal structure size and morphology of the particles many of the physical properties of the synthesized materials can be explained The study has also shown how several complementary techniques often are needed to get a comprehensive image of a certain material systems Neutron and X ray diffraction as well as powder diffraction total scattering and small angle scattering are all highly complementary and the combination with spectroscopy and microscopy gives broad information about the sample on several different length scales The chapter also introduces the strength of in situ total scattering The following chapters will focus on this technique and show how valuable knowledge about oxide crystallization can be extracted

121 Chapter Mechanisms of SnO Nanoparticle Formation And Growth 6 Mechanisms of SnO2 Nanoparticle Formation and Growth 6.1 Introduction The two previous chapters mainly focused on the structural and microstructural changes occurring after crystallization of a material during hydrothermal synthesis (owever to fully understand the formation of crystalline nanoparticles in a hydrothermal synthesis it is also necessary to consider the atomic structure of the solution before the particles crystallize how does the transformation from complexes in solution or an amorphous precursor to a final crystalline phase take place This was touched upon in section and on SAXS and total scattering studies of LiFePO synthesis and will now be further discussed )n this chapter ) present the use of in situ total scattering with a time resolution of few seconds in the study of the hydrothermal synthesis of SnO SnO is a wide band gap ev n type semiconductor and has been studied extensively owing to its optical and electrical properties combined with high chemical and mechanic stability SnO is thus used in e g transparent conductive electrodes photovoltaic devices and photosensors (owever presently its most important application is in gas sensors where measurements of electronic conductivity allows the concentration of inflammable and toxic gasses such as ( CO or C( to be monitored As this relies on gas adsorption on the surface layer reducing the size of the particles to nanometers is of interest because the sensitivity of the sensors may be greatly enhanced by increasing the active surface )n )dota et al first introduced Sn based anode materials for Li ion batteries and much research has since then been directed to enhance the electrochemical properties of the material system When initially lithiated SnO is reduced to metallic Sn while Li is incorporated in amorphous Li O After the first cycle a reversible reaction occurs as the newly formed metallic Sn alloys with Li which is reduced in the cell reaction Sn based anodes are attractive since they exhibit times the volumetric capacity of graphite (owever the main drawback for applying of SnO in anodes is the large volume difference between the lithiated and delitihated states By using nanostructures the strain induced in the anode may be reduced especially if incorporated in a matrix that can accompany the volume changes

122 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Several studies of hydrothermal synthesis of SnO have been published and for many applications hydrothermally synthesized particles show superior properties compared to materials synthesized by high temperature methods (ere ) have used total scattering to dig deeper into the synthesis and reveal the mechanisms behind particle formation and growth The rutile crystal structure of SnO is shown in Figure The structure crystallizes in the P4 2 /mnm spacegroup with a single Sn site octahedrally coordinated to oxygen in the tetragonal unit cell Compared to LiFePO and LiCoO the structure is very simple and the unit cell smaller )n this study we thus took a step back in structural complexity in order to obtain an understanding of some of the very fundamental processes happening in a hydrothermal synthesis First total scattering studies will be presented to give insight in the formation and growth mechanisms while additional PXRD data give further information on the size structure relation of the nanoparticles The main results were published in Journal of the American Chemical Society in Figure 6.1 SnO unit cell Sn is shown in red while oxygen is blue The cell is tetragonal with a=b= Å c Å

123 Chapter Mechanisms of SnO Nanoparticle Formation And Growth 6.2 Experimental Methods The SnO nanoparticles were crystallized from clear aqueous solutions of SnCl ( O Sigma Aldrich of various concentrations M M and M The in situ total scattering measurements were performed at the )D B beamline at APS Argonne National Laboratory USA using the setup described in Chapter The precursor solutions were injected into the reactor which consisted of a thin fused silica tube measuring mm in inner diameter and mm in wall thickness For all experiments the pressure was set to bar whereas the temperature was varied between o C and o C A Perkin Elmer amorphous silicon detector measuring by cm was placed mm from the sample The X ray wavelength was Å and q max was Å The time resolution was seconds Further experiments were done in which the SnCl was precipitated with NaO( prior to the synthesis ml M SnCl was thus thoroughly mixed with ml M NaO( producing a white gel which was injected into the fused sapphire capillary These experiments were done at beamline P at PETRA))) (amburg Germany also with a PerkinElmer amorphous silicon detector With an X ray wavelength of Å and a detector distance of cm the q max available was Å The time resolution was s Additional synchrotron powder X ray diffraction PXRD experiments were performed at beamline i at MAX)) MAX lab Sweden using the same experimental setup (ere experiments were done both in fused silica capillaries and sapphire capillaries For these experiments the pressure was again fixed at bar whereas the temperature was varied from o C to o C For these data the wavelength was Å and the detector to sample distance mm The detector was an Oxford Diffraction Titan CCD measuring cm in diameter and the time resolution between the frames seconds The q range went to q max Å Nanoparticles synthesized in the same setup in our home laboratory using M SnCl ( O Sigma Aldrich at o C and bar for minutes were used for ex situ TEM characterization The TEM characterization was done using a Phillips Model CM TEM microscope working at kv Due to inhomogeneous heating of the capillary when moving away from the centre of the tube care has to be taken when comparing the X ray results from data collected from the centre of the reactor with TEM images obtained on material from the entire hot zone of the reactor

124 Chapter Mechanisms of SnO Nanoparticle Formation And Growth 6.3 Data Treatment The raw total scattering data were integrated in Fit2D 146 and the PDFs were subsequently obtained using PDFgetX3 Scattering from the capillary with deionized water at the appropriate conditions was subtracted from the integrated pattern before using data in the q range from to Å in the Fourier transformation The PDFs were modelled to extract structural and microstructural parameters using SrFit unpublished and PDFgui. 72 The refinements in SrFit are described in the result section )n PDFgui, the model of the nanocrystalline SnO was refined using the G(r) data range from Å applying Nyquist data sampling The structure was described in P4 2 /mnm. )n all cases the last frame in the data series was treated first and the scale factor the unit cell the x coordinate of O and the isotropic thermal factors for both Sn and O were refined along with the sp diameter of the particles The instrumental resolution was included by applying the Qdamp parameter which had been found by refinement of data from N)ST LaB The correlated motion parameter delta2 was kept fixed at Å )n the sequential refinement the thermal parameters were kept fixed at the value found in the treatment of the last data frame except in the M o C series where all parameters were refined throughout the whole data set Estimated standard deviations of the parameters are found in PDFgui from the least squares refinement however uncertainties on the G r need to be provided as input These were estimated after an initial fit of the model using Nyquist data sampling and found as Using this method it is assumed that the model gives a good description of the sample and that the difference between the model and the data therefore describes the noise on the observed G(r) The denominator is the number of independent variables in the fit and the Nyquist sampling is used since the neighboring G obs (r) in this case are not correlated The total scattering data were also analysed by Rietveld refinement using FullProf Suite where the data range from was used The background was described by linear interpolation between points with refinable heights and the peak shape was described by the Thompson Cox (asting formulation of the Pseudo Voigt function The instrumental contribution to the peak width

125 Chapter Mechanisms of SnO Nanoparticle Formation And Growth was determined by refinement of the N)ST LaB pattern The strain contribution to the peak width was neglected and the sample broadening was assumed to stem only from particle size )t was found that an anisotropic size broadening model was necessary and the first spherical harmonics were used i e Y 00 and Y 20 The SnO structure was refined in space group P42/mnm The last frame in the data series was the first to be refined and here the scale factor the unit cell and the x position of the O atom as well as a common temperature factor B for both O and Sn )n the sequential refinement the atomic position and the B value was kept fixed at the value found in the refinement of the last frame The MAX lab PXRD data were integrated using Fit2D 146 and treated by single Gaussian peak fitting as described further below 6.4 Results and Discussion Structures in Aqueous Solutions of SnCl 4 Figure A shows room temperature total scattering data from the precursor at different concentrations )t is clear that the concentration of SnCl dramatically affects the scattering pattern The structural differences causing this difference can be understood by considering the reduced pair distribution functions PDF shown in Figure B )n the data for the M and M SnCl solutions a large peak is present at r Å along with several smaller peaks at Å These features agree well with the formation of SnCl x ( O x x complexes which have been reported in NMR studies of SnCl solutions Sn and Cl have Shannon ionic radii of Å and Å respectively giving Sn Cl bond lengths of ca Å i.e. close to the r value for the most intense peak A model describing this complex was applied using SrFit, as is shown in Figure C The previous NMR studies of SnCl solutions showed formation of several species with different stoichiometries such as SnCl ( O and SnCl ( O in different quantities (owever in order to reduce the number of parameters only one complex was included in the final model mer SnCl ( O Figure D which has the weighted average stoichiometry of the species reported in M SnCl solution For simplicity ( O was replaced by O The model gives a good description of the main Sn ligand peak as well as the ligand ligand distances between Å Sn Cl and Sn O distances of Å and Å respectively were obtained in the refinements which agrees well with single crystal diffraction studies of cis SnCl ( O reporting Sn Cl distances of Å and Sn O distances between Å and Å

126 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Figure 6.2: A Raw total scattering data from M red M green and M blue solutions of SnCl( O at room temperature The scattering pattern from the capillary filled with water is shown in black almost overlapped by the pattern from the M solution B PDFs obtained from the data shown in A C Fit of mer SnCl ( O to data recorded of M SnCl at room temperature The thick black curve shows the observed G r the red curve the model and the blue the difference between the two (owever as can be seen in the difference curve plotted in Figure C the shoulder at Å does not originate from the aquachlorotin )V complex This can instead be ascribed to the Sn O distances in Sn ( O Figure E which is believed to form simultaneously with SnCl x ( O x x species Sn is a Lewis acid and hexaaquatin )V is therefore partially deprotonated yielding an acidic solution and complexes of the type Sn ( O y O( y y No significant structural features from either complex are seen in the PDF from the M solution This is most likely due to the relatively low concentration of the precursor as the scattering signal arising from Sn species is insignificant compared to that of the water in the capillary

127 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Formation of SnO 2 Nanoparticles From SnCl 4 Solutions )n Figure A the raw data collected after min at o C are shown Bragg peaks from crystalline SnO nanoparticles are now clearly visible on top of the large diffuse scattering signal especially for the M and M syntheses Figure B shows the PDFs obtained from the total scattering in Figure A (ere all significant peaks above r Å can be ascribed to the rutile SnO structure (owever for the M and M experiments the Sn Cl peak is still present and it remains in the PDF throughout all experiments performed with the high precursor concentrations Intensity (Arb. units) 4M 2M 1M A q Å 1 G(r) (Arb. units) 4M 2M 1M r (Å) B G(r) (Arb. units) C r (Å) Figure 6.3: A Raw total scattering data from M red M green and M blue solutions after minutes at o C Black Scattering from the capillary filled with water at o C B PDFs obtained from the data shown in A C Fit to the G r obtained after minutes at o C M Black observed G r Red Calculated G r Orange Contribution from SnCl ( O Green SnO Blue Difference curve

128 Chapter Mechanisms of SnO Nanoparticle Formation And Growth The metal complexes present in the precursor solution are the building blocks for the SnO nanoparticles The precise formation mechanism could therefore be elucidated by modelling the PDFs of mer SnCl ( O and the SnO nanoparticles simultaneously as is illustrated in Figure C in the frame obtained after minutes at o C M The fitting was done using the unpublished program SrFit from the Billinge group which allow flexible modelling of both crystalline and molecular species )n the modelling of the time resolved data the scale factor for mer SnCl ( O was refined along with the bond distances and the anisotropic thermal parameters for the ligands These were restrained such that the factors expressing the vibrations along the bond longitudinal were all constrained to take the same value u l and all vibrations perpendicular to the bond transverse were constrained to one value u t. For the crystalline phase the scale factor the unit cell the atomic positions and the isotropic thermal parameters were refined Additional examples of the fits are shown in Appendix )V along with resulting parameters The time and temperature dependent scale factors obtained from the modelling are plotted in Figure A The values have been normalized such that the scale factor obtained for the complex at time was set to )n the beginning of the reaction the SnO scale factor rapidly increases but interestingly a similar decrease in the value for the aquachlorotin V) complex scale factor is not observed This is also evident in the PDFs obtained for the first few frames after the initiation of the experiment as shown in Figure B where the intensity of the Sn Sn peak at ca Å increases significantly more than the Sn Cl intensity at Å decreases This shows that the SnO nanoparticles do not form directly from the Sn ions bound in the chloride complex but from Sn ions coordinated in the hexaaquatin )V complex The Sn O peak at Å remains constant in intensity as SnO nanoparticles form and indeed the Sn O bond length in the crystalline SnO refines to an identical bond length value The data conclusively show that the SnO nanoparticles must form from clustering and condensation of octahedrally coordinated aquahydroxotin )V complexes as illustrated in Figure C and the formation mechanism can be written as Sn ( O y O( y y aq SnO s y( O l y ( O aq As the reaction progresses aquachlorotin )V slowly disproportionate causing more and more SnO to form as is seen in the gradual decrease of the mer SnCl ( O scale factor at the highest temperatures

129 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Figure 6.4: A Normalized scale factors for the complex open symbols and SnO closed symbols Black o C Blue o C Green o C and red o C All data shown are obtained with M solutions B G r obtained from the three first frames of the experiment done at o C and M C Formation mechanism for SnO nanoparticles where Sn is shown as red and O as blue ( is not shown D Refined u values open symbol shows transverse displacements and closed symbols longitudinal displacements. The colour codes are as in B. As seen in Figure B the Cl Cl peak at Å broadens as the heating is initiated and can subsequently no longer be distinguished from the SnO peaks The broadening of the peak is due to strong thermal vibrations of the ligands transverse to the Sn ligand bond This is illustrated in Figure D where the refined thermal parameters for the ligands of the chloride complex are plotted )n all cases the transverse movement open symbols is much larger than the movement along the bond closed symbols For the high temperature experiments a gradual increase is seen simultaneous with the decrease of the tinchloro complex scale factor Most probably the two are closely related as the chloride ligands vibrate rapidly around Sn they can easily be substituted to create hexaaquatin V) complexes which can condensate to SnO

130 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Growth of Nanocrystalline SnO 2 from SnCl 4 Solutions The spatial extent of the correlations in the PDF provides information about the growth of the nanoparticles as illustrated by the G(r) in Figure A The data shown were all recorded after minutes with the M precursor at different temperatures )t is clear that increasing the synthesis temperature extends the PDF oscillations to larger r values (owever to get an estimate of the particle size the instrumental resolution has to be taken into account since this dampens the oscillations at high r and causes them to completely disappear above Å Therefore both the instrument effect and the particle size were included in the model Examples of the fits along with the resulting parameters and estimated standard deviations are given in Appendix )V The resulting spherical particle diameters sp diameter are shown in Figure B The results for the M experiments clearly reveal that it is possible to control the particle size by means of the reaction temperature This is seen when comparing the growth curves obtained from the and o C syntheses (owever below o C the particle size is not temperature dependent and appears to be stable around nm as shown in the inset in Figure B The effect of SnCl concentration on particle size can be seen when comparing the growth curves from the syntheses done using M M and M at a reaction temperature of o C With increasing precursor concentration the particles grow larger and in order to synthesize very small particles nm the SnCl concentration should be reduced to M or less Note that for the experiment done at o C with M precursor particle sizes well above the instrumental resolution limit are obtained and for these values the uncertainties are significant The growth mechanisms at different temperatures can be understood when considering the increase in particle volume along with the total amount of SnO nanoparticles formed The quantity V=(sp) 3 proportional to the volume of the particles is plotted with the scale factors in Figure For the experiments done at o C o C and o C the growth curves and scale factors follow exactly the same path i e the particles grow because more SnO can be formed from hexaaquatin )V (owever at o C the scale factor initially increases rapidly and then stabilizes after ca. minutes After the stabilization of the scale factor the particle volume continues to increase indicating extended particle growth by consummation of already existing particles The extended growth explains the different dependency of the particle size on temperature below and above o C

131 Chapter Mechanisms of SnO Nanoparticle Formation And Growth A G(r) (Arb. units) o C nm 250 o C nm 200 o C 4.2 nm o C nm 160 o C sp diamter (nm) r Å B 2M, 180 o C 2M, 200 o C 4.5 2M, 160 o C M, 350 o C 2M, 250 o C 4M, 200 o C 2M, 200 o C 1M, 200 o C Time (minutes) Figure 6.5: A G r s obtained from the frames recorded after min for the experiments performed with M precursor The refined sp diameter is marked by the black ticks B sp diameters plotted as function of time for all experiments The insert shows the size region from to nm The growth curves from the three experiments done at and o C with M are almost completely overlapping Normalized scale factor A: 2M, 160 o C Time (minutes) Volume (nm 3 ) Normalized scale factor B: 2M, 180 o C Time (minutes) Volume (nm 3 ) Normalized scale factor C: 2M, 200 o C Volume (nm 3 ) Normalized scale factor D: 2M, 250 o C Volume (nm 3 ) Time (minutes) Time (minutes) Figure 6.6: Normalized scale factor black plotted with the particle volume red A o C M B o C M C o C M D o C M E o C M

132 Chapter Mechanisms of SnO Nanoparticle Formation And Growth The total scattering data were also treated by Rietveld refinement The refinements gave satisfactory fits to the data when introducing anisotropy of the particle shape The refined volume weighted particle sizes are shown in Figure and the particles are observed to be elongated along the crystallographic c axis The aspect ratio between the sizes in the a b and c direction is shown in Figure C This plot shows that not only the particle size but also the aspect ratio can be controlled by the synthesis temperature Generally the volume weighted crystallite sizes obtained from Rietveld analysis are smaller than the particle sizes obtained in the PDF analysis but the time and temperature trends of the growth are similar The growth mechanisms were further studied by LSW kinetic analysis of the growth curves The expression D(t) D 0 =k (t t 0 ) 1/x was fitted to the growth curves along a for the M experiments from o C between minutes here D is the particle diameter at time t D 0 is the diameter at time t 0 while k and x are free variables The resulting values and fits are shown in Figure The LSW theory states that if the volume of the particles increases linearly with time the reaction is limited by diffusion of the precursor and not by the reaction at the surface of the particles )n this case x should take a value of which is close to the results obtained here (owever as was discussed previously the kinetic models describe very complex phenomena in a simple manner and it is therefore crucial not to over interpret the parameters The main result from the kinetic modelling is thus that the growth seems to happen through similar mechanisms and is dependent on diffusion of Sn complexes to the growing particles A B C 6 D a (nm) Dc (nm) D a /D c Time (minutes) Time (minutes) Time (minutes) Figure 6.7: Volume weighted crystallite sizes along the crystallographic a direction obtained from Rietveld refinement B Volume weighted crystallite sizes along c. C Crystallite size ratio Black symbols show the data for M and o C blue M and o C green M and o C and red M and o C

133 Chapter Mechanisms of SnO Nanoparticle Formation And Growth D a (nm) A: 2M, C B: 2M, C 2.2 C: 2M, C 3.0 D: 2M, C k=0.425(5) 1.8 k=0.358(5) k=0.164(2) k=1.23(1) x=3.31(4) x=2.93(6) 2.0 x=3.46(4) 2.7 x=2.64(2) t t 0 (minutes) t t 0 (minutes) t t 0 (minutes) t t 0 (minutes) Figure 6.8: LSW fits to the data for the experiments from o C with M The data points are shown as black dots the fit as a red line The expression D(t) D0=k (t t0) 1/x was fitted in the range t minutes D is the particle diameter in the a direction at time t D0 was chosen as the diameter at time t0 min while k and x are free variables Figure 6.9: TEM images of SnO synthesized using M SnCl o C and bar for min Figure shows TEM image of nanoparticles recovered from a synthesis using M SnCl done at o C for minutes The images give information about the general morphology and size range of particles synthesized by this method but it is important to note that it cannot be directly related to the in situ diffraction results which only probed the centre of the reactor i e hottest zone The TEM images show large dense aggregates consisting of individual particles ranging from nm The images are of rather poor quality and it is hard to distinguish individual particles (owever the particle size is in the same range was seen from the total scattering data and indications of the ellipsoidal particle morphology are also observed

134 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Synthesis of SnO 2 from Tin Hydroxide Gels )n order to investigate the formation of SnO without the effect of the chloride complex SnO was synthesized from a hydroxide gel obtained by mixing SnCl and NaO( solutions The synthesis was done at o C and bar with final Sn concentration M The gel was prepared such that n NaO( n SnCl to precipitate all Sn The PDF obtained from the precursor is shown in Figure A The I(q) S(q) and F(q) were plotted in the description of total scattering in section Although no clear Bragg peaks were seen in q space features similar to the SnO structure are observed in the PDF The bulk SnO crystal structure was therefore fitted to the data with a spherical particle envelope and the model is seen to describe the main features well Already before initiation of the heating amorphous tinoxide like nanoparticles with a refined particle size of ca nm have formed The data illustrate that hydroxide ions bind stronger to the Sn than chloride suppressing the tinchloride complex (owever Sn O( is not stable and form oxide like particles even at room temperature most probably through the same mechanism as illustrated in Figure C The sp diameter of nm corresponds to clusters condensed by Sn O( units and the cluster structure is most likely a highly defective version of the bulk SnO structure with the O sites partly occupied by hydroxide groups especially in the terminal positions The defective structure means that the SnO model cannot fully describe the experimental PDF and the poor fit around r Å where an unfitted peak is seen most probably arises due to surface structure effects Further modelling is needed to fully explain this The difference curve also clearly shows an additional PDF peak at Å This value corresponds to the Sn Cl bond distance observed in the aqueous SnCl solutions and may thus arise from additional Sn not incorporated in the amorphous particles or from chloride ions bound to Sn on the surface of the particles Furthermore the Na O distance which is expected due to octahedral complexation of water to the Na ions is in the same r range The interaction between chloride and water may give a weak broad peak around r Å i e overlapping with the first Sn Sn peak which is much more intense The PDF obtained after minutes at o C is plotted in Figure B Now nanocrystalline SnO particles have formed and a good fit can be obtained from the structural modeling Still additional peaks are seen in the local order arising from Na and Cl interactions The time resolved refined particle size is shown in Figure C Although care should be taken when comparing particle sizes obtained from different beamtimes and beamlines

135 Chapter Mechanisms of SnO Nanoparticle Formation And Growth the particles are generally smaller than those obtained without NaO( added with a final size of ca nm after min compared to nm without NaO( This is surprising as it would be expected that the higher amount of reactive Sn would lead to larger particles The growth mechanism is also different than for the SnCl solution experiments Figure D shows the normalized scale factor plotted along with the particle volume Although the uncertainties on the scale factor are rather large as seen by the scattered data points the figure indicates that the scale factor stabilizes quickly after the initiation of the reaction while the particles continue to grow When NaO( is added extended growth of the particles is thus seen even at low temperatures Most likely this is due to the reactive O( surface groups G(r) (Arb. units) A: Precursor r (Å) G(r) (Arb. units) B: SnO 2 nanoparticles, 15 minutes at 200 o C sp diameter r (Å) C Time (minutes) Normalized scale factor D Time (minutes) Volume (nm 3 ) Figure 6.10 A PDF fit to the G r from the precursor Black Observed G r Red Calcualtde G r Blue Difference curve B PDF fit to the frame obtained after minutes at o C C Refined sp diameter as function of time D Normalized scale factor black and particle volume red

136 Chapter Mechanisms of SnO Nanoparticle Formation And Growth Structural Changes of SnO 2 During Synthesis Figure A B show the relative changes in unit cell parameters as function of the particle size obtained in Rietveld refinement of the M SnCl solution data Only changes are considered since the absolute values again are uncertain due to the inherent lack of internal standard As the particles grow the unit cell decreases along the c direction This effect is smaller in the a direction and the size dependent structural changes seem anisotropic Expansion of the bulk unit cell in nanoparticles is well known for many other metal oxide systems and different explanations have been given such as valence reduction stacking faults and surface defect effects The present in situ data are not of sufficient quality to probe in detail the origin of the unit cell size dependency The PXRD experiments at MAX lab provide additional information about the relation between nano sized particles and crystal structure For the experiments using M SnCl the diffraction peaks are abnormally broad as is especially clear for the (110) peak at ca o shown in Figure The full data ranges are shown as contour plots in Appendix )V For the o C and o C data the line shape is clearly not symmetric This is most likely due to the coexistence of two different polymorphs of SnO namely the bulk tetragonal phase and an orthorhombic modification The orthorhombic phase is a high pressure polymorph and has only previously been reported to exist in the bulk phase above GPa )t has the CaCl structure space group Pnnm and forms through a second order phase transition from the tetragonal phase At pressures above GPa this structure turns into another orthorhombic phase PbO structure and at even higher pressures a cubic phase becomes stable Earlier studies of tin oxide nanoparticles have reported formation of the high pressure polymorphs due to the large surface to volume ratio of the nanoparticles elevating the pressure on the particles (owever these studies only show formation of the PbO polymorph whereas the CaCl structure has not earlier been reported as a stable phase due to size effects

137 Chapter Mechanisms of SnO Nanoparticle Formation And Growth A B a a final c c final D a (nm) D a (nm) Figure 6.11: Changes in the unit cell plotted as function of particle size Da for the M experiments A Changes in the a axis a afinal B Changes in the c axis c cfinal Black M and o C Blue M and o C Green M and o C Red M and o C A: 160 o C, 1M, 3 min B: 180 o C, 1M, 3 min C: 250 o C, 1M, 3 min Intensity (Arb. units) D: 160 o C, 2M, 3 min E: 180 o C, 2M, 3 min F: 250 o C, 2M, 3 min (degrees) Figure 6.12: Section of the PXRD frames collected minutes after initiation of the experiments showing the peaks of the SnO structures The data points are seen as black dots and the fitted Gaussian curves are shown as red lines For the experiments done with M SnCl at o C double peaks were observed and these were fitted with two Gaussians shown in blue and light blue Phase Space Structure Lattice Unit cell 56 group type Bulk phase Pmnm Rutile Tetragonal Å Å Å Phase )) (P Pnnm CaCl Orthorhombic Å Å Å Phase ))) (P Pbcn PbO Orthorhomic Å Å Å Phase )V (P Pa Flourite Cubic Å Table 6.1 Structures of SnO

138 Chapter Mechanisms of SnO Nanoparticle Formation And Growth As presented in Table the unit cells of the bulk phase and the first high pressure phase are very similar and distinguishing between the two structures is quite difficult due to the large peak broadening and the lack of an internal standard The weight fractions of the orthorhombic tetragonal phase were therefore only roughly estimated by fitting Gaussian curves to the (110) peaks and determining the ratio between the two intensities The results are shown in Figure For the M o C data it is not clear whether or phases were present the peak shows slight asymmetry but it is not possible to get a stable fit using two Gaussian functions Therefore the M o C data will not be considered any further For all the M data only the bulk tetragonal rutile phase was present At M and o C the tetragonal phase fraction is whereas at o C this fraction has increased to The estimated fractions seem constant throughout the experiments This shows that by choosing appropriate hydrothermal synthesis parameters not only the size and the morphology of the nanoparticles can be controlled but also the specific crystal structure I Tetragonal / (I orthorhomic +I Tetragonal ) T=250 o C T=180 o C Time (Minutes) Figure 6.13: The ratio between the intensity from the tetragonal peak and the sum of the tetragonal and orthorhombic peak intensities

139 Chapter Mechanisms of SnO Nanoparticle Formation And Growth PXRD Results from the Sapphire Reactor All the SnO results presented so far have been obtained in fused silica tubes (owever similar PXRD experiments were done with M SnCl in a sapphire tube (ere it was found that high pressure orthorhombic structure formed phase pure at o C while both phases were seen at o C and o C At o C only the tetragonal phase formed The data can be seen as contour plots in Appendix )V The results thus differ significantly from those obtained using fused silica capillaries where a phase mixture was observed already above o C The difference between the results obtained in sapphire vs fused silica illustrates the influence of the reactor material whether the difference is due to the varying heating rate in the capillary or the surface structure of the reactor is not clear Nonetheless further details regarding the size structure relation could be extracted from the experiments as it was possible to study the transformation from the orthorhombic to the tetragonal phase further At both o C and o C there was a clear shift in the intensity contribution from the orthorhombic to the tetragonal phase The data from the sapphire reactor experiment at o C M are shown in Figure A )n the raw data it is seen how both phases form and how the tetragonal peak at lowest value rises in intensity The weight fraction of the tetragonal phase is plotted in Figure B After the initial crystallization the weight fraction of the tetragonal phases continue to increase as the particles grow indicating a transformation from the orthorhomic to the tetragonal phase (owever the results should again be interpreted with great care because of the large peak overlap Figure 6.14: A Raw data obtained from the synthesis of SnO at o C M in sapphire The time between the frames is seconds B ratio between the intensity from the tetragonal peak and the sum of the tetragonal and orthorhombic peak intensities

140 Chapter Mechanisms of SnO Nanoparticle Formation And Growth 6.5 Conclusions Based on in situ total scattering experiments the formation mechanism for SnO nanoparticles from aqueous solutions of SnCl was established Both SnCl x ( O x and Sn ( O u O( u u form in the solution when dissolving the SnCl salt (owever SnO nanoparticles crystallize uniquely from Sn ions coordinated to ( O O( when heating is initialized Only after prolonged heating at high temperatures o C the SnCl x ( O x complexes starts decomposing to yield additional SnO The decomposition is most likely related to fast thermal movement of the chloride ligands in the tin chloride complex By addition of NaO( to the precursor prior to the hydrothermal treatment the formation of SnCl x ( O x was suppressed and amorphous hydrated tinoxide like nanoparticles formed already at room temperature due to the reactivity of Sn O( When the hydrothermal treatment was commenced these quickly formed nanocrystalline particles For syntheses done from SnCl solutions it was shown how the nanoparticle size and aspect ratio can be controlled by adjusting the precursor concentration the reaction temperature and time The growth was generally found to be limited by diffusion of precursor to the growing nanoparticle but only at temperatures above o C the particles grow after the crystallization equilibrium The unit cell is found to be dependent on the particle size and it expands for small particle sizes probably due to surface effects For very small particles nm the high pressure orthorhombic polymorph of SnO is observed CaCl structure Adjustment of hydrothermal synthesis parameters not only provides control over particle size and morphology but also over the crystal structure The study also illustrates the strength of total scattering for mechanistic studies PDF analysis allows studies of structure of non crystalline species that cannot be obtained using conventional crystallographic techniques This opens up huge uncharted territory for in situ studies of chemical reactions where amorphous and nanostructured compounds take part )n the case of synthesis studies identification of precursor and intermediate phases can be used to investigate formation and growth mechanisms beyond the traditional kinetic models which in many cases are insufficient )f the actual structure of a precursor complex is known the chemistry happening in particle formation and growth can be considered rather than just physical processes

141 Chapter Formation and Growth of Fe O Nanoparticles 7 Formation and Growth of Fe2O3 Nanoparticles 7.1 Introduction The SnO study in the previous chapter illustrated how total scattering can be used to understand the crystallization of a simple oxide material This chapter also concerns the formation of oxides but here ) have investigated the formation of a slightly more complex structure with two different metal sites in the unit cell namely maghemite Fe O The structure is in its bulk form ferrimagnetic but when nanosized the particles are superparamagnetic and have potential applications in various fields including drug delivery and medical imaging Furthermore Fe O has been considered a potential anode materials for Li ion batteries For all these applications size control during particle synthesis is crucial as well as understanding the size structure relationship to optimize the material performance The present study concerns the hydrothermal synthesis of iron oxide nanoparticles from ammonium iron citrate This synthesis has been reported several times in the literature although there has been some confusion about the structure and oxidation state of the product i e if it is magnetite Fe O or maghemite Fe O nanoparticles The bulk structures of the two compounds are very closely related as they both crystallize in the spinel structure which have tetrahedrally Fe t and octahedrally Fe o coordinated metal sites (owever while magnetite Fe O contains both Fe and Fe all iron in Fe O is in the trivalent state )n the present synthesis it has previously been reported that the citrate molecules decompose and yield carbon monoxide during the hydrothermal treatment The CO gas which mixes with the hydrothermal media can then partially reduce Fe to Fe while CO is oxidized to CO This may allow the formation of magnetite from the iron ))) precursor (owever the previous studies of the citrate based synthesis have not included careful structural analyses and the exact structure and oxidation state of the product has therefore not been clear With this study we wish to investigate this in further detail and as will be shown later the product is in fact closer to maghemite nanoparticles Fe O

142 Chapter Formation and Growth of Fe O Nanoparticles Figure 7.1: A Spinel structure space group Fd 3m The red polyhedra show tetrahedral FeO units the yellow show octahedral FeO B Disordered spinel structure P4332. Vacancies are only present on the octahedral iron site shown as green spheres which are thus only partially occupied C Superstructure of the unit cell shown in B space group P )n Fe O charge neutrality in the spinel structure is obtained by the presence of vacancies on the octahedrally coordinated cation sites Ordering of the vacancies has been subject to extensive research and maghemite has over the years been reported in several different space groups As a simple magnetite like spinel in Fd 3m with vacancies randomly distributed on the octahedral site Figure A as a closely related cubic structure in space group P with distinct octahedral sites and vacancies on only one of them Figure B or as a tetragonal structure in space group P with further vacancy ordering Figure C The latter has c/a and is a superstructure of the P cell Other studies of maghemite synthesis have shown that vacancy ordering depends on both the particle size the synthesis method and synthesis duration and precise structural characterization is thus necessary to fully understand the chemistry of the nanoparticles as well as their size structure relation (owever distinguishing between nanoparticles of magnetite and ordered disordered maghemite by simple powder diffraction experiments can be difficult as the structural similarities make the powder diffraction patterns of the structures very similar The main diffraction peaks can in all cases be

143 Chapter Formation and Growth of Fe O Nanoparticles indexed in the simple spinel structure but the lower symmetry of the ordered maghemite unit cell gives rise to additional weak Bragg peaks The calculated patterns for the magnetite structure Fd 3m) and vacancy ordered maghemite P and P are seen in Figure The vacancy ordering in P yields three additional peaks in the low angle region Figure B while the tripled unit cell in P further increases the number of Bragg reflections (owever due to peak broadening from the small crystallite size in nanoparticles the weak peaks can be hard to distinguish even in the best data To fully characterize the formation and structure of hydrothermally synthesized nanoparticles from ammonium iron citrate ) here combine time resolved in situ total scattering X ray studies and in situ PXRD studies with high quality ex situ powder diffraction and total scattering studies as well as Mössbauer analysis The combination of mechanistic studies with thorough structural studies allows us to obtain a novel insight in the size structure relation of maghemite nanoparticles The studies are ongoing and the results presented in the following are therefore only preliminary The project is done in collaboration with master student (enrik Lyder Andersen who has done the sample preparation for ex situ characterization and been the main responsible for the in situ PXRD experiments First the in situ total scattering studies are discussed to elucidate the formation mechanism Subsequently results concerning particle growth from PXRD is briefly discussed and finally the ex situ characterization is introduced A B Intensity (Arb. units) Fd 3m P Intensity (Arb. units) P Figure 7.2: A Calculated PXRD pattern for magnetite Fd m and maghemite P and P for Å B Low angle range for the three structure

144 Chapter Formation and Growth of Fe O Nanoparticles 7.2 Experimental Methods In situ Total Scattering Experiments The precursor for the iron oxide particles was aqueous solutions of ammonium iron citrate Sigma Aldrich reagent grade at various concentrations M For all experiments the pressure was set to bar whereas the temperature was varied between C and C In situ studies were done at beamline )D at the ESRF Grenoble France The reactor capillary was a thin fused silica tube measuring mm in inner diameter and mm in wall thickness The X ray wavelength was Å and a Frelon M CCD camera was used With a sample detector distance of cm the q max value obtained was Å The time resolution was s Analysis of In Situ Total Scattering Data The recorded total scattering data were treated by PDF analysis First the raw D images were integrated in Fit2D and the PDFs were subsequently obtained using PDFgetX3 Scattering from the capillary with deionized water at the appropriate conditions was subtracted from the integrated pattern before the Fourier transform Due to low signal to noise levels at high q values the q range used in the Fourier transform was limited to ÅÅ The PDFs were modelled to extract structural and microstructural parameters using PDFgui. 72 To limit the number of parameters the structure was refined as vacancy disordered in space group Fd 3m The occupancy of the octahedral iron site was kept fixed at to obtain the maghemite Fe O ratio The scale factor the unit cell the sp diameter and the occupancy on the tetrahedral iron site was refined as well as the delta2 value expressing correlated motion )n each data series the position of oxygen and the isotropic thermal parameters were refined in the final frame but kept fixed at this value in the sequential refinements In Situ PXRD Experiments In situ PXRD measurements were conducted during three different beam times at the ) beamline MAX)) MAX lab Lund Sweden The precursor was a M solution of ammonium iron citrate but here the reactor was a sapphire capillary with inner diameter of mm and outer diameter of mm The X ray wavelength was Å and the Oxford Diffraction Titan CCD detector with diameter cm was placed mm from the sample The exact wavelength and detector distance as well as the instrumental broadening in

145 Chapter Formation and Growth of Fe O Nanoparticles the given beam time were determined by calibration with a N)ST LaB sample using Fit2D Analysis of In Situ PXRD Data The time resolved PXRD data were analysed using sequential Rietveld refinement in Fullprof. The background was modelled using linear interpolation between a set of background points Again the refinements of the in situ data were done in the Fd 3m space group The scale factor the unit cell parameters peak profile parameters Y and ) G and background points were refined Whole powder pattern modeling WPPM of selected diffraction patterns were performed using the program PM2K (ere the background pattern was described using a Chebyshev polynomial while the instrumental profile components were determined by a Caglioti function fit to the LaB diffraction pattern The size contribution to the sample peak broadening was implemented as originating from a lognormal size distribution of nanosized coherent scattering domains Ex Situ Characterization The samples for ex situ characterization were synthesized using the flow reactor at Aarhus University The precursor was a M solution of ammonium iron citrate and samples were synthesized in flow at p bar and temperatures varying between o C with reaction times in the second scale The synthesized product can therefore not be directly compared to that observed in the in situ studies as the reaction conditions are somewhat different (igh resolution powder X ray diffraction PXRD data for Rietveld refinement were measured at beamline BL B at Spring Japan using a large Debye Scherrer camera The X ray wavelength was determined to be Å by Rietveld refinement of a CeO standard a Å The samples were loaded into mm glass capillaries and the measurements were done at room temperature X ray total scattering data were measured at )D at the ESRF as described above (ere mm borosilicate capillaries were used The data analysis in Fullprof 59 and PDFgui 73 is discussed below

146 Chapter Formation and Growth of Fe O Nanoparticles 7.3 Results and Discussion: In Situ Studies Formation of Iron Oxide Nanoclusters Figure A B shows the q space data and the corresponding PDFs recorded during the formation of Fe O at o C bar from a M ammonium iron citrate aqueous solution Selected PDFs from the first two minutes of the synthesis are seen in Figure C Before heating i e at t s a large complex with PDF features to ca Å is observed )t has a clear single peak at Å and further features at Å Å and Å as well as less intense peaks between Å and Å By considering the ionic radii of the species present in the solutions is it clear that the sharp peak at Å corresponds to a Fe O bond whereas the peaks between Å and Å arise from different Fe Fe interactions Previous studies have shown that when in solution Fe and citrate form a range of large complexes that can be either mononuclear dinuclear or trinuclear all with octahedral iron coordination Generally the Fe O bond distance in octahedral environments is ca Å and the data thus points towards large iron citrate complexes all with octahedral Fe O coordination The distinct Fe Fe peaks indicate that several different complexes are present As the heating is initiated the precursor molecules decompose to CO CO N( and ( O When performing the experiment this process was observed visually as small gas bubbles appearing in the capillary which then redissolved in the liquid phase )n the q space data a large change in the diffuse scattering signal is seen and in the PDFs this can be correlated to structural changes )mmediately after a decrease in the intensity of all PDFs features possibly due to gas formation new broad Fe O peaks appears around Å and in the Fe Fe region a double peak is now observed with maxima at Å and Å Subsequently the Fe O peaks sharpen and the Fe Fe peak at Å increase rapidly in intensity After ca minutes intense peaks corresponding to the crystalline maghemite structure are clearly seen

147 Chapter Formation and Growth of Fe O Nanoparticles Figure 7.3: A Time resolved q space data obtained in the experiment done at o C M bar The intensity scale goes from blue to red B Time resolved PDFs corresponding to the q space data shown in A C Selected PDFs from the first minutes in the same experiment

148 Chapter Formation and Growth of Fe O Nanoparticles Atoms in pair Interatomic distance Number of pairs in unit cell Fet O Å Feo O Å O O Å Feo Feo Å O O Å O O Å Feo Fet Å Fet O Å Feo O Å Fet Fet Å Table 7.1: Atomic pairs contributing to the low r PDF peaks The atomic pairs contributing to the first PDF peaks in the bulk maghemite structure are listed in Table The primary contribution to the peak at ca Å is the octahedral iron sites pairs termed Fe o Fe o whereas that at Å arises mainly due to Fe o Fe t pairs i e between the octahedral and tetrahedral sites When considering the PDFs from the initially formed iron oxide clusters the double peak observed around Å indicate that two related Fe environments are seen immediately after the decomposition of the citrate (owever the second peak at Å is initially much less intense than in the bulk structure and the first peak at Å is seen at higher r values than the Fe o Fe o peak in crystalline maghemite The first Fe Fe region in the PDFs from the cluster can be described by a maghemite like assembly of iron atoms as shown in Figure A (ere iron octahedrally coordinated to oxygen water form a central cubic rock salt like cluster which is then bonded to tetrahedrally coordinated iron through an oxygen bridge A calculation of the first Fe Fe peaks of the PDF of this structure is shown in Figure B along with the data obtained seconds after initiation of the heating The atomic positions thermal parameters and Fe t occupancy have been optimized to fit the data and are given in Table where they are compared to the values obtained for the maghemite crystal structure observed after minutes The structure in Figure A is very similar to the subunits of maghemite except for the longer Fe o Fe o distances i e expansion of the cubes defined by Fe o and oxygen

149 Chapter Formation and Growth of Fe O Nanoparticles Figure 7.4 A Structure of iron oxide cluster Orange Octahedrally coordinated iron Red Tetrahedrally coordinated iron Blue Oxygen (ydrogen has been omitted B Fe Fe region of the PDF obtained after seconds The red line shows the calculated PDF from a structure based on the cluster in A Cluster, 20 seconds Fe2O3, 10 minutes Feo Feo Å Å Fet Feo Å Å Feo O Å Å Fet/Feo Table 7.2: Parameters obtained for the optimization of the cluster structure and maghemite )n the calculated PDF shown in Figure B which represents the Fe Fe region of the cluster structure after seconds of synthesis the ratio between the tetrahedrally and octahedrally iron atoms in the model is The clusters thus mainly consist of octahedrally coordinated iron just as the final maghemite structure (owever with the present cluster model the relatively low intensity of the Fe o Fe t structure arises mainly because the tetrahedrally coordinated iron atoms are terminal and only coordinated to one octahedral iron cube )f considering the Fe ion in conventional Crystal Field Stabilization Energy CFSE theory octahedral and tetrahedral coordination are equally favorable (owever in acid and neutral aqueous solutions octahedral iron is more commonly observed and if dissolving a simple salt such as FeCl in water FeCl x ( O x forms The formation of complexes with tetrahedrally coordinated iron leading to Fe O from the citrate precursor is thus

150 Chapter Formation and Growth of Fe O Nanoparticles surprising especially because octahedral coordination was seen in the precursor before heating The citrate decomposition process must therefore play a large role in the formation of the cluster )t is important to note that the structure shown in Figure A does not represent a unique description of a cluster giving the PDF observed and several different maghemite like structures are probably present Reverse Monte Carlo modelling of the data and theoretical calculations of clusters energies could possibly reveal the most probable structure but this is currently beyond the scope of the work From Clusters to Nanocrystals: Structural Changes As the reaction proceeds the second Fe o Fe t at ca Å peak intensity rises while the Fe o Fe o peak stays almost constant in intensity This is highlighted in Figure A and shows that an increasing amount of correlations between octahedral and tetrahedral iron appear in the clusters Simultaneously with the intensity increase PDF features at higher r values are observed after only seconds peaks up to Å appear )n the q space data Figure B very weak diffractions peaks are now also visible The data thus indicate that iron oxide clusters similar to that in Figure condensate by the tetrahedrally coordinated iron to form structures with longer range order as illustrated in the first step in Figure B Figure 7.5: A Top )nitial structural changes in the low r region B Bottom Proposed formation mechanism

151 Chapter Formation and Growth of Fe O Nanoparticles The high order maghemite peaks quickly get more intense and after ca seconds satisfactory fits to the high r range of the PDFs can be obtained by refining the maghemite structure as seen in Figure A (owever the r range below Å cannot be fitted well with the crystallographic model showing that the local structure in the nanoclusters is different from the long range order The fit to the frame recorded after minutes is shown in Figure B for quality comparison )n the early stages of crystallization the Fe O peaks at ca Å is much more intense in the data than in the PDF calculated from the crystalline maghemite structure This is most likely due to a large number of terminal Fe O ( O bonds covering the extensive surface of the small nanoparticles Furthermore a very poor fit is seen in the Fe Fe region from Å and the local expansion of the cube formed by the octahedrally coordinated iron which was seen in the cluster giving rise to longer Fe o Fe o bonds remains during the particle crystallization G(r) (Arb. units) G(r) (Arb. units) A: 80 seconds r (Å) B: 3 minutes r (Å) Figure 7.6: Real space Rietveld fits to the PDFs obtained after A seconds at o C and B minutes The black line shows the PDF obtained from the total scattering data the red line the PDF obtained from the model and the blue line the difference between the two

152 Chapter Formation and Growth of Fe O Nanoparticles To determine the local Fe Fe distance the peaks in the Fe Fe region were fitted with two Gaussian functions representing the Fe o Fe o and Fe o Fe t interatomic distances The time and temperature dependent Fe o Fe o distance are plotted in Figure A and as the particles crystallize the bond distances go towards a relaxed final value At o C it takes ca minutes until an equilibrium Fe o Fe o bond length is observed The same effect is seen at o C but as expected the bulk maghemite structure appears much faster )n Figure B the Fe o Fe o distance is plotted as function of the PDFgui refined particle size discussed further below An almost linear correlation between size and Fe Fe bond distance is apparent Furthermore the correlation between size and bond length is independent of the synthesis conditions the curves from o C and o C are almost completely overlapping The changes in bond distance are also directly reflected in the unit cell parameter from PDFGui refinements plotted against time in Figure C This has previously been observed and due to the PDF analysis we are now able to relate this directly to the Fe o Fe o distance in the local structure d(fe Fe) d(fe Fe) final A d(fe Fe) d(fe Fe) final B Time (minutes) sp diameter (nm) a a final (Å) C Time (minutes) Figure 7.7: Change of Feo Feo distance plotted as function of A time and B sp diameter C Changes in unit cell parameter as function of time The black line shows the data points for o C the red line is for o C

153 Chapter Formation and Growth of Fe O Nanoparticles occupancy(fe tet ) A occupancy(fe tet ) B Time (minutes) sp diameter (nm) Figure 7.8: Occupancy of the Fet site plotted as function of A time and B sp diameter The occupancy of the Feo site has been locked to )n bulk vacancy ordered maghemite the occupancy on the tetrahedral site is The black line shows the data points for o C the red line is for o C The change in Fe o Fe o is seen simultaneously with the rise of intensity of the Fe t Fe o peak The data thus indicate that as more tetrahedrally coordinated iron is included in the crystalline structure and coordinated to Fe o the octahedral iron units are squeezed together until the bulk maghemite structure is obtained Figure A shows the refined occupancy of the tetrahedral a site as function of time for two different temperatures )n the bulk maghemite structure this value should be with the occupancy of the octahedral 6d site locked to (owever even after maghemite particles with refinable structures have formed after ca. min for the experiment done at o C a large deficiency of tetrahedral iron is seen Figure B shows the same tetrahedral site occupancy plotted as function of particle size Again independently of the synthesis conditions there is a clear correlation between particle size and Fe t site occupancy This observation could indicate that the occupancy of Fe t and thus the prolonged Fe o Fe o distance is directly related to the surface structure A spherical particle with nm diameter has a volume of nm and a surface area of nm With a unit cell volume of nm and tetrahedral irons per unit cell this corresponds approximately to Fe t in the total particle The area of one unit cell side is nm )f counting one tetrahedral iron pr unit cell side the spherical particle contains very roughly tetrahedrally coordinated surface iron atoms which represents ca. of the total number of Fe t This is close to the deficiency seen in the refined crystal structure The low Fe t occupancy could thus be caused by a large number of terminal Fe t atoms which cannot be described in the structural

154 Chapter Formation and Growth of Fe O Nanoparticles model Although this is all rather speculative the large surface to volume ratio in any case makes is very likely that the size structure relationship is related to surface defects Particle Growth The growth curves obtained from the sequential PDF refinements are seen in Figure A Clearly the final crystallite size is dependent on temperature and can be varied from to nm by adjusting the temperature from o C to o C Furthermore the particle size is highly dependent of precursor concentration and the higher the concentration the larger the particles (owever although the final crystallite size is dependent on the ammonium iron citrate concentration the data show that the initial growth behaviour is mainly temperature dependent as seen from the similarity of the three growth curves obtained at o C with different precursor concentrations This is clear in the time dependent growth rates i e the differentiated growth curves which are plotted for the o C and o C experiments in Figure B The growth rates for the three low temperature experiments behave very similarly the rate initially increases reaches a maximum after ca. minutes and subsequently decreases This observation can be directly related to the condensation of the nanoclusters as the maximum growth rate is seen at the exact same time as the appearance of well defined Bragg peaks in the q space data and of intense long range order A sp diameter (nm) o C, 2M 320 o C, 4M 320 o C, 1M 270 o C, 2M Time (min) 320 o C, 2M Time (min) Figure 7.9: A Refined sp diameter plotted as function of time for different temperature and precursors concentrations B Growth rates for the same experiments using the same colour codes Before differentiation the growth curves were smoothed by adjacent averaging with a window of points B Growth rate (nm/minute)

155 Chapter Formation and Growth of Fe O Nanoparticles features in the PDFs The fastest growth thus happens during the assembly of the clusters and the concentration dependence of the final particle size may be explained by the larger amount of clusters available for condensation At o C the growth initially happens much faster and after less than two minutes the sp diameter remains constant A maximum in the growth rate is seen after seconds which can again be directly related to the formation mechanism Results from PXRD Experiments: Rietveld and WPPM The synthesis was also investigated with PXRD at i MAX lab for further studies of the temperature dependency of the particle growth The experiments and data analysis have been done in collaboration with master student (enrik Lyder Andersen and only the most important results are given The crystallite sizes obtained by Rietveld analysis Scherrer size and WPPM analysis Volume averaged size from log normal distributions are shown in Figure at o C o C and o C As WPPM analysis was done only for certain data sets selected points along the growth curves are shown While the trends in size and growth resemble those obtained from PDF analysis the absolute sizes seen from PXRD analysis are somewhat larger This can have several explanations Firstly the experiments are done at different beamlines and during different beamtimes Although the instrument resolution is characterized by analysis of N)ST LaB this might not be completely accurate Secondly the PXRD experiments were done in sapphire capillaries while the total scattering studies were performed in fused silica tubes As was seen in the SnO study this can influence the growth kinetics due to both heating rates and capillary surface structure Crystallite size (nm) C Rietveld 370 C WPPM 320 C Rietveld 320 C WPPM Time (min) Figure 7.10: Crystallite sizes obtained from Rietveld and WPPM analysis

156 Chapter Formation and Growth of Fe O Nanoparticles By means of WPPM analysis it was possible to extract size distributions of the crystalline nanoparticles from the PXRD data Selected results are seen in Figure where the refined size distributions are plotted for various stages in the synthesis at o C A and o C B The refinements assume a log normal size distribution and yield a mean size and variance which can be used to calculate the distribution curves The data convincingly show that with increased synthesis time the size distribution rapidly broadens and the average size shifts towards higher values )nitially the size distribution is very narrow )n order to obtain small monodisperse particles with well defined magnetic properties it is therefore crucial to limit the reaction time and quench the synthesis before ripening effects occur By varying the temperature rather than the reaction time a high degree of size control can be obtained Comparable results were obtained from in situ SAXS WAXS studies by Bremholm et al who studied the same synthesis in the Aarhus pulse flow reactor (ere particle size distributions were determined from SAXS data This allowed refinements of the size distribution of the semi amorphous clusters seen in the PDF data before crystallization The SAXS data showed that during the initial crystallization phase i e cluster condensation the size distribution stayed very narrow and size distribution broadening was not observed until highly crystalline particles had formed Freq. (a.u.) A: T=320 C 2min 5min 10min 25min Freq. (a.u.) B: T=370 C 0.5min 1min 2min 5min 10min 25min Size (nm) Size (nm) Figure 7.11: Crystallite size distributions obtained from WPPM analysis at o C A and o C B

157 Chapter Formation and Growth of Fe O Nanoparticles 7.4 Results and Discussion: Ex Situ Studies )n Jørgensen et al studied the decomposition of iron nitrate in lauric acid They saw that when Fe O first formed from an intermediate of almost amorphous FeOO( the disordered Fd 3m structure initially appeared After prolonged heating however the superlattice peaks corresponding to the P structure emerged due to vacancy ordering )n our in situ data both total scattering and PXRD we do not observe superstructure peaks at any point and acceptable fits can be obtained when refining the structure in Fd 3m This can have several causes First the previous assumptions regarding the reduction during the synthesis could be correct and the product might in fact be magnetite Second the vacancies could be disordered as observed by Jørgensen et al in the beginning of their synthesis This may be due to both the small particle size and the elevated temperature as reported by Bastow et al. Third the vacancies might be ordered but the size of the coherently diffracting domains is too small to allow the P peaks to be observed As the in situ data did not allow for a full refinement of the structure ex situ characterization of particles synthesized in our home laboratory was carried out (owever as described in section these samples were produced in the flow reactor at Aarhus University The product can thus not be directly compared to that obtained in the in situ reactor but nevertheless the study gives some insight in the reaction mechanisms for the citrate synthesis The PXRD data obtained at Spring for samples synthesized in the flow apparatus at o C o C and o C are plotted in Figure along with patterns from the refined structural models Clearly additional peaks compared to the simple spinel structure are observed at low angles as emphasized in the insert The peaks observed correspond to those seen in the P structure Figure while the additional weak superstructure peaks from P are not readily observed To limit the number of parameters in the refinement while still allowing a tetragonal unit cell the data were therefore modelled in space group P with a smaller tetragonal cell a=b c as previously done by Jørgensen and Greaves This unit cell corresponds to an average subunit of the large superstructure and while the P structure requires positional parameters the P structure is described with only The main results from the refinements are presented in Table and further details can be found in Appendix V Acceptable fits are obtained for all three samples Rather large discrepancies are observed in the difference curve for the sample synthesized at o C where extensive peak broadening due to small particles size makes the structural refinement difficult

158 Chapter Formation and Growth of Fe O Nanoparticles A Intensity (Arb. units) (degrees) B 2 (degrees) Intensity (Arb. units) (degrees) C 2 (degrees) Intensity (Arb. units) (degrees) (degrees) Figure 7.12: Experimental PXRD data black calculated model red difference blue and Bragg positions green for the three samples synthesized at o C A o C B and o C C The inserts show the low angle region and demonstrates the presence of peaks arising from vacancy ordering

159 Chapter Formation and Growth of Fe O Nanoparticles Sample 340 o C 390 o C 440 o C RBragg Crystallite size (nm) a (Å) c (Å) occupancy, Fe 4a site Fe/O ratio Mössbauer Magnetite fraction Table 7.3: Main results from Rietveld refinements with full occupancy on all other sites than Fe a Further details are given in appendix V The refinements did not converge when refining the atomic positions and the positional parameters were therefore kept fixed at the values reported by Jørgensen et al. 253 Furthermore the Debye Waller factors were constrained to one value for all Fe sites while that of O was kept fixed For all samples the occupancy of all each individual iron site was initially refined (owever there was a clear tendency towards full occupancy of all sites but the octahedral Fe4 4a position This is the same Fe vacancy site observed by i a Braun Greaves 240 and Jørgensen et al and confirms the vacancy ordering )n the final refinements the fractional occupancies of all other sites were thus kept fixed at )f considering the total stoichiometry of the three samples the refined models has Fe O ratios of For magnetite this ratio is while it is for vacancy ordered maghemite The PXRD data thus indicate that the oxidation state in the samples is somewhere between those of magnetite and maghemite This is confirmed by preliminary Mössbauer analysis of the samples by Dr (araldur P Gunlauggsen Department of Physics Aarhus University which demonstrates the presence of both magnetite and maghemite The Mössbauer analysis shown in Appendix V indicates that the three samples contained and magnetite for the samples synthesized at o C o C and o C respectively The crystallite domain sizes were determined by Scherrer analysis giving a volume weighted size of nm nm and nm for particles synthesized at o C o C and o C respectively For nano sized samples total scattering experiments may yield further structural information than standard Rietveld refinements in q space PDFs obtained from X ray total scattering data measured at )D ESRF for the two samples synthesized at T o C and T o C are shown in Figure along with the refined model The main

160 Chapter Formation and Growth of Fe O Nanoparticles results are presented in Table while further details are given in Appendix V Unfortunately total scattering data were not obtained for the sample synthesized at o C The PDF refinements yielded convergence when refining all atomic positions for oxygen and iron The Debye Waller factors for both oxygen and iron could furthermore be refined Again the occupancies of all iron atoms were initially allowed to vary but only that of Fe4 refined to partial occupancy As seen in Table the occupancies obtained from the PDF refinements are associated with quite large uncertainties (owever from the PDF refinements it seems as the synthesis temperature does in fact affect the vacancy concentration Where the occupancy obtained for the sample synthesized at o C is comparable to that obtained from the q space refinements ca the occupancy of Fe4 for T o C is much lower in the PDF fitting ca giving a Fe O ratio of indicating pure Fe i e maghemite (owever for the high temperature sample the Fe O is again thus indicating a mixture between maghemite and magnetite as confirmed by Mössbauer spectroscopy and PXRD G(r) (Arb. units) G(r) (Arb. units) A: 340 o C r (Å) B: 440 o C r (Å) Figure 7.13: Experimental PDFs black PDFs calculated from fitted models red and difference curves blue for maghemite synthesized at o C and o C

161 Chapter Formation and Growth of Fe O Nanoparticles Sample 340 o C 440 o C RBragg Size (nm) a (Å) c (Å) occupancy, Fe 4a site Fe/O ratio Table 7.4: Results from ex situ real space Rietveld refinements The crystallite sizes obtained from the PDF modelling are smaller than those obtained from q space refinements This is most likely due to the poor q resolution in the PDF experiment and the Scherrer sizes obtained from Rietveld refinement thus seem more reliable This preliminary ex situ characterization indicates that the citrate maghemite synthesis does result in vacancy ordering in the final product although the P or P Bragg peaks were not observed in the in situ data The ex situ data further suggest that when the synthesis is performed at high temperatures above the critical point of water the citrate synthesis leads to a mixed phase between magnetite and maghemite Whether it is a phase system or a solid state like compound such as Fe O x Fe O x is not yet clear The PXRD points to the latter as no peak splitting is apparent which would be expected due to differences in unit cell sizes for the two phases Possibly the temperature dependency of the average iron oxidation state is due to gas solubility in the liquid phase during the hydrothermal synthesis CO gas is highly miscible with supercritical water and the possibility for reduction of Fe is therefore larger at elevated temperatures (owever before any final conclusions can be made further ex situ analyses are to be done Apart from the X ray total scattering data neutron total scattering data have also been measured at NOMAD at SNS Oak Ridge National Laboratory and combined with the X ray data refinement of these may give a better understanding of the vacancy ordering and oxidation of the particles Furthermore detailed analysis of the Mössbauer data is done and further temperature dependent measurements will be used for characterization of the superparamagnetism of the particles This will complement measurements of the magnetic properties of the samples

162 Chapter Formation and Growth of Fe O Nanoparticles 7.5 Conclusions and Outlook From combined in situ and ex situ studies novel insight in the formation of magnetic iron oxide nanoparticles have been elucidated The in situ total scattering data showed that aqueous solutions of ammonium iron citrate contains large Fe citrate clusters most probably all with octahedral coordination When heating is initiated and the citrate decomposes iron oxide clusters containing both octahedrally and tetrahedrally coordinated iron form As the reaction proceeds these clusters condensate and structures with longer range order resembling that of magnetite and maghemite appear After minutes at o C and less than minute at o C crystalline particles have formed During the cluster condensation and crystallization the Fe o Fe o bond distance decreases due to the formation of the denser crystalline structure This change in local order explains the unit cell particle size dependency which has previously been observed from PXRD experiments The occupancy of the tetragonal site in the crystalline structure increases as the particles crystallizes especially during the very first steps of the particle formation This indicates that the cluster condensation happens along the tetrahedral sites on the surface of the clusters particles The crystallite size is dependent of reaction time and temperature The primary growth happens during the cluster condensation and the maximum growth rate is seen when crystalline particles have just formed The growth rate maximum is almost independent of the precursor concentration while the final equilibrium crystallite size is dictated by the concentration Whole Powder Pattern Modelling of in situ PXRD data showed that the size distribution broadens rapidly as the reaction proceeds Small monodisperse samples can thus be obtained from short syntheses at high temperatures This is important as the magnetic properties are highly size dependent The in situ data did not reveal any vacancy ordering in the particles and from these it was not possible to distinguish between Fe O disordered Fe O or vacancy ordered Fe O Therefore ex situ characterization using PXRD total scattering and Mössbauer analyses is currently carried out The high quality PXRD data from the hydrothermally synthesized samples clearly show additional Bragg peaks arising from vacancy ordering in space group P Superstructure peaks from P were not observed possibly due to the small size of the particles Detailed structural refinements of the ex situ PXRD data were not possible due to peak broadening To complement the PXRD analyses total scattering analyses were therefore carried out The preliminary results indicate that for the sample synthesized at low

163 Chapter Formation and Growth of Fe O Nanoparticles temperatures the product is Fe O with vacancy ordering in the P space group (owever for the sample synthesized at o C the Fe O ratio was between that of maghemite and magnetite indicating the formation of a Fe O x Fe O x solid solution The presence of a minor magnetite component ca was confirmed by Mössbauer spectroscopy This indicates that only at elevated temperatures above the critical point of water partial reduction by CO can take place Further ex situ analyses are to be done to confirm the preliminary conclusions )f considering the complex formation mechanism elucidated from the in situ total scattering data it is highly probable that the vacancy ordering happens after the initial crystallization from the iron oxide clusters as also seen by Jørgensen et al in a different synthesis Most probably the ordering is dependent on crystallite size especially for the formation of the P superstructure due to the large unit cell (owever it is important to note that even though the ex situ and in situ studies are complementary the samples cannot be directly compared )t is i e not clear at which temperatures the partial reduction to Fe happens or if the vacancy ordering actually takes place in the capillary synthesis As the product from the in situ reactor is difficult to recover without mixing it with un and partial reacted precursor from the reactor capillary the product cannot easily be characterized by e g Mössbauer analysis The present chapter again showed the strength of PDF analysis for studies of crystallization as well as ex situ analysis (owever although new information about the formation mechanisms have been proposed from the in situ data further modelling is needed to fully understand the cluster formation Currently only the first Fe Fe region has been considered in the structural description of the amorphous clusters and valuable information has been left out Further modelling where the large cluster structure is refined might reveal novel knowledge

164 Chapter Concluding Remarks 8 Concluding Remarks The past four chapters have illustrated how detailed in situ X ray scattering studies of hydrothermal synthesis combined with thorough ex situ characterization can be used to understand some of the fundamental processes taking place during the formation and growth of advanced functional materials By combining different scattering techniques several length scales in the sample can be probed and a comprehensive picture of the mechanisms dictating the synthesis process can be obtained Specifically the studies presented in the dissertation have provided detailed knowledge regarding the syntheses of four important functional materials LiCoO LiFe x Mn x PO SnO and Fe O Although the conditions used in the in situ capillary reactor cannot be directly transferred to large scale synthesis mapping of the general parameter space can help optimize the conditions used in e g a flow reactor Furthermore from a more general perspective the investigations of the individual materials have provided us with a broader understanding of the complexity of hydrothermal synthesis The novel use of X ray total scattering for in situ studies allowed us to illuminate how nanoparticles crystallize and grow from molecular clusters or ionic complexes and the studies underpin how challenging it is to advance a general mechanism for nanoparticle formation and growth To fully describe the crystallite formation process it is necessary to include considerations of both the chemical reactions between the clusters and growing particles as well as the geometric constraints of the cluster structures during assembly The investigations of Fe O revealed that nanocrystals form from rather large clusters while smaller ionic complexes were seen in the crystallization of SnO Further on going studies of CeO YSZ CuO WO Fe O ZnO and TiO indicate that the occurrence of simple mononuclear ionic complexes in SnCl is more the exception than the rule and often concentrated aqueous solutions of inorganic salts are not as simple as one would first assume Only by further studies of these crystallite precursors we can start to obtain a general understanding of fundamental inorganic reaction mechanisms The projects in this dissertation represent only the beginning and further studies are now taken on in the )versen group The large complexes and clusters challenge our modelling abilities of the time resolved data First of all we have to think beyond crystallography Relatively few peaks in the PDF arise from dozens of atoms which are no longer

165 Chapter Concluding Remarks constrained by symmetry )n the modelling process the atomic parameters must therefore be restrained by other means to avoid structural models with unphysical and nonchemical atomic distances and coordination numbers Furthermore finding a realistic start model for the structural studies is often a challenging process when considering the many atoms in the clusters The structure of the final crystalline phase as well as the precursor salt can serve as a point of departure for determining the complex cluster structure (owever extensive alterations of these models may be needed and most often the PDFs can be described by more than one unique structure New approaches to data modelling are thus needed to take full advantage of the information in our in situ total scattering data Theoretical calculations of cluster formation energies may help determine the most probable cluster complex structures and modelling using Reverse Monte Carlo methods is a natural next step in the analysis of crystallization data This method has previously been used to determine the structure of highly disordered compounds Nonetheless even with simple modelling or even model free analysis in situ total scattering opens up for a whole new realm of studies )n the case of material synthesis we can now study local atomic structural changes before crystallization as well as the long range structural evolution after particle formation using one single technique This strength of total scattering and PDF analysis applies to many other fields and with the increasing number of dedicated RA PDF beamlines and the development of new software for PDF analysis in situ total scattering studies of various chemical reactions are becoming more and more accessible for the broad scientific community Recently time resolved total scattering studies of solid state gas reactions have been done to elucidate the structural changes of catalysts under operating conditions as well as in operando studies of Li ion batteries and fuel cells Other time resolved studies now appear in the literature and most probably we will see many more papers of this kind in the near future The development of new characterizations techniques should be seen as a chance to take a step back in complexity and investigate apparently simple problems in a new light For example the reported syntheses of SnO or Fe O are by no means new and both materials are produced commercially Still by studying known structures or processes and obtaining novel information about the fundamental mechanisms dictating the synthesis

166 Chapter Concluding Remarks product we will be better prepared to tackle new problems e g synthesis of novel highly complex nanostructures While total scattering is clearly useful and allows processes to be studied in a new light it is important not to forget the possibilities with other scattering techniques such as powder diffraction small angle scattering as well as spectroscopy methods such as EXAFS Each technique has its own strengths and the appropriate method depends solely on the information sought for in the specific experiment As illustrated in the studies of LiFe x Mn x PO SnO and Fe O powder diffraction and total scattering are highly complementary due to the difference in q/r resolution and most studies can benefit from both techniques The studies of LiFe x Mn x PO and Fe O further illustrate the importance of combining mechanistic in situ studies with detailed ex situ structural studies Time resolved studies are always a compromise between data quality and time resolution and the in situ data are thus not suited for exhaustive investigations of e g defects or superstructure The dissertation has presented only the key projects conducted during my PhD Apart from the studies included in the main chapters ) have done numerous exploratory studies of the hydrothermal synthesis of other materials i a NaCoO Mn O Zn SnO Co SnO as well as being involved in and co supervised other student s projects on e g YAG YSZ CeO BaTiO Li TiO ZnO etc Together the group has thus obtained knowledge about a broad range of materials and the in situ studies of hydrothermal reactions are continued in the group Several new initiatives are planned apart from continuing the fundamental total scattering studies in situ PXRD studies of new synthesis techniques such as the microwave hydrothermal method and spark plasma sintering are currently developed Generally ) believe that doing thorough structural characterizations is crucial in the development of new and improved energy materials Running a quick PXRD scan after a synthesis to determine the product phase only reveals a fraction of the information needed to advance materials chemistry As functional materials become more and more complex e g nanostructured in depth characterization of the structure is only more important and new techniques needs to be implemented in order to fully understand the relation between synthesis structure and properties (opefully our research contributes to this understanding and helps in the development of new improved materials and greener synthesis methods

167 Chapter Concluding Remarks Figure 8.1 Beam teams at )D B APS A and C P PETRA))) B and E i MAX lab D and F and NPDF LANSCE G long neutron experiments

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176

177 Appendices

178 Appendix ) Appendix I: Experimental considerations The majority of our in situ PXRD experiments are done at at i at MAX lab in Lund Sweden (ere data suitable for Rietveld refinement are obtained with exposure times between seconds depending on the material studied The i beamline sits on a wiggler providing X rays in the wavelength range Å For our experiments the energy is tuned to ca Å to give reasonable transmission through the capillary as discussed above The beam is monochromatized with a single Si crystal This provides relatively good flux on the sample but reduces the instrument resolution compared to a double crystal monochromator The focused i beam is mm but most often the beam is slit down to be mm The current detector at i is a D Titan CCD detector with a diameter of mm and usually this is placed ca. cm from the sample depending on the information sought for in the experiment A short detector distance gives a large q range but only on the expense of q resolution This limits the crystallite size range that can reliably be studied due to larger instrument broadening and from our MAX lab data care should generally be taken when studying crystals larger than nm as this is beyond the resolution limit The total scattering data presented in the dissertation have been obtained at )D B at APS PO at PETRA))) and at )D at the ESRF Common for these beamlines are that they provide very high flux at X ray energies at and above kev which is needed for RA PDF studies The specific energies and beamline setups during the various beamtimes are discussed the respective chapters The experiments are done as RA PDF in much the same way as the PXRD studies described above Thus a large plate D detector is needed At APS and PETRA ))) we have used Perkin Elmer amorphous Silicon detectors with large active areas of cm At )D at the ESRF the detector was a smaller FreLoN M CCD camera measuring cm To obtain an appropriate q range a higher X ray energy was used and the detector was off centred as shown in Figure along with a detector image from PETRA ))) As only partial Debye Scherrer rings are obtained the integrated intensity is lower in an off centred image and for time resolved studies centring of the detector is therefore usually preferred (owever with the high flux at )D this was not a problem

179 Appendix ) Figure S1 Left Detector image from PO PETRA ))) using cm Perkin Elmer detector Right Detector image from )D ESRF cm FreLoN M camera To minimize additional background in the data it is important to avoid air scattering from the direct beam both before and after the capillary A collimator with a small beam opening is therefore installed before the capillary while a beamstop is placed directly after sample An additional beamstop is usually placed closer to the detector to ensure that the direct beam does not damage the detector The importance of collimation and front beamstop is illustrated in Figure S showing LaB data recorded in a mm glass capillary at kev at different settings The low q background is reduced by more than with elimination of the majority of air scattering Intensity (Arb. units) Intensity (Arb. units) q (nm 1 ) Collimator and front beamstop No collimator, front beamstop Collimator, no front beamstop No front beamstop, no collmator q (nm 1 ) Figure S Effect of front beamstop and collimator on LaB6 diffraction pattern packed in 0.5 mm glass. The data are recorded at P02, PETRA III at kev, using a Perkin Elmer amorphous silicon detector.

180 Appendix )) Appendix II: LiCoO2 Representative refinements from the LiCoO 2 study 1: Experiment done at T=160 o C and Li/Co=1.3. The frame was recorded after ca. 1 min. Only CoOOH is present. Number of Bragg peaks Number of data points Number of background and profile parameters Total number of parameters Rwp RF a c A A A

181 Appendix )) 2: Experiment done at T=160 o C and Li/Co=1.3. The frame was recorded after ca. 34 minutes. Both LiCoO2 and CoOOH are present. The LiCoO2 peak shape and unit cell parameters were locked, while all CoOOH parameters were refined. Number of LiCoO Bragg peaks Number of CoOO( Bragg peaks Number of data points Number of background and profile parameters Total number of parameters Rwp RF CoOO( RF LiCoO Weight percent CoOO( LiCoO a CoOO( c CoOO( A CoOO( A CoOO( A CoOO(

182 Appendix )) 3: Experiment done at T=160 o C and Li/Co=1.3. The frame was recorded after ca. 80 minutes. Both LiCoO2 and CoOOH are present. The CoOOH peak shape and unit cell parameters were locked, while all LiCoO2 parameters were refined. Number of LiCoO Bragg peaks Number of CoOO( Bragg peaks Number of data points Number of background and profile parameters Total number of parameters Rwp RF CoOO( RF LiCoO Weight percent CoOO( LiCoO a CoOO( c CoOO( A CoOO( A CoOO( A CoOO(

183 Appendix )) 4: Experiment done at T=160 o C and Li/Co=1.3. The frame was recorded after ca. 1h and 40min. Only LiCoO2 is present. Number of Bragg peaks Number of data points Number of background and profile parameters Total number of parameters Rwp RF A C A A A

184 Appendix )) 5: Experiment done at T=250 o C and Li/Co=10. The frame was recorded after ca. 30 min. Only LiCoO2 is present. The data only goes to 2theta=32 degrees due to a different detector distance. Number of Bragg peaks Number of data points Number of background and profile parameters Total number of parameters Rwp RF a c A A A

185 Appendix ))) Appendix III: LiFePO4 Representative Rietveld refinements from the in situ study The observed intensities are plotted together with the intensities calculated from the model The lower line shows the difference between the two 1: Frame obtained during the experiment synthesizing LiFePO4 from precursor A at T=170 o C, after 5 minutes of reaction time. Bragg peaks Data points Background points Total Refined parameters RBragg a b c Fe on Li site U Boverall Å Å Å Å 2: Frame obtained during the experiment synthesizing LiFePO4 from precursor A at T=170 o C, after 5 minutes of reaction time. Bragg peaks Data points Background points Total refined parameters RBragg a b c Fe on Li site U Boverall Å Å Å Å

186 Appendix ))) Rietveld parameters obtained in the ex situ study LiFePO4, 170 o C, 40 min Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Fe Fe site Li Fe site P O O O a, b, c (Å) R factors Bank Bank Bank Bank X ray U,V,W,X,Y LiFePO4, 170 o C, 2 h Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Fe Fe site Li Fe site P O O O a, b, c (Å) a b c R factors Bank Bank Bank Bank X ray U,V,W,X,Y LiFePO4, 170 o C, 7 h Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Fe Fe site Li Fe site P O

187 Appendix ))) O O a, b, c (Å) a c R factors: Bank Bank Bank Bank X ray U,V,W,X,Y LiFe0.75Mn0.25PO4, 170 o C, 40 min, model Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: Bank Bank Bank Bank X ray U,V,W,X,Y LiFe0.75Mn0.25PO4, 170 o C, 7 h, model 1: Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: Bank Bank Bank Bank Bank U,V,W,X,Y

188 Appendix ))) LiFe0.75Mn0.25PO4, 170 o C, 40 min, model 2: Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: X ray profile LiFe0.75Mn0.25PO4, 170 o C, 7 h, model 2 Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: Bank Bank Bank Bank X ray X ray profile LiFe0.50Mn0.50PO4, 170 o C, 40 min, model 1: Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site

189 Appendix ))) P O O O Cell R factors: Bank Bank Bank Bank X ray X ray profile: LiFe0.50Mn0.50PO4, 170 o C, 7 h, model 1: Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: X ray profile LiFe0.50Mn0.50PO4, 170 o C, 40 min, model 2: Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: Profile

190 Appendix ))) LiFe0.50Mn0.50PO4, 170 o C, 7 h, model 2 Type x y z Ui/Ue Occupancy 100/Å 2 Li Li site Li Li site Fe Li site Mn Li site Fe Fe site Mn Fe site Li Fe site P O O O Cell R factors: Bank Bank Bank Bank X ray X ray profile

191 Appendix ))) Calculation of strain S Microscopic strain in the crystal results in broadening of the peak profile with a tan dependency which in the Thompson Cox (astings formulation of the Pseudo Voigt function used in GSAS is described by the U and Y parameters For the present data the U parameter describes the largest contribution to the peak width and using the instrument corrected X ray profile parameters the microstrain S has been calculated S = (8 ln(2)( U Ui) *100% U i has been found from refinement of a CeO standard sample Crystallinity calculations The crystallinty has been calculated as m% Crystalline_LiFePO m 4 Crystallinity= m% m diamond diamond LiFePO4 100% The values found are given below The uncertainties on the crystallinty has been estimated to Sample LiFePO min LiFePO hours LiFePO hours Refined Refined Mass Mass C mass mass LiFePO LiFePO C Crystalllinty mg mg mg mg mg mg

192 Appendix )V Appendix IV: SnO2 Fits to selected G(r) in PDFgui G(r) (Arb. units) 0 A: 2M, 200 o C, 30 minutes G(r) observed G(r) calculated Difference B: 2M, 250 o C, 6 minutes G(r) (Arb. units) G(r) (Arb. units) 1 0 C: 2M, 250 o C, 30 minutes D: 2M, 350 o C, 6 minutes G(r) (Arb. units) E: 2M, 350 o C, 30 minutes G(r) (Arb. units) r( Å )

193 Appendix )V 2M, 200 o C, 30 minutes (last frame) 2M, 250 o C, 6 minutes Data range Å Data range Å Number of data points Number of data points All Nyquist All Nyquist Number of refined Number of refined parameters parameters Qdamp Qdamp Rw Rw scalefactor scalefactor a Å a Å c Å c Å xo xo uo Å uo Å usn Å usn Å sp diameter Å sp diameter Å 2M, 250, 30 minutes (last frame) 2M, 250, 30 minutes (last frame) Data range Å Data range Å Number of data points Number of data points All Nyquist All Nyquist Number of refined Number of refined parameters parameters Qdamp Qdamp Rw Rw scalefactor scalefactor a Å a Å c Å c Å xo xo uo Å sp diameter Å usn sp diameter Å Å

194 Appendix )V Modeling of the PDFs in SrFit G(r) (Arb. units) A: 2M SnCl 4, room temperature G(r) (Arb. units) B: 2M, 250 o C, 7 seconds G(r) (Arb. units) C: 2M, 250 o C, 14 seconds B: 2M, 250 o C, 30 minutes G(r) (Arb. units) r ( Å

195 Appendix )V A: 2M SnCl4solution at room temperature Data range Number of points Number of refined parameters Å Rw Scale factor of complex Sn Cl in complex Sn O in complex Ul of ligands in complex Ut of ligands in complex Å Å Å Å B: 2M, 250 o C, 7 seconds after start Data range Number of points Number of refined parameters Å Rw Scale factor of complex Scalefactor of SnO Sn Cl in complex Sn O in complex ul of ligands in complex ut of ligands in complex a SnO c SnO u Sn u O xo Å Å Å Å Å Å Å Å Å B: 2M, 250 o C, 30 minutes after start Data range Number of points Number of refined parameters Å Rw Scale factor of complex Scalefactor of SnO Sn Cl in complex Sn O in complex ul of ligands in complex ut of ligands in complex a SnO c SnO u Sn u O xo Å Å Å Å Å Å Å Å Å

196 Appendix )V Contour plots: SnO 2 PXRD experiments at MAX lab 160 o C, fused silica, 1M (left) and 2M (right): 180 o C, fused silica, 1M (left) and 2M (right): 200 o C, fused silica, 1M (left) and 2M (right):

197 Appendix )V 250 o C, fused silica, 1M (left) and 2M (right): 200 o C, sapphire, 1M 250 o C, sapphire, 1M

198 Appendix )V 300 o C, sapphire, 1M

199 Appendix V Appendix V: Fe2O3 Results from ex situ Rietveld refinements of Spring 8 X ray data. The data were refined in spacegroup P using Atomic coordinates from Jørgensen et al. Sample 1: Synthesis temperature 340 o C theta range Number of Bragg peaks Number of data points Number of refined parameters Number of refined background points o RBragg RF RP Rwp a Å c Å occ Fe BFe BO Å Å fixed )G O fixed Y Sample 2: Synthesis temperature 390 o C theta range Number of Bragg peaks Number of data points Number of refined parameters Number of refined background points o RBragg RF RP Rwp

200 Appendix V a Å c Å occ Fe BFe BO Y Å Å fixed )G Sample 3: Synthesis temperature 440 o C theta range Number of Bragg peaks Number of data points Number of refined parameters Number of refined background points o RBragg RF RP Rwp a Å c Å occ Fe BFe BO Y Å Å fixed )G

201 Appendix V Results from ex situ Real space Rietveld refinements of ESRF X ray data. The data were refined in spacegroup P43212 using Atomic coordinates from Jørgensen et al. Sample 1: Synthesis temperature 340 o C qmax rrange Number of refined parameters Å Å Rw a c sp diameter Å Å nm Refined atomic parameters: Fe b Fe a Fe b Fe a O b O b O b O b x y z u occ

202 Appendix V Sample 3: Synthesis temperature 440 o C qmax rrange Number of refined parameters Å Å Rw a c sp diameter A Refined atomic parameters Fe b Fe a Fe b Fe a O b O b O b O b x y z u occ

203 Appendix V Results from Mössbauer analysis MD(F Magnetic (yperfine Field Distribution Maghemite D Broadened quadropole doublet superparamagnetic maghemite Sample 1: Synthesis temperature 340 o C Transmission Velocity (mm/s) Bpeak T Bav T mm s M(FD Fe ))) Magnetite A Magnetite B EQ or mm s mm s mm s Area Sample 2: Synthesis temperature 390 o C 1.01 Transmission Velocity (mm/s)

204 Appendix V Bpeak T Bav T M(FD Fe ))) D Magnetite A Magnetite B mm s EQ or mm s mm s mm s Area Sample 3: Synthesis temperature 440 o C 1.01 Transmission Velocity (mm/s) Bpeak T Bav T M(FD Fe ))) D Magnetite A Magnetite B mm s EQ or mm s mm s mm s Area

205 Appendix V) Appendix VI: Published papers The following pages contain the papers given in List of publications page xi The papers are appended chronologically with the newest publication appearing first

206 RSC Advances PAPER View Article Online View Journal Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. Cite this: DOI: /c3ra41854e Received 17th April 2013, Accepted 20th June 2013 DOI: /c3ra41854e Introduction In situ synchrotron powder X-ray diffraction study of formation and growth of yttrium and ytterbium aluminum garnet nanoparticles in sub- and supercritical water3 Peter Nørby, Kirsten M. Ø. Jensen, Nina Lock, Mogens Christensen and Bo B. Iversen* The formation and growth of yttrium and ytterbium aluminium garnet (Y 32x Yb x Al 5 O 12, x = ) nanoparticles in sub- and supercritical water have been followed by in situ synchrotron powder X-ray diffraction. At a pressure of 256 bar the formation of crystalline garnet nanoparticles occurs within seconds when the temperature is above 300 uc, and it takes place through an intermediate phase of (Y/ Yb) 4 O(NO 3 )(OH) 9. Below the critical point of water (T c = 374 uc, P c = 221 bar), AlOOH crystallizes simultaneously with the garnet phase, and it is observed that both very rapid heating of the reactants and supercritical conditions are necessary to achieve phase pure YAG. Thus, under supercritical conditions YAG forms directly within the time resolution of the experiments (5 s). The particle growth is dependent on the Yb content, the Yb source and the synthesis temperature, and the crystallite size decreases from 35 nm for pure Y 3 Al 5 O 12 to 20 nm for Y 2.4 Yb 0.6 Al 5 O 12. After initial particle formation, growth is much slower in subcritical water than in supercritical water. Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark. bo@chem.au.dk 3 Electronic supplementary information (ESI) available. See DOI: / c3ra41854e Yttrium aluminium garnet (Y 3 Al 5 O 12, YAG) has widespread applications e.g. as a thermal barrier coating, a corrosion resistant material, or as a solid-state laser material. 1 For the latter, trivalent rare-earth doped YAG has traditionally been used in single crystalline form, but more recently polycrystalline ceramics have been applied. 1,2 Generally, polycrystalline materials are easier to synthesize on a large scale, and homogeneous doping as well as high doping concentrations can be obtained, making it possible to produce complex laser materials. 2,3 Ytterbium doped YAG ceramics have promising optical properties allowing highly efficient laser designs. 4 The material properties strongly depend on the particle size, size distribution, and morphology, and for optimal optical performance spherical nanoparticles with a narrow size distribution are preferred. 5 Therefore, it is crucial to develop synthesis methods with control over these particle characteristics. Garnets have traditionally been synthesized using solid state routes, which require long, high temperature treatments ( uc for h). 6 For the production of nanoparticles, other synthesis routes have been developed, such as coprecipitation methods, 4,5 sol gel methods, 1,7,8 spray-pyrolysis, 9 and hydrothermal supercritical synthesis methods Supercritical synthesis exploits the dramatic reductions in both the dielectric constant and density of water near the critical point Inorganic salts dissolved in water, hydrate and form metal hydroxides, which upon rapid heating to temperatures above the critical point in a pressurized reactor instantaneously dehydrate and form metal oxide nanoparticles with a narrow size distribution. 20,21,23,24 Supercritical synthesis can be performed in both batch and continuous flow reactors, 22 and it has been shown to be useful for synthesis of many complex multi-component oxides. 10,11,14 18,20,22,25 29 The method has also been used for synthesis of YAG particles. Zheng et al. carried out batch hydrothermal synthesis of YAG and found that phase pure YAG nanoparticles were only formed under supercritical conditions. 17 Sahraneshin et al. have shown that the morphology of YAG nanoparticles in a batch synthesis can be controlled by adding organic surfactants, e.g. oleic acid, prior to reaction in supercritical water. 30 Yoon et al. studied the difference between batch and continuous supercritical hydrothermal synthesis for Eu-doped YAG, 15 and found that the continuous flow technique results in small spherical particles, whereas larger needle-like particles formed in batch synthesis. Thus, several studies have used the hydrothermal supercritical technique for production of YAG nanoparticles, but the reaction mechanisms during the synthesis are still not understood. In this This journal is ß The Royal Society of Chemistry 2013 RSC Adv.

207 View Article Online Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. Paper context, in situ studies have proven very useful, and we have recently used a range of in situ X-ray scattering techniques to follow reactions taking place under sub- and supercritical conditions Here we employ in situ powder X-ray diffraction (PXRD) to follow the evolution of crystalline phases in real time, and thereby obtain an understanding of the formation mechanism and crystal growth of nanocrystalline YAG in real time. Since the heating during our in situ experiments only occurs at the center of the reactor capillary, it is not possible to recover a representative synthesis product after the experiments, and thus subsequent ex situ characterization e.g. using microscopy techniques is not possible. We therefore focus on following the phase content and the crystallite growth by PXRD during hydrothermal synthesis of Y 32x Yb x Al 5 O 12 nanoparticles. Experimental The following reagents were used as purchased without further purification: Al(NO 3 ) 3?9H 2 O (ACS reagent), Y(NO 3 ) 3?6H 2 O (99.8%), YbCl 3?6H 2 O (99.9%), Yb(NO 3 ) 3?5H 2 O (99.9%), and KOH. Aqueous solutions of the metal salts were mixed thoroughly corresponding to the desired molar ratios between Y, Al and Yb in YAG ((Y+Yb) 3 Al 5 O 12 ). The ph of the mixture was adjusted to approximately 9 by drop-wise addition of an aqueous 4 M KOH solution, resulting in a viscous white gelatinous solution. The precursor was then centrifuged and washed repeatedly until the ph of the supernatant was neutral. The precursor gel was subsequently suspended in deionised water. For the YAG synthesis the precursor was obtained from yttrium and aluminum nitrates, but for the Yb doped samples, experiments were done with both YbCl 3 and Yb(NO 3 ) 3. For YbAG the precursor was made from ytterbium and aluminium nitrates. All in situ experiments were carried out at 256 bar and the synthesis conditions are summarized in Table 1. The in situ experiments were performed at beam line I711 at MAX-lab 49 (Lund, Sweden) during three different beam time periods. The setup used for the experiments has been described in detail by Becker et al. 50 The precursor gel was injected into a thin sapphire capillary (0.7 mm inner diameter), which was pressurized to 256 bar. Sequential X-ray exposures were started at the same time as the reaction was initiated by blowing a jet of hot air onto the sapphire capillary. Due to the efficiency of the heater and the small volume of the capillary, the desired temperature in the range uc was reached within approximately 10 s. Each experiment was allowed to run for min at constant temperature and pressure. For YAG an additional experiment was conducted, where the temperature was gradually increased by 3 uc min 21 from 150 uc to 408 uc. During the three different beam time periods, the synchrotron beam had wave lengths of l 1 = Å, l 2 = Å, and l 3 = Å, respectively. For the first two beam times, the time resolution of the X-ray exposures was 9 s, while it was 5 s for the third. The scattered X-rays were detected by a MAR 165 mm CCD detector during the first two beam times whereas an Oxford Diffraction Titan CCD detector was used during the last beam time. A detector-to-sample distance of y80 mm (calibrated from a NIST LaB 6 standard) was used, which resulted in a Q-range (Q =4psin(h)/l) from 0.5 to 5 Å 21. The 2D diffraction frames were masked to remove single crystal diffraction peaks originating from the sapphire capillary and then integrated to 1D patterns using Fit2D. 51,52 The integrated data were analyzed by sequential Rietveld refinement using the FullProf program package, 53 and details on the refinements can be found in the supporting information. The weight fractions of the crystalline phases as well as the volume weighted size of the crystalline nanoparticles were extracted from the refined parameters. The crystallite sizes were estimated from the Scherer equation using the refined profile parameters corrected for instrumental broadening. 54 Results and discussion Formation of YAG RSC Advances The in situ data reveal that the formation mechanism for YAG is highly temperature dependent, and that phase pure YAG can only be synthesized above the critical point of water. The raw in situ PXRD data are shown in the supporting information, while Fig. 1 shows single frames obtained after 17 min. of synthesis. At 250 uc, very weak peaks from Y 4 O(NO 3 )(OH) 9 appear after approximately 3 min and remain throughout the synthesis. A large signal from water and the remaining Al-containing amorphous precursor is seen underneath the weak Bragg peaks. At 300 uc, Y 4 O(NO 3 )(OH) 9 also forms initially, but in addition YAG and AlOOH are observed. At 350 uc and 375 uc, Y 4 O(NO 3 )(OH) is not observed within the time resolution of the experiments (9 s), and only YAG and AlOOH form from the beginning. Only at 400 uc, i.e. above the critical point of water, Table 1 Synthesis conditions for in situ data collections at P = 256 bar (X) Compound Y(NO 3 ) 3 precursor YbCl 3 precursor 250 uc 300 uc 350 uc 375 uc 400 uc Y 3 Al 5 O 12 X X X X X X Y 2.7 Yb 0.3 Al 5 O 12 X X X Y 2.7 Yb 0.3 Al 5 O 12 X X X Y 2.4 Yb 0.6 Al 5 O 12 X X X Y 2.4 Yb 0.6 Al 5 O 12 X X X Yb 3 Al 5 O 12 X X X X RSC Adv. This journal is ß The Royal Society of Chemistry 2013

208 View Article Online RSC Advances Paper Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. Fig. 1 In situ PXRD data measured after 17 min during synthesis of YAG at different temperature. (*) indicate YAG, (n) indicate AlOOH, and (+) indicate Y 4O(NO 3)(OH) 9. the garnet phase is obtained in phase pure form. The refined weight fractions of the three phases are illustrated as function of time in Fig. 2. As the reaction proceeds at 300 uc, the fraction of YAG increases at the expense of Y 4 O(NO 3 )(OH) 9, while the AlOOH weight fraction remains constant. At 350 uc, the weight fractions of AlOOH and YAG remain almost constant throughout the synthesis, but at 375 uc a small decrease in AlOOH with a simultaneous a small increase in YAG is observed. Overall, the in situ results indicate that the reaction initially occurs as a transformation from an amorphous precursor to Y 4 O(NO 3 )(OH) 9. The aluminium and part of the yttrium stay bound in the amorphous phase. As the reaction proceeds, YAG is formed at the expense of Y 4 O(NO 3 )(OH) 9, with Al coming from the amorphous phase. At the same time AlOOH crystallizes, and only at near- and supercritical conditions formation of YAG is more favourable than formation of AlOOH. This scenario is corroborated by the experiment where the temperature was gradually increased from 150 uc to 408 uc, Fig. 3. For this experiment Y 4 O(NO 3 )(OH) 9 starts crystallizing at y240 uc, while AlOOH appears at 270 uc. YAG forms just below the supercritical temperature of water at the expense of AlOOH, but even at the end of the experiment Y 4 O(NO 3 )(OH) 9 is still present. The intensity of the Y 4 O(NO 3 )(OH) 9 peaks decrease at the same rate as the YAG peaks increase, and at the critical temperature the AlOOH phase is almost gone. In combination the two types of experiments show that both a rapid temperature increase and temperatures above the critical point are needed to synthesize phase pure YAG. It is interesting that previous studies have indicated a range of impurity phases present in syntheses done under similar conditions, i.e. YOOH, Y 2 O 3, Y 4 Al 2 O 9, and YAlO ,16 18 None of these other phases are observed in the present study. The main difference from earlier results is that the present experimental setup has a very rigorous temperature control, where the set point temperature is reached within seconds. In typical batch syntheses the heating is slow (minutes or hours) and this makes the reaction conditions less well defined, and thus the interplay between kinetic and thermodynamic factors more complex. Formation of Y 32x Yb x Al 5 O 12 Synthesis of Yb substituted YAG was carried out using two different Yb sources, YbCl 3 and Yb(NO 3 ) 3. The weight fractions observed in the experiments carried out with YbCl 3 and Yb(NO 3 ) 3 at 350 uc are shown in Fig. 4, and it is seen that only AlOOH and the garnet phase, Y 32x Yb x Al 5 O 12, form simultaneously in all the experiments. The weight fractions of the two phases stay almost constant throughout the experiments. With YbCl 3 as precursor the equilibrium weight fraction of the garnet phase increases with increasing Yb content, indicating that it is easier to synthesize Y 32x Yb x Al 5 O 12 than pure YAG. However, this trend is not seen with Yb(NO 3 ) 3 as ytterbium source. As in the case of the synthesis of pure YAG (x = 0), the garnet phase is only observed as a single phase above the critical point when YbCl 3 is the precursor, and this is independent of the Yb content. In the experiments with Yb(NO 3 ) 3 as the ytterbium source it was not possible to synthesize phase pure garnet even at 400 uc, and 10 18% AlOOH was still present depending on the Yb content as seen in Fig. 4. This shows that the counter ion is non-innocent in the reaction and that the nature and/or the concentration of the anion have a significant influence on the formation of aluminum garnets. The reaction mechanism seems to differ when Cl 2 ions are introduced in the system, resulting in modified characteristics of the synthesized nanoparticles, e.g. higher garnet content at low temperature and smaller particle sizes. Fig. 2 Refined weight fractions as function of the reaction time obtained from sequential Rietveld refinement of in situ PXRD data. Green symbols are for Y4O(NO3)(OH)9, red symbols are for AlOOH, and black symbols are for YAG. This journal is ß The Royal Society of Chemistry 2013 RSC Adv.

209 View Article Online Paper RSC Advances Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. Fig. 3 (a) Raw in situ PXRD data for the synthesis of YAG, where the temperature is gradually increased (3 uc min 21 ) from 150 uc to408uc. The high background intensity around y2.0 Å 21 is caused by water, and it decreases significantly above the critical point. (*) indicate YAG, (n) indicate AlOOH, and (+) indicate Y4O(NO3)(OH)9 peak positions. (b) High temperature region. Formation of YbAG Fig. 5 shows single frame data measured after 8 min during the synthesis of YbAG using Yb(NO 3 ) 3 as precursor. At 350 uc both Yb 4 O(NO 3 )(OH) 9, 55 AlOOH and YbAG are present during synthesis, but already at 375 uc phase pure YbAG is formed in less than one minute (see ESI3). At 400 uc only the YbAG phase is observed within the time resolution of the experiment (5 s). Fig. 6 shows the refined weight fractions at 350 uc. It is seen that Yb 4 O(NO 3 )(OH) 9 initially crystallizes together with AlOOH, and then the garnet phase gradually increases in weight fraction at the expense of Yb 4 O(NO 3 )(OH) 9. The fraction of AlOOH is almost constant as the reaction proceeds further, and just as for the YAG experiments, this indicates that the YbAG phase does not initially form through AlOOH. Crystal growth The size of the nanoparticles as function of synthesis time and temperature has been calculated from the refined profile parameters corrected for instrumental broadening using the Scherer equation. The YAG particle size is plotted in Fig. 7, and the initial observable size of the garnet nanoparticles ranges from 18 nm to 24 nm depending on the synthesis temperature. Below the critical point the crystallite size is almost independent of temperature, and the particles furthermore show very limited growth after the initial formation. Above the critical point the crystal growth is quite different from what is observed at sub-critical conditions. During the first couple of minutes the particle size apparently has a steep increase followed by a sudden drop before settling to a more regular curve with gradual crystal growth (data not shown in the plot). As shown in the supporting information, the refined scale factor has a similar behavior, and this indicates that the effect in fact is due to particles entering and leaving the beam position in the turbulent supercritical conditions. Nevertheless, after 4 min at supercritical conditions it appears that a significant particle growth from y25 nm to y35 nm occurs with time. Thus, at supercritical conditions the particles size potentially can be controlled to some extent by adjusting the synthesis time. In Fig. 8 the growth curves are shown for synthesis with different Yb content, and it is seen that the garnet crystallite size decreases with increasing ytterbium content, when YbCl 3 is used as ytterbium source. Just as for the synthesis of pure YAG, at sub-critical conditions there is limited crystal growth after the initial crystal formation. At supercritical conditions the growth curves again exhibit a strange behavior in the beginning, but then settle to a gradual growth, which depend on the Yb content. The growth of the pure YbAG is different from the growth of the YAG particles. For YbAG the crystal growth stops after complete transformation of Yb 4 O(NO 3 )(OH) 9 to the garnet phase after y12 min. Comparison of the experiments carried Fig. 4 Refined weight fractions as function of the reaction time obtained from sequential Rietveld refinement of in situ PXRD data. (a) Synthesis of Y 32xYb xal 5O 12 at 350 uc with YbCl 3 as the ytterbium source. (b) Synthesis of Y 32xYb xal 5O 12 at 350 uc with Yb(NO 3) 3 as the ytterbium source. (c) Synthesis of Y 32xYb xal 5O 12 at 400 uc with Yb(NO3)3 as the ytterbium source. For the synthesis of Y32xYbxAl5O12 at 400 uc with YbCl3 only the garnet phases is observed. Green symbols are for x = 0.6, red symbols are x = 0.3 and black symbols are x = 0. Crosses are AlOOH, and circles the garnet phase. Only data points with approximately 25 s apart are shown for clarity. RSC Adv. This journal is ß The Royal Society of Chemistry 2013

210 View Article Online RSC Advances Paper Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. Fig. 5 In situ PXRD data measured after 8 min during synthesis of YbAG at different temperatures. (*) indicate YbAG, (n) indicate AlOOH, and (+) indicate Yb 4O(NO 3)(OH) 9. out with different precursors shows that the nanoparticles are twice as large for the Yb(NO 3 ) 3 precursor as for YbCl 3 precursor. This implies that in the presence of chloride ions formation of the garnet phase is more favorable than formation of Yb 4 O(NO 3 )(OH) 9 even below supercritical conditions. Conclusion In situ PXRD studies have revealed how YAG and YbAG garnet nanoparticles form during sub- and supercritical synthesis from metal chloride and metal nitrate gels. Initially, (Y/ Yb) 4 O(NO 3 )(OH) 9 and AlOOH crystallize and as the reaction proceeds Y 32x Yb x Al 5 O 12 nanoparticles form. Below the critical point the AlOOH content in the reaction does not change, once it has been formed. Near and above the critical point, the formation of YAG was found to be more favourable than AlOOH, and phase pure YAG was obtained at the experiment done at 400 uc. Furthermore, it was shown that fast heating to 400 uc is needed to ensure full transformation from AlOOH and (Y/Yb) 4 O(NO 3 )(OH) 9 to the garnet phase. Yb substitution Fig. 7 The sizes of YAG nanoparticles as a function of the reaction time for the different synthesis temperatures. The uncertainties are in the same range for all four data series, but only shown for the last data point. using the YbCl 3 source gives phase pure garnet nanoparticles already at 375 uc. However, when the Yb source is Yb(NO 3 ) 3, phase pure garnet particles do not form even at supercritical condition (400 uc). The nature of the anion thus affects the reaction mechanisms. The crystallite sizes of the initially formed YAG nanoparticles range from nm, and stay almost constant with time when below the critical temperature. Above the critical point, significant particle growth takes place to about 35 nm after 20 min. Thus, under supercritical conditions the nanoparticle size to some extent can be controlled by adjustment of synthesis time. During the first y10 min of synthesis at subcritical conditions, where (Yb) 4 O(NO 3 )(OH) 9 is transformed to YbAG, the size of the YbAG nanoparticles stays almost constant at about y25 nm. Subsequently a fast growth to a constant size of about y40 nm is observed, and thus particle size control is more difficult for the YbAG system. For the intermediate phases the crystallite size doubles when the Yb source is Yb(NO 3 ) 3 compared with YbCl 3. Furthermore, for the YbCl 3 precursor the crystallite size decreases with increasing ytterbium content (y20 nm for Y 2.7 Yb 0.3 Al 5 O 12 and y10 nm for Y 2.4 Yb 0.6 Al 5 O 12 ) at subcritical conditions. Under supercritical conditions a growth is seen to y28 nm for x = 0.3 and y25 nm for x = 0.6 after 20 min. For the nitrate precursor the crystallite size stays almost constant at both subcritical and supercritical conditions. Fig. 6 Refined weight fractions as function of the reaction time obtained from sequential Rietveld refinement of in situ PXRD data. Synthesis of YbAG at 350 uc with Yb(NO 3) 3 as the ytterbium source. Green symbols are for Yb 4O(NO 3)(OH) 9, red symbols are for AlOOH, and black symbols are for YbAG. Acknowledgements The work was supported by the Danish National Research Foundation (Center for Materials Crystallography, DNRF93) and the Danish Research Council for Nature and Universe (Danscatt). MAX-lab is acknowledged for beam time. Jacob Becker-Christensen, Christoffer Tyrsted and Espen D. Bøjesen are thanked for assistance during the experiments. This journal is ß The Royal Society of Chemistry 2013 RSC Adv.

211 View Article Online Paper RSC Advances Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. Fig. 8 The size of Y 32xYb xal 5O 12 nanoparticles as a function of synthesis time for the different synthesis temperatures using YbCl 3 as precursor (top), and Yb(NO 3) 3 as precursor (bottom). The uncertainties are in the same range for all four data series, but only shown for the last data point. Purple symbols are for x = 3, green symbols are for x = 0.6, red symbols are x = 0.3 and black symbols are x =0. References 1 H. M. Wang, M. C. Simmonds and J. M. Rodenburg, Mater. Chem. Phys., 2003, 77, A. P. Patel, M. R. Levy, R. W. Grimes, R. M. Gaume, R. S. Feigelson, K. J. McClellan and C. R. Stanek, Appl. Phys. Lett., 2008, T. Taira, IEEE J. Sel. Top. Quantum Electron., 2007, 13, A. Ikesue and Y. L. Aung, Nat. Photonics, 2008, 2, Y. S. Wu, J. Li, Y. B. Pan, Q. Liu and J. K. Guo, Ceram. Int., 2009, 35, B. Hoghooghi, L. Healey, S. Powell, J. McKittrick, E. Sluzky and K. Hesse, Mater. Chem. Phys., 1994, 38, E. De la Rosa, L. A. Diaz-Torres, P. Salas, A. Arredondo, J. A. Montoya, C. Angeles and R. A. Rodriguez, Opt. Mater., 2005, 27, E. Garskaite, M. Lindgren, M. A. Einarsrud and T. Grande, J. Eur. Ceram. Soc., 2010, 30, Y. C. Kang, I. W. Lenggoro, S. B. Park and K. Okuyama, Mater. Res. Bull., 2000, 35, Y. Hakuta, K. Seino, H. Ura, T. Adschiri, H. Takizawa and K. Arai, J. Mater. Chem., 1999, 9, Y. Hakuta, T. Haganuma, K. Sue, T. Adschiri and K. Arai, Mater. Res. Bull., 2003, 38, X. Li, H. Liu, J. Y. Wang, H. M. Cui, F. Han, X. D. Zhang and R. I. Boughton, Mater. Lett., 2004, 58, A. Cabanas, J. Li, P. Blood, T. Chudoba, W. Lojkowski, M. Poliakoff and E. Lester, J. Supercrit. Fluids, 2007,40, J. H. In, H. C. Lee, M. J. Yoon, K. K. Lee, J. W. Lee and C. H. Lee, J. Supercrit. Fluids, 2007, 40, M. J. Yoon, Y. S. Bae, S. H. Son, J. W. Lee and C. H. Lee, Korean J. Chem. Eng., 2007, 24, J. W. Lee, J. H. Lee, E. J. Woo, H. Ahn, J. S. Kim and C. H. Lee, Ind. Eng. Chem. Res., 2008, 47, Q. X. Zheng, B. Li, H. D. Zhang, J. J. Zheng, M. H. Jiang and X. T. Tao, J. Supercrit. Fluids, 2009, 50, M. N. Danchevskaya, Y. D. Ivakin, A. V. Maryashkin and G. P. Muravieva, Russ. J. Phys. Chem. B, 2011, 5, N. Akiya and P. E. Savage, Chem. Rev., 2002, 102, C. Aymonier, A. Loppinet-Serani, H. Reveron, Y. Garrabos and F. Cansell, J. Supercrit. Fluids, 2006, 38, K. Byrappa and T. Adschiri, Prog. Cryst. Growth Charact. Mater., 2007, 53, H. Hayashi and Y. Hakuta, Materials, 2010, 3, P. Hald, J. Becker, M. Bremholm, J. S. Pedersen, J. Chevallier, S. B. Iversen and B. B. Iversen, J. Solid State Chem., 2006, 179, J. Becker, P. Hald, M. Bremholm, J. S. Pedersen, J. Chevallier, S. B. Iversen and B. B. Iversen, ACS Nano, 2008, 2, Y. Hakuta, H. Ura, H. Hayashi and K. Arai, Mater. Lett., 2005, 59, H. Reveron, C. Elissalde, C. Aymonier, C. Bousquet, M. Maglione and F. Cansell, Nanotechnology, 2006, 17, K. Matsui, T. Noguchi, N. M. Islam, Y. Hakuta and H. Hayashi, J. Cryst. Growth, 2008, 310, X. Wei, G. Xu, Z. Ren, Y. Wang, G. Shen and G. Han, J. Cryst. Growth, 2008, 310, H. Hayashi, T. Noguchi, N. M. Islam, Y. Hakuta, Y. Imai and N. Ueno, J. Cryst. Growth, 2010, 312, A. Sahraneshin, S. Takami, K. Minami, D. Hojo, T. Arita and T. Adschiri, Prog. Cryst. Growth Charact. Mater., 2012, 58, B. S. Clausen, G. Steffensen, B. Fabius, J. Villadsen, R. Feidenhansl and H. Topsoe, J. Catal., 1991, 132, A. Michailovski, J. D. Grunwaldt, A. Baiker, R. Kiebach, W. Bensch and G. R. Patzke, Angew. Chem., Int. Ed., 2005, 44, P. Norby, Curr. Opin. Colloid Interface Sci., 2006, 11, A. Clearfield, A. Tripathi, D. Medvedev, A. Celestian and J. B. Parise, J. Mater. Sci., 2006, 41, RSC Adv. This journal is ß The Royal Society of Chemistry 2013

212 View Article Online Published on 20 June Downloaded by Aarhus University Library on 25/07/ :12:41. RSC Advances 35 X. F. Shen, Y. S. Ding, J. C. Hanson, M. Aindow and S. L. Suib, J. Am. Chem. Soc., 2006, 128, S. Mitchell, T. Biswick, W. Jones, G. Williams and D. O Hare, Green Chem., 2007, 9, Y. Du, K. M. Ok and D. O Hare, J. Mater. Chem., 2008, 18, S. Cheong, J. Watt, B. Ingham, M. F. Toney and R. D. Tilley, J. Am. Chem. Soc., 2009, 131, N. Pienack and W. Bensch, Angew. Chem., Int. Ed., 2011,50, H. Jensen, M. Bremholm, R. P. Nielsen, K. D. Joensen, J. S. Pedersen, H. Birkedal, Y. S. Chen, J. Almer, E. G. Sogaard, S. B. Iversen and B. B. Iversen, Angew. Chem., Int. Ed., 2007, 46, M. Bremholm, J. Becker-Christensen and B. B. Iversen, Adv. Mater., 2009, 21, M. Bremholm, M. Felicissimo and B. B. Iversen, Angew. Chem., Int. Ed., 2009, 48, C. Tyrsted, J. Becker, P. Hald, M. Bremholm, J. S. Pedersen, J. Chevallier, Y. Cerenius, S. B. Iversen and B. B. Iversen, Chem. Mater., 2010, 22, N. Lock, M. Christensen, K. M. O. Jensen and B. B. Iversen, Angew. Chem., Int. Ed., 2011, 50, K. M. O. Jensen, M. Christensen, C. Tyrsted and B. B. Iversen, J. Appl. Crystallogr., 2011, 44, 287. Paper 46 K. M. O. Jensen, M. Christensen, P. Juhas, C. Tyrsted, E. D. Bojesen, N. Lock, S. J. L. Billinge and B. B. Iversen, J. Am. Chem. Soc., 2012, 134, C. Tyrsted, K. M. O. Jensen, E. D. Bojesen, N. Lock, M. Christensen, S. J. L. Billinge and B. B. Iversen, Angew. Chem., Int. Ed., 2012, 51, C. Tyrsted, B. R. Pauw, K. M. O. Jensen, J. Becker, M. Christensen and B. B. Iversen, Chem. Eur. J., 2012, 18, Y. Cerenius, K. Stahl, L. A. Svensson, T. Ursby, A. Oskarsson, J. Albertsson and A. Liljas, J. Synchrotron Radiat., 2000, 7, J. Becker, M. Bremholm, C. Tyrsted, B. Pauw, K. M. O. Jensen, J. Eltzholt, M. Christensen and B. B. Iversen, J. Appl. Crystallogr., 2010, 43, A. P. Hammersley, S. O. Svensson, M. Hanfland, A. N. Fitch and D. Hausermann, High Pressure Res., 1996, 14, A. P. Hammersley, ESRF Internal Report, ESRF98HA01T, J. Rodriguez-Carvajal, Phys. B, 1993, 192, A. L. Patterson, Phys. Rev., 1939, 56, L. J. McIntyre, T. J. Prior and A. M. Fogg, Chem. Mater., 2010, 22, This journal is ß The Royal Society of Chemistry 2013 RSC Adv.

213 Article pubs.acs.org/cm Defects in Hydrothermally Synthesized LiFePO 4 and LiFe 1 x Mn x PO 4 Cathode Materials Kirsten M. Ø. Jensen, Mogens Christensen, Haraldur P. Gunnlaugsson, Nina Lock,, Espen D. Bøjesen, Thomas Proffen, and Bo B. Iversen*, Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University, DK-8000 Aarhus C, Denmark Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark Institut fu r Anorganische Chemie, Georg-August-Universita t Go ttingen, D Go ttingen, Germany Neutron Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee , United States *S Supporting Information ABSTRACT: The crystal structure and defect chemistry of hydrothermally synthesized LiFe 1 x Mn x PO 4 (x = 0, 0.25, and 0.50) particles have been characterized by simultaneous neutron and X-ray Rietveld refinement as well as X-ray and neutron pair distribution function (PDF) analysis, crystallinity determination, Mo ssbauer spectroscopy, ion coupled plasma (ICP) studies, and scanning electron microscopy (SEM). The very detailed structural refinements show that fast hydrothermal synthesis causes partial Feoccupancy and vacancies on the Li (M1) site, while the Fe (M2) site is always fully occupied by iron. Thus, the defect is not merely a Li/ Fe antisite defect, and excessive amounts of Fe are the origin of the disorder in the structure. Neutron and X-ray total scattering with PDF analysis show that after fast hydrothermal synthesis, the crystalline, defective Li x Fe y PO 4 coexists with amorphous Li/ Fe-PO 4 structures having just short-range order. Iron excess is only seen in the crystalline part of the particles, and as the crystallinity of the samples increases with longer synthesis time, the crystalline Fe/Li ratio approaches 1. The present data thus suggest that when crystalline particles initially form, Fe is included faster in the structure from the amorphous precursor than Li, causing the defects in the structure. Only when all Li have been incorporated into the crystal structure and 100% crystallinity is achieved, fully ordered, defect free samples can be obtained. The Fe occupancy on the M1 site is therefore directly linked to the crystallinity of the sample. In LiFe 1 x Mn x PO 4 samples, the transition metal defect on the M1 site is only Fe and not Mn. Furthermore, the presence of Mn locks in the defects, and thus the Fe disorder is not suppressed with extended synthesis time. KEYWORDS: LiFePO 4, defects, powder diffraction, total scattering INTRODUCTION Ever since Goodenough et al. first suggested the use of LiFePO 4 as a cathode material for Li ion batteries in 1997, 1 the compound has received immense interest. LiFePO 4 is cheap and nontoxic, and it shows good electrochemical properties such as high energy density, good cyclability, and high stability. 2 5 As shown in Figure 1a, it crystallizes in the olivine structure and has an orthorhombic unit cell (space group Pnma), where edge-sharing LiO 6 octahedra (M1 site, violet) form chains along b, while corner-sharing FeO 6 octahedra (M2 site, red) form a zigzag pattern in the b/c-plane. During charge and discharge the 1D Li-ion diffusion takes place along the b- direction as illustrated in Figure 1b. 6 8 During delithiation, the iron is oxidized to yield FePO 4 through a two phase reaction for bulk material 9 11 and as a single phase reaction for small nanoparticles. 12 LiFePO 4 is already used in commercial Li-ion batteries, but much effort still goes into developing new synthesis methods to reduce the cost of the batteries. 13,14 During the past decades, hydrothermal synthesis has proven itself as a cheap, environmentally benign, and easily scalable way of producing inorganic materials. In 2001 Whittingham et al were the first to hydrothermally prepare LiFePO 4, and many studies have since been published for both LiFePO 4 and LiFe 1 x Mn x PO However, when synthesized hydrothermally at low temperatures, the material shows disappointing electro-chemical properties due to defects in the crystal structure. This is believed to be due to the transition metal partly occupying the Li M1 sites and thereby blocking the Li-ion diffusion pathway. 16 The exact nature of the defect has been discussed in the literature using several approaches. Islam et al. have shown by theoretical calculations that Fe/Li interchange is the defect of lowest energy, 7,26 and the Fe/Li antisite defect has also been studied experimentally using both diffraction and microscopy methods. 27,28 Further theoretical studies of antisite defects have also been done However, other studies Received: March 13, 2013 Revised: May 1, 2013 Published: May 2, American Chemical Society 2282 dx.doi.org/ /cm Chem. Mater. 2013, 25,

214 Chemistry of Materials Figure 1. a) LiFePO 4 structure where violet octahedra show LiO 6, red octahedral show FeO 6, and blue dots are the P atoms. b) Illustration of the 1D Li channels along b. The red octahedra are FeO 6 and the blue tetrahedra are PO 4. report defects due to nonstoichiometry with Li deficiency resulting in Fe on the M1 sites. 33,34 Masquelier et al. have studied the structure of LiFePO 4 nanoparticles synthesized by precipitation, and they observed Fe on the M1 site and Fe deficiency on the M2 site. 12 We have previously investigated the hydrothermal synthesis of LiFe 1 x Mn x PO 4 by in situ X-ray diffraction 35 and observed that when LiFe 1 x Mn x PO 4 particles are initially formed, a large amount of Fe is present at the Li site. The structure orders with increasing synthesis time and higher temperature. However, in situ studies are inherently a compromise between data quality and time resolution, and our in situ data were therefore not suited for a detailed investigation of the true nature of the defect chemistry. Here we present an ex situ study, where we have combined neutron and X-ray diffraction data for both simultaneous Rietveld refinements and PDF (pair distribution function) analysis. The structural analysis is complemented with ICP elemental analysis, Mo ssbauer spectroscopy, SEM images, and crystallinity determination. Only by a combination of all these techniques, we are able to get a full picture of the defect chemistry of the hydrothermally synthesized samples. Especially the simultaneous refinement of X-ray and neutron data is essential to understand the crystal structure and defects in the compounds. For X-rays, Mn and Fe are both strongly scattering but practically indistinguishable due to the similar Article atomic numbers, while Li only scatters weakly. In the case of neutrons, Li and Mn both have negative scattering lengths, while Fe has a positive scattering length. By combining neutron and X-ray data in a simultaneous analysis, we are able to get complete information on Fe, Mn, and Li as well as P and O positions and occupancies. Furthermore, by use of PDF analysis, we are able to get atomic structural information from the noncrystallized material in the sample. The present study thus provides a detailed analysis and understanding of the structure of hydrothermally synthesized LiFe 1 x Mn x PO 4 particles, and based on the results we propose an explanation for the formation of defects in LiFePO 4 during hydrothermal synthesis. Our studies show that the presence of Fe disorder is directly related to partial sample crystallinity, which will strongly affect the electrochemical properties. EXPERIMENTAL METHODS Synthesis. All samples were synthesized hydrothermally in 14 ml steel autoclaves with Teflon linings. For the LiFePO 4 synthesis, 2 ml of 1.9 M H 3 PO 4 (Riedel de Haen) was mixed with 2 ml of 1.9 M FeSO 4 (Sigma-Aldrich, >99%). 15 Then 4 ml of 2.85 M 7 LiOH (Sigma-Aldrich, >98%, 97% 7 Li) was added, forming a thick green precursor gel. 7 Li 97% OH was used because of the lower neutron absorption cross section of 7 Li. The LiFe 1 x Mn x PO 4 (x = 0.25 and 0.50) samples were prepared in the same way, by replacing the appropriate amount of FeSO 4 with MnSO 4 (Sigma-Aldrich, >98%) of the same concentration. 23 All syntheses were performed at 170 C. In order to obtain different defect concentrations the reaction time was varied with synthesis durations of 40 min, 2 h, and 7 h. For all syntheses, 0.08 g of ascorbic acid (Sigma-Aldrich, >99%) was added to act as a reducing agent to avoid the formation of iron(iii)-compounds. The pressure was autogenously generated in the autoclaves, which were 50% filled. In summary, the following samples were prepared: 1 LiFePO 4 (170 C, 40 min.), 2 LiFePO 4 (170 C, 2 h), 3 LiFePO 4 (170 C, 7 h), 4 LiFe 0.75 Mn 0.25 PO 4 (170 C, 40 min.), 5 LiFe 0.75 Mn 0.25 PO 4 (170 C, 7 h), 6 LiFe 0.50 Mn 0.50 PO 4 (170 C, 40 min.), 7 LiFe 0.50 Mn 0.50 PO 4 (170 C, 7 h). For each sample, four identical syntheses (using identical autoclaves in the same position in the oven) were performed to obtain enough material for neutron experiments. X-ray and Neutron Scattering Experiments. High resolution powder X-ray diffraction (PXRD) data for Rietveld refinement were measured at beamline BL44B2 at Spring-8, Japan using a large Debye Scherrer camera. 36 The X-ray wavelength was determined to be (2) Å by Rietveld refinement of a CeO 2 standard (a = Å). The samples were loaded into 0.2 mm glass capillaries, and the measurements were done at room temperature. For the LiFePO 4 samples, X-ray data for crystallinity determination were measured by mixing a small amount of LiFePO 4 with 100% crystalline diamond powder. X-ray total scattering data were obtained at beamline 11-ID-B, Advanced Photon Source, USA, using an X-ray wavelength of 0.212(1) Å and a Perkin-Elmer amorphous silicon detector. The samples were loaded in 1.0 mm kapton capillaries, and the measurements were done at room temperature. Neutron powder diffraction and total scattering data were measured at room temperature at the time-of-flight diffractometer NPDF, Los Alamos National Laboratory, USA. The samples of ca. 2 g were loaded into vanadium cans (6 mm in diameter). Background corrections were determined by measurements on the empty sample chamber and the empty vanadium sample can. The detector efficiency was normalized by measuring data on a vanadium rod. Each data collection took 8 h. Rietveld Refinement. The X-ray and neutron diffraction data were analyzed by simultaneous Rietveld refinement in GSAS 37 using the EXPgui interface. 38 For the X-ray synchrotron data, the 2θ range from 3 to 65 (i.e., q max = 13.5 Å 1 ) was included in the refinement. The background was modeled by interpolation between points with refinable intensity values. The scale factor and the zero point were refined as well as the peak shape, which was described by the 2283 dx.doi.org/ /cm Chem. Mater. 2013, 25,

215 Chemistry of Materials Article Figure 2. Simultaneous Rietveld refinement of the data collected on sample 3, i.e. LiFePO 4 particles obtained after 7 h synthesis at 170 C. a-d) Neutron banks. e) X-ray data. The black lines show the data, the red the pattern calculated from the model, and the blue line the difference between the two. Thompson-Cox-Hasting pseudo-voigt function using U, V, W, X, and Y. Corrections for X-ray absorption were done by GSAS. For the neutron data, measurements from all 4 detector banks at the NPDF instrument were included in the fit, covering q-space to 30 Å 1. For all banks, the background was described by GSAS model 4 (sum of exponential functions) where 4 parameters were refined. Furthermore, for each bank, a scale factor was refined along with the zero point, and the profile parameters were refined in profile function 4 in GSAS, which is a convolution of back-to-back exponential functions and a Pseudo-Voigt function. Corrections for neutron absorption were done by GSAS. The X-ray and neutron data were weighted equally in the refinement as the counting statistics are similar. No correlation between refined parameters larger than 80% were observed. The structure was described in the Pnma space group, and unit cell, atomic positions, and isotropic Debye Waller factors were refined for each site. An average of the neutron scattering length of 6 Li and 7 Li was used in accordance with their abundance in the samples. Fe was allowed on the Li site and Li on the Fe site independently without constraints. For the Mn containing samples two models were refined: 1) both Mn and Fe on the M1 defect site and 2) only Fe on the M1 defect site. For the crystallinity determination, the weight fractions of crystalline LiFePO 4 and diamond in the mixed samples were found by Rietveld refinement using the FullProf program package. 39 The crystallinity of the samples was then obtained from the amounts of sample according to m% CrystallineLiFePO4 mdiamond Crystallinity = 100% m% m diamond LiFePO4 PDF Analysis. PDF analysis was done for the LiFePO 4 and LiFe 0.50 Mn 0.50 PO 4 samples. Neutron PDFs were calculated from the TOF data using PDFgetN. 40 All 4 detector banks were included to obtain the total scattering function S(q) which was Fourier transformed using q max = 25 Å 1. X-ray PDFs were obtained in PDFgetX2 41 using q max =23Å 1. Both the neutron and X-ray PDFs were modeled individually in PDFgui. 42 The structure was described as for the Rietveld refinements, however with the difference that the metal occupancies were not refined but kept fixed at the values obtained from the Rietveld refinements. The pair distribution r-ranges from 1 5 Å and 5 20 Å were used in the analysis. Apart from the structural parameters, the scale factor and the quadratic dynamic correlation factor were refined. 43 For the X-ray measurements, the q damp value was obtained from refinement of a LaB 6 standard. For the neutron data, q damp and q broad were provided for the instrument. ICP Analysis. The elemental composition of the samples was analyzed by ICP analysis using a Spectro Arcos ICP spectrometer. Prior to the analysis, the samples were dissolved in an aqueous HNO 3 solution. Scanning Electron Microscopy. Scanning electron microscopy (SEM) images were recorded using a Nova 600 Nano SEM from FEI. A Low Vacuum Detector was used due to the insulating nature of the particles, and a water atmosphere (61 Pa) was applied. Mo ssbauer Spectroscopy. Mo ssbauer spectra were obtained for the LiFePO 4 samples at room temperature in transmission geometry using a 57 Co:Rh source of 5 10 mci mounted on a conventional drive system. Velocities and isomer shifts are given relative to the center of the spectrum of α-fe. The spectra were analyzed with one component due to Fe 3+ and one component due to Fe 2+ which was simulated using a quadrupole splitting distribution based on linear segments in the distribution function. 44 The coupling between the quadrupole splitting and isomer-shift was assumed to be the same in all cases. RESULTS AND DISCUSSION Crystal Structure of LiFePO 4 Dependence on Synthesis Time. Figure 2 shows examples of the Rietveld fits to both X-ray and neutron data. As seen from the difference curves, good fits with R F values around 5% were obtained for all the data sets. Generally, the quality of the fit decreased slightly with shorter synthesis time indicating some structural disorder not included in the model. The refined parameters and R-values for all samples can be found in the Supporting Information. The Rietveld refinements reveal that the unit cell size is dependent on the synthesis time. This is seen in Figure 3a, where the changes in the unit cell parameters are plotted relative to the final values (7 h data) as function of synthesis time. As reported earlier 16,34,35 the unit cell size decreases along a and c with synthesis time, while b increases slightly. The change in cell volume is believed to be related to the defects in the sample, which is apparent from the occupancy of Fe on the M1 site shown as the black line in Figure 3b. The refinements show that short syntheses times produce disordered samples with a high concentration of Fe on the Li site, and this agrees 2284 dx.doi.org/ /cm Chem. Mater. 2013, 25,

216 Chemistry of Materials Article The macroscopic strain in the crystal results in broadening of the peak profile with a tan(θ) dependency and based on the instrument corrected profile parameters, the strain S can thus be calculated (see the Supporting Information). 37 This is plotted as a function of synthesis time in Figure 3c. The plot suggests that the strain arises from the differences in unit cell sizes due to the Fe occupancies on the M1 site. Formation of LiFePO 4 from Amorphous Particles: Relation between Crystallinity and Defects. Previously, we have shown by means of in situ PXRD studies that LiFePO 4 forms from a precursor gel consisting of small particles of iron and lithium phosphates, which are only slightly crystalline and where the precise structure depends on the local ph value in the gel. 35 From the present diffraction data, there are no clear observations of any remaining crystalline precursor gel and good Rietveld fits are obtained for all data sets. However, from the crystallinity measurements of the LiFePO 4 samples, it is clear that a considerable fraction of the samples synthesized for 40 min and 2 h is not crystalline LiFePO 4 as shown in Figure 4a Figure 3. a) Change in unit cell parameter for LiFePO 4 relative to the value obtained after 7 h. b) Refined concentration of Fe (black) and vacancies (red) on the M(1) Li site (red). c) Microstrain plotted as function of Fe occupancy on M1 (Li) sites. The error bars on all refined parameters are smaller than the size of the symbols. well with the unit cell changes. Due to the slight size difference of Li + and Fe 2+ (Shannon ionic radii of 76 and 78 pm, 45 respectively) the presence of Fe 2+ will expand the unit cell slightly along a and c, while it is almost unaffected along b, where there is more space for the Fe 2+ ion in the Li diffusion channels. The Rietveld refinements show that after short syntheses, large amounts of Fe are present on the M1 site, while there is no Li on the M2 site. For all samples M2 is fully occupied with Fe. The results thereby confirm earlier studies stating that the crystallographic disorder present in hydrothermally synthesized LiFePO 4 samples is not an antisite defect but rather Fe excess. 33,34 We suggest that this deviation from ideal LiFePO 4 stoichiometry is caused by reaction kinetics and is directly linked to the crystallinity of the samples, as will be discussed further below. The simultaneous refinement of X-ray and neutron data allow refinement of the full site occupancy of Li and Fe on the two metal sites, and this also provides a determination of the metal site vacancy concentration; calculated as occ(vacancy M1 ) =1 occ(li M1 ) occ(fe M1 ). This is plotted as the red curve in Figure 3b. The vacancy and Fe concentration on M1 sites follow the same trend, and fewer vacancies are seen with longer synthesis time. However, the vacancy concentration is always slightly higher than the Fe occupancy and for charge balance conservation; substitution of a Li + ion with Fe 2+ requires formation of only one single Li-site vacancy. The additional M1 vacancies in the refined model are believed to be due to the presence of Fe 3+ on the M2 (Fe) sites, as is corroborated by the Mo ssbauer measurements discussed below. In powder diffraction, the Bragg peak width is affected by the finite extent of coherently diffracting domains in the crystal. Figure 4. a) Crystallinity of the LiFePO 4 samples as a function of synthesis. The uncertainties have been estimated to be 5%. b) Ratio between the scale factors from the low r-range PDFs and the high r- range PDFs. The neutron results are shown in black, while the X-ray results are in red. c) Fe/Li ratio from Rietveld analysis (black) and ICP (red) as a function of synthesis time. In b and c, the error bars are smaller than the symbols. (see the SI for details). Although the absolute crystallinity values are associated with rather large uncertainties arising from the sample preparation and data analysis, it is clearly seen that the mass fraction of crystalline LiFePO 4 increases with increasing synthesis time. The atomic structure of the amorphous material can be characterized by PDF analysis. The PDF is based on total scattering data, and it provides therefore information on both 2285 dx.doi.org/ /cm Chem. Mater. 2013, 25,

217 Chemistry of Materials Article Figure 5. Modeling of the neutron and X-ray PDF data in the range from 5 20 Å. Figure 6. SEM images of LiFePO 4 particles synthesized at 170 C for 40 min (A), 2 h (B), and 7 h (C). the amorphous and crystalline parts of the particles. Neutron and X-ray PDF fits for the three LiFePO 4 samples are shown in Figure 5. The data are fitted in the r-range from 5 to 20 Å, and in this region the crystallographic model fits well with the experimental PDFs. However, when extending this model to r values below 5 Å, a large fraction of the peak intensities in the experimental PDF is not well described, showing that amorphous lithium and iron phosphate nanoclusters with only local order coexist with the crystalline LiFePO 4. The peak seen at 1.5 Å originates from the P O bond, while the range from 2 to 2.7 Å covers the first Li O and Fe O distances. The first metal P distance is seen around 3.2 Å, and this peak is particularly poorly described in the X-ray data from the shorter syntheses time. To quantify the difference in intensity in the different r-regions, fits based on the LiFePO 4 structure were made from both 1 5 Å and 5 20 Å. The low r-region fits are plotted in the Supporting Information. Here, it is seen that the region from 1 to 5 Å can in fact be fitted well with the crystalline LiFePO 4 structural model. This shows that the atomic structure of the amorphous nanoclusters is very closely related to the bulk phase. The ratio between the scale factors obtained for the 1 5 Å and 5 20 Å fits are plotted in Figure 4b, which clearly shows that the shorter the synthesis time, the larger the amount of amorphous LiFePO 4 with only shortrange order. It should be noted that an additional origin of the poor fit at low r for the defective phase could be local structural disorder induced by the presence of Li at the Fe sites, leading to a split metal site. When using our small-box structural models, this is not observed. However, to fully characterize whether the cation disorder changes the local structure of the metal sites, large box 2286 dx.doi.org/ /cm Chem. Mater. 2013, 25,

218 Chemistry of Materials modeling (e.g., by the Reverse Monte Carlo technique) is needed. The Fe/Li ratios obtained from the crystallographic analysis as well as from ICP are plotted in Figure 4c. The stoichiometry of the crystalline LiFePO 4 changes as a function of synthesis time, and for all samples the Fe/Li ratio is higher than 1. The ICP results show similar trends, although here the ratio between Fe and Li is much closer to that of stoichiometric LiFePO 4. The diffraction results express the stoichiometry of the crystalline part of the sample, while the ICP analysis gives the composition of the entire sample, including the amorphous part. The discrepancy between the results from the two techniques thus indicates that there are differences in the way that Li and Fe are incorporated into the crystal structure during the synthesis. Thus, Fe is included relatively faster into both the M1 and M2 sites of the crystal structure than Li, leading to the Fe excess. SEM images of the three LiFePO 4 samples are shown in Figure 6. All the samples are very heterogeneous and consist of particles of several different sizes and shapes. After 40 min at 170 C, rhombic shaped particles coexist with smaller, spherical-like particles. The smallest particles are most likely amorphous, while the rhombic particles are crystalline. After 2 h, the rhombic particles have grown bigger, and the size distribution has broadened. The largest particles are more irregular but still keep the basic rhombic shape. Again, smaller particles without the rhombic morphology are also observed. After 7 h of synthesis, some of the particles have grown significantly to more than 10 μm, Much smaller rhombic and some irregular particles are also observed. By combining the results from Rietveld analysis, PDF analysis, ICP, and SEM, a picture of the formation mechanism emerges, as illustrated in Figure 7. The amorphous structures Article have previously been suggested to increase the performance of the cathode material, 30 there is no doubt that the presence of Fe in the Li channels blocking the diffusion pathway will reduce the electrochemical capacity significantly. However, the main reason for the low capacity of hydrothermally synthesized samples might very well be the presence of a large amorphous fraction. The lithium and iron phosphate nanoclusters do not contribute to the electrochemical capacity or the electronic or ionic conductivity of the samples. Furthermore, as the amorphous clusters seem to reside on the surface of the crystalline particles, their presence could hinder the diffusion of Li + into the crystalline particles. Only by ensuring 100% crystallinity, high quality materials can thus be obtained. This can be done by high synthesis temperatures, longer synthesis times, and/or postsynthesis high temperature treatment. Low crystallinity is generally a problem for samples synthesized at low temperatures and affects the properties of almost all functional materials. Although PXRD is a standard characterization technique, simple crystallinity measurements using a crystalline standard are rarely done. By measuring this along with characterization of the crystal structure, size, and morphology, many of the physical properties of the synthesized materials can be explained. Mo ssbauer Analysis of LiFePO 4 Samples. Figure 8 shows the Mo ssbauer spectra obtained from the LiFePO 4 samples. The overall shape of the spectra is due to a dominating Fe 2+ component, but close inspection shows two distinct features in the samples compared with a single phase Fe 2+ compound. First, there is a feature at v 0.85 mm/s, most clearly seen in the sample from the shortest synthesis. Most Figure 7. Formation mechanism for LiFePO 4. present after short synthesis surround the crystalline, defective particles, and more of the lithium phosphates may be found in solution. The amorphous particles then act as ion donors to the growing crystallites. The Fe-PO 4 parts are incorporated in the crystal structure faster than Li, leading to defects in the structure. However, as the synthesis proceeds, more LiFePO 4 crystallize, and the remaining amorphous lithium phosphate is included in the crystalline particles. As this happens, the structure orders, and Fe is moved from the M1 site to the M2 site. Thus, only when full crystallinity is obtained, defect free LiFePO 4 can be achieved. The presence of defects is thus directly related to the crystallinity of the particles. With our novel understanding of defects and crystallinity of hydrothermally synthesized LiFePO 4, a new interpretation of the poor electrochemical properties of samples synthesized using this method can be given. First, we have confirmed that the defects present are not antisite defects but in fact excess Fe and vacancies occupying the Li sites. Although Li vacancies Figure 8. a-c) Room-temperature Mo ssbauer spectra of the three LiFePO 4 samples. The experimental data are shown as black dots, while the solid lines shows the fitting components from Fe 2+ (green), Fe 3+ (blue), and their sum (red). d) Quadrupole splitting distribution determined for the LiFePO 4 sample synthesized for 40 min dx.doi.org/ /cm Chem. Mater. 2013, 25,

219 Chemistry of Materials Article Table 1. Hyperfine Parameters and Spectral Areas Found from Simultaneous Analysis of the Mo ssbauer Spectra a Fe II b,c sample δ (mm/s) ΔE Q (mm/s) area (%) δ (mm/s) ΔE Q (mm/s) Γ (mm/s) area (%) LiFePO 4, 40 min 1.24(4) 2.73(5) 88(1) 0.30(4) 1.13(7) 0.57(9) 12(1) LiFePO 4, 2 h 1.23(4) 2.78(5) 93(2) 7(1) LiFePO 4, 7 h 1.23(4) 2.85(4) 98(1) 2(1) a The table lists the values of (average) isomer-shift (δ), quadrupole splitting (ΔE Q ), and FWHM line width (Γ). b The coupling between isomer shift and quadrupole splitting was found as dδ/dδe Q = 0.08(1). c The same parameters of Fe III were used for all samples. d In all cases, the peak of the quadrupole splitting distribution was at 2.92(4) mm/s. Fe III d likely, this is due to the right-leg of a quadrupole split Fe 3+ component, where the left-leg overlaps with the left-leg of the dominating peak due to Fe 2+. Second, there is an asymmetry in the line-shape of the Fe 2+ component, suggesting the presence of additional component(s) with lower quadrupole splitting than the dominating component. The results of the modeling are summarized in Table 1. The Fe 3+ content is highest for the shortest syntheses, and after 7 h only very small amounts of Fe 3+ are observed. The results agree with the trends from Rietveld analysis, which indirectly showed the Fe 3+ as additional vacancies. However, the Mo ssbauer results show 12(1)% Fe 3+ in the sample synthesized for 40 min, which is much higher than the 2% extra vacancies seen. This indicates that a large fraction of the Fe 3+ ions could be present in the amorphous part of the sample. As the amount of Fe 3+ decreases with synthesis time, the results indicate that Fe 3+ does not actually form during the synthesis. Possibly, it comes from Fe 2+ in the amorphous phase that gets oxidized during handling of the samples after the synthesis, when the reducing ascorbic acid is no longer present. Masquelier et al. have studied nanoparticles of LiFePO 4 after moderate thermal treatments in air, 46 and they also observed a large fraction of Fe 3+ in their samples but concluded that this was present at the M1 site in the structure. They saw that the unit cell volume decreased with increasing Fe 3+ content due to the smaller ionic radii of Fe 3+ (63 pm). 45 We see the opposite effect (the unit cell is largest for the samples with the highest Fe 3+ content), indicating that the content and position of Fe 3+ in the crystal structure is very dependent on both particle size and treatment method. The hyperfine parameters for Fe 2+ in the peak of the quadrupole splitting distribution (δ = 1.22(3) mm/s, ΔE Q = 2.92(4) mm/s) are in a reasonable agreement with parameters obtained on natural LiFePO 4 i.e. triphylite. 47 The lower average quadrupole splitting for the sample synthesized for 40 min and 2 h (cf. Table 1) are due to the quadrupole splitting distribution as shown in Figure 8d. The Mo ssbauer results thus indicate that several different Fe 2+ environments exist, in agreement with the diffraction and total scattering results, where Fe 2+ was observed at M2, M1, and in the amorphous Fe-PO 4 structure. Bini et al. 48 saw a similar asymmetry of the Fe 2+ component in samples produced by microwave-assisted hydrothermal synthesis route. They analyzed their spectra in terms of three Fe 2+ components and saw a similar negative trend between isomer shift and quadrupole splitting as observed here. Metal Disorder in LiFe 1 x Mn x PO 4. The refined unit cell parameters for the manganese substituted compounds are plotted in Figure 9. As Mn 2+ has a larger ionic radius than Fe 2+, substitution of Fe for Mn increases the unit cell volume. Just as for the LiFePO 4 samples, the unit cell also increases for short synthesis time due to disorder on the metal sites. The results Figure 9. Unit cell parameters for all samples as a function of synthesis time. The error bars on the refined parameters are smaller than the symbols. from refinements using the two different disorder models are shown in Table 2. When both Mn and Fe are allowed on the Li site (model 1), the refinement increases the vacancy concentration significantly (20% for LiFe 0.50 Mn 0.50 PO 4, 40 min), which does not seem reasonable and does not agree with the ICP results. Model 2, where only Fe is allowed on the M1 site, gives a comparatively better and more physical result. This indicates that in LiFe 1 x Mn x PO 4 only Fe defects and not Mn defects are present. The Shannon ionic radii of Mn 2+ and Fe 2+ are 83 pm and 78 pm, respectively, compared with 76 pm for Li +, and thus the manganese ion may be too large to be incorporated on the M1 site. 45 The defect concentrations from model 2 are plotted in Figure 10, which includes a comparison with LiFePO 4. For short syntheses (40 min) less Fe occupancy is seen on M1 with increasing Mn content. However, after long synthesis times (7 h), where the disorder is almost completely suppressed in 2288 dx.doi.org/ /cm Chem. Mater. 2013, 25,

220 Chemistry of Materials Article Table 2. Defect Concentration and Sample Compositions in LiFe 1 x Mn x PO 4 a total Fe and Mn occupancy on M1 (%) vacancy concentration on M1 (%) LiFePO 4, there are still significant amounts of Fe on the Li site, when Mn is present in the structure. Thus, Mn seems to lock the defective structure, making it challenging to synthesize defect free LiFe 1 x Mn x PO 4 nanoparticles hydrothermally. This agrees with theoretical calculations. 26 When comparing the Rietveld and ICP stoichiometry results, the Fe/Li ratio is higher in the crystalline part of the sample than in the whole sample, just as for pure LiFePO 4, again showing that Fe is incorporated faster into the crystal structure than Li. However, the Mn/Li ratios found from the two methods are almost the same, even after short synthesis times. This indicates that Mn is immediately incorporated in the crystal structure when the synthesis is initiated. This agrees well with our previous in situ study showing that Mn substituted samples form faster than LiFePO The PDF results for LiFe 0.5 Mn 0.5 PO 4 are similar to those of LiFePO 4, and details are given in the Supporting Information. Poor fits to the low r- region are seen, which is believed to be due to the presence of amorphous content. Again, local disorder induced by the split cation site (from both Fe, Mn, and Li) is not apparent in our small-box refinements. CONCLUSION Simultaneous Rietveld refinement of high quality neutron and X-ray powder diffraction data has been used to obtain unprecedented detailed information about the structure of hydrothermally synthesized LiFe 1 x Mn x PO 4 particles. Initially in the synthesis, Fe is found to partially occupy the M1 Li site and fully occupy the M2 site, and overall the structure therefore contains excess Fe. The defects arise due to differences in the rate with which Li and Fe are introduced in the crystalline LiFePO 4 structure as shown by the fact that Li x Fe y PO 4 coexists with amorphous Li/Fe-PO 4 units. For the 100% crystalline particles the defects are suppressed, and thus high quality battery materials are obtained either from extended synthesis time or from higher synthesis temperature. LiFe 1 x Mn x PO 4 is also disordered on M1, but the refinements show that only Fe occupies the Li site. The presence of Mn in the structure locks the Fe disorder even for long synthesis times, and suppression of the defect formation is challenging for hydrothermal synthesis. The present study underpins the need for thorough structural investigations of cathode materials synthesized by low temperature methods. The disappointing electrochemical properties of hydrothermally synthesized LiFePO 4 have so far been explained by the presence of Fe in the Li channels. Although there is no doubt that this will influence the capacity of the resulting cathode, the low crystallinity of defective samples might have an even larger effect. ASSOCIATED CONTENT *S Supporting Information Refined parameter values and R-factors for all Rietveld refinements. Calculations of strain from peak widths. Crystallinity calculations. Low r PDF fits of LiFePO 4. PDF analysis of LiFe 0.50 Mn 0.50 PO 4. This material is available free of charge via the Internet at AUTHOR Fe:Mn:Li Rietveld crystalline stoichiometry sample model 1 model 2 model 1 model 2 model 1 model 2 Fe:Mn:Li ICP total sample stoichiometry 4, LiFe 0.75 Mn 0.25 PO 4 (40 min) 7.2(1) 6.6(1) 12.8(1) 7.4(1) 0.96:0.38:1 0.90:0.33:1 0.84:0.34:1 5, LiFe 0.75 Mn 0.25 PO 4 (7 h) 3.8(1) 3.6(1) 8.2(1) 4.7(1) 0.85:0.33:1 0:85:0.31:1 0.77:0.29:1 6, LiFe 0.50 Mn 0.50 PO 4 (40 min) 4.0(1) 6.2(1) 20.1(1) 7.8(1) 0.72:0.82:1 0.61:0.62:1 0.56:0.64:1 7, LiFe 0.50 Mn 0.50 PO 4 (7 h) 2.7(1) 4.0(1) 19.6(1) 4.0(1) 0.66:0.74:1 0.55:0.58:1 0.52:0.61:1 a In model 1, both Mn and Fe were allowed on the M1 site, whereas for model 2, only Fe was allowed on the M1 site. Figure 10. Fe occupancy on the M1 site in LiFe 1 x Mn x PO 4 as a function of synthesis time. The error bars on the refined parameters are smaller than the symbols INFORMATION Corresponding Author * bo@chem.au.dk. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the Danish National Research Foundation (Center for Materials Crystallography, DNRF93) and the Danish Research Council for Nature and Universe (Danscatt). The research was performed on the NPDF instrument at the Lujan Center at Los Alamos National Laboratory supported by DOE-Basic Energy Sciences under FWP #2012LANLE389. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH The synchrotron radiation experiment at the SPring-8 synchrotron was conducted with the approval of the Japan Synchrotron Radiation Research Institute. The RIKEN-SPring8 Center is thanked for access to the BL44B2 beamline. REFERENCES (1) Padhi, A. K.; Nanjundaswamy, K. S.; Goodenough, J. B. J. Electrochem. Soc. 1997, 144 (4), (2) Yamada, A.; Chung, S. C.; Hinokuma, K. J. Electrochem. Soc. 2001, 148 (3), A224 A229. dx.doi.org/ /cm Chem. Mater. 2013, 25,

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222 Nanoscale PAPER View Article Online View Journal View Issue Published on 25 January Downloaded by Aarhus University Library on 25/07/ :16:48. Cite this: Nanoscale, 2013, 5, 2372 Received 11th October 2012 Accepted 22nd January 2013 DOI: /c3nr33127j Introduction Pulsed supercritical synthesis of anatase TiO 2 nanoparticles in a water isopropanol mixture studied by in situ powder X-ray diffraction Jakob Rostgaard Eltzholtz, Christoffer Tyrsted, Kirsten Marie Ørnsbjerg Jensen, Martin Bremholm, Mogens Christensen, Jacob Becker-Christensen and Bo Brummerstedt Iversen* A new step in supercritical nanoparticle synthesis, the pulsed supercritical synthesis reactor, is investigated in situ using synchrotron powder X-ray diffraction (PXRD) to understand the formation of nanoparticles in real time. This eliminates the common problem of transferring information gained during in situ studies to subsequent laboratory reactor conditions. As a proof of principle, anatase titania nanoparticles were synthesized in a 50/50 mixture of water and isopropanol near and above the critical point of water (P ¼ 250 bar, T ¼ 300, 350, 400, 450, 500 and 550 C). The evolution of the reaction product was followed by sequentially recording PXRD patterns with a time resolution of less than two seconds. The crystallite size of titania is found to depend on both temperature and residence time, and increasing either parameter leads to larger crystallites. A simple adjustment of either temperature or residence time provides a direct method for gram scale production of anatase nanoparticles of average crystallite sizes between 7 and 35 nm, thus giving the option of synthesizing tailor-made nanoparticles. Modeling of the in situ growth curves using an Avrami growth model gave an activation energy of 66(19) kj mol 1 for the initial crystallization. The in situ PXRD data also provide direct information about the size dependent macrostrain in the nanoparticles and with decreasing crystallite size the unit cell contracts, especially along the c-direction. This agrees well with previous ex situ results obtained for hydrothermal synthesis of titania nanoparticles. Inorganic nanoparticles form an integral part of diverse human technologies ranging from simple pigments in paints to photoactive centers in solar cells. 1,2 Several synthesis approaches try to span the gap between the control of laboratory synthesis needed for well-de ned particle characteristics and the scalability of industrial production. Few have been as successful as continuous ow hydrothermal (supercritical) synthesis originally introduced by Adschiri and co-workers in In this technique, an aqueous metal salt stream is mixed with a preheated solvent stream for fast initial heating, leading to instantaneous precipitation of inorganic nanoparticles, followed by ripening in a heated reactor before nally quenching the reaction by rapidly cooling the nanoparticle suspension stream. 3 The supercritical ow synthesis method provides superior control of nanoparticle characteristics such as size, Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark. bo@chem. au.dk Electronic supplementary information (ESI) available. See DOI: /c3nr33127j size distribution, morphology, purity and crystallinity, while still allowing high throughput and scalability for possible industrial applications. 4 6 Many groups have reported continuous ow supercritical synthesis of inorganic nanoparticles with ever increasing complexity, including the recently devised approach of supercritical micro uidics However, due to an unavoidable ow inhomogeneity, a distribution of residence times is likely for conventional ow systems. This leads to a broadening of the nanoparticle size distributions. In addition, even an ideal ow reactor has limitations on the residence time, which in practical applications can be neither very short (seconds) nor very long (hours). This brings certain limitations to the types of reactions and chemistry that may be successfully accomplished in a ow reactor. An exempli cation of this is the challenge of producing defect-free LiFePO 4 nanoparticles given the requirement for prolonged synthesis durations. 14 Recently, we reported on the construction of a new type of supercritical reactor, which we coined pulsed supercritical synthesis. 15 The pulsed method makes it possible to rapidly inject a well-de ned volume of a chemical solution into a heated reactor zone in which it stays for a predetermined residence time. Herea er, the product is rapidly ejected from the heated zone into a cooled zone thereby quenching the reaction. Each step of injection is 2372 Nanoscale, 2013, 5, This journal is ª The Royal Society of Chemistry 2013

223 View Article Online Paper Nanoscale Published on 25 January Downloaded by Aarhus University Library on 25/07/ :16:48. undertaken in pulses in contrast to a continuous ow of chemical solution through the heated zone. The result of this is minimal ow inhomogeneity combined with a high degree of control over heating durations leading to a narrowing of the size distribution of the crystalline product, thus removing several limitations of continuous ow reactors. In the development of new reactions in supercritical uids, in situ synchrotron investigations are rapidly gaining popularity Indeed, in situ investigations of chemical reactions or materials under non-ambient conditions are one of the current focus points of materials science with a wide arsenal of structural probes based on both scattering (small-angle scattering, powder diffraction, total scattering) and spectroscopy (infrared, Raman, X-ray absorption spectroscopy) being developed at a rapid pace. All techniques are fundamentally aimed at opening the black box of synthesis and obtaining a direct observation of the reaction or material at hand rather than having to rationalize and infer conclusions from indirect ex situ data. However, one of the main problems with in situ investigations is that the reactors are typically very different from the experimental setups used for particle production in the laboratory. Very o en static reactors are used since ow reactors tend to have non-constant deposition of material on the inner reactor surface or even clogging, making data reduction highly problematic. This dissimilarity between reactors makes it difficult to transfer the knowledge gained from in situ studies to subsequent large scale continuous ow production. 18 Here we resolve this problem by using the exact same reactor for both in situ studies and laboratory nanoparticle production thereby allowing direct transfer of knowledge of optimum parameters. The present paper is the rst time the new pulsed reactor is used in an in situ synchrotron study, and as a test case we have chosen synthesis of anatase TiO 2 nanoparticles. This material is a benchmark nanoparticle material and therefore an excellent proof of principle of the pulse method. This study focuses on the size-development of anatase nanoparticles as dependent on synthesis duration, as this is the key to the industry's need for smaller particles and narrower size distributions. Furthermore, this investigation provides fundamental insights into the growth mechanisms and the macrostrain as a function of size, showing the heavy dependence of the macrostrain on the synthesis route for the TiO 2 system. Experimental section A 1 M precursor solution was prepared from 97% Titanium Tetra-IsoPropoxide (Sigma Aldrich CAS # , TTIP) and isopropanol. The precursor solution was mixed with deionized water in a 1 : 1 ratio immediately prior to the injection into the heated reactor. Six experiments were conducted at a pressure of 250 bar and varying temperatures: 300 C, 350 C, 400 C, 450 C, 500 C, and 550 C. The in situ X-ray diffraction experiments were carried out at beam line ID15B of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The in situ experimental setup is depicted in Fig. 1. Reactant and deionized water were pumped through the two bottom inlets, mixing in the T-piece before being injected into the heated Fig. 1 Setup used for in situ diffraction experiments at ESRF. High-energy X-rays are directed at the reaction chamber and the resulting diffraction is recorded on the detector. Two steel rings are mounted directly on the detector to attenuate the diffraction from the steel reactor itself. reactor tube. Subsequently, nanoparticles formed in the reactor, while sequential X-ray scattering patterns were recorded with a time-resolution of 0.5 seconds, of which the exposure time was 0.4 s and readout was 0.1 s. The steel heat reservoirs are slotted to allow X-rays to penetrate the central reaction-chamber without being absorbed. The diffraction from the polycrystalline steel reactor saturates the detector and physical masking was therefore required. The (111) and (002) steel (austenite) Debye Scherrer rings were attenuated by two semi-circular, 10 mm thick steel rings mounted on the detector (Fig. 1). A monochromatic beam with a wavelength of Å and a beam size of 200 mm 200 mm was used to penetrate the steel reactor. The scattering was detected using a Trixell Pixium 4700 detector. Integrated diffraction patterns were treated by sequential Rietveld re nement using the GSAS package. 24 For a detailed description of the experimental setup, readers are referred to the ESI and the study of Eltzholtz and Iversen. 15 For the ex situ pulsed syntheses, a 1 M precursor solution was prepared from 97% Titanium Tetra-IsoPropoxide (Sigma Aldrich CAS # , TTIP) and isopropanol. The precursor solution was mixed with deionized water in a 1 : 1 ratio immediately prior to injection. The reactor temperature was set to 500 C and a residence time of 100 seconds was used. For the TEM measurements, a single drop of the raw product suspension was diluted in 10 ml isopropanol and evaporated onto a TEM-grid at room temperature. Measurements were performed on a Philips CM20 FEG running at 200 kv. Results and discussion The real-time development of size- and unit cell parameters based on sequential Rietveld re nements of in situ synchrotron PXRD data is shown in Fig. 2. A general expansion of the anatase c-axis with time is observed, whereas the a-axis changes very little (Fig. 2a). The unit cell change is seen to be related to a change in crystallite dimensions (Fig. 2b) as commonly observed for nanocrystallite growth. 25 The nal crystallite size obtained is seen to be a simple function of temperature and residence time, where increased synthesis temperature or residence time yields larger crystallites. Data quality is enhanced with increasing synthesis time and temperature i.e. crystallinity. This journal is ª The Royal Society of Chemistry 2013 Nanoscale, 2013, 5,

224 View Article Online Nanoscale Paper Published on 25 January Downloaded by Aarhus University Library on 25/07/ :16:48. Fig. 2 (a) Unit cell a and c axes for in situ experiments conducted at 300 C, 350 C, 400 C, 450 C, 500 C and 550 C. (b) The crystallite size development of the six runs. For clarity only every 10 th data point has been plotted. The unit cell evolution for the 300 C synthesis has therefore been omitted here and may be observed in the ESI instead. An absolute offset in the a-unit cell dimension is apparent for the 550 C run compared with the other measurements. This is believed to be a systematic error caused by an experimental effect and should not be interpreted as a real offset of the crystal lattice dimensions. This, however, does not affect the relative change in unit cell dimensions during synthesis (see below). Since the in situ experiments were performed with a pulsed reactor identical to what is used for laboratory synthesis, Fig. 2b directly provides the synthesis conditions necessary to obtain titania nanoparticles with a volume weighted crystallite size between 7 and 35 nm. This is in a sense true nanoparticle size control, although a calibration synthesis might be necessary to correct for a possible systematic size-offset. For the design of a given batch of titania nanoparticles utilizing the results shown here, the synthesis temperature has to be considered together with the residence time depending on the desired properties of the particles. Both high temperature and long residence time give larger particles, but higher temperatures will yield particles of higher crystallinity. Longer residence times may, however, be preferable since it makes the sizes less susceptible to slight differences in residence time, yielding a more homogenous product. This has to be balanced against the fact that faster synthesis allows for a decreased batch production time. To check the transferability of the synthesis conditions to actual production, a test synthesis at 500 C with a residence time of 100 s was performed. From Fig. 2b the expected size of this synthesis is about 26 nm, and in Fig. 3a a transmission electron microscopy image of the obtained products is shown. The product can be seen to include both square faceted and smaller round particles. From TEM micrographs, 369 particles were used to construct the size distribution shown in Fig. 3b, which has an average crystallite size of 23(1) nm. The agreement between the volume weighted PXRD size estimate (26 nm) and the number weighted TEM size estimate (23 nm) is good, con- rming that the transfer of parameters between in situ and ex situ syntheses is possible. To broaden our understanding of the growth behaviour observed by the in situ experiments, we attempted to model the initial 10 seconds of all growth curves (Fig. 4a). They are all tted by a linear expression to obtain the initial growth rates for each series. In Fig. 4b the growth rates are plotted and seen to increase with increased temperature as expected. The 550 C series has some outlier points in Fig. 4a, but excluding these ve points only changes the value from 1.49(9) nm s 1 to 1.48(4) nm s 1. This indicates that the steep increase in growth rate above 500 C is a genuine effect. Fig. 3 (a) TEM micrograph of the product from the pulsed synthesis at 500 C and a residence time of 100 s. (b) Size analysis based on 369 particles where the frequency count has been normalized to percent. The average size is 23 (1) nm Nanoscale, 2013, 5, This journal is ª The Royal Society of Chemistry 2013

225 Published on 25 January Downloaded by Aarhus University Library on 25/07/ :16:48. Paper Fig. 4 (a) Initial 10 seconds of anatase particle growth showing linear fits to each series. (b) Growth rates found from the linear fits of the first 10 seconds (20 frames) of each series. The growth of the crystallites provides a way to estimate the activation energy from the fraction or the extent of a reaction as described by the Johnson Mehl Avrami equation, f ¼ 1 exp [ k(t t 0 ) n ] Fig. 5 shows a Sharp Hancock plot of the form ln [ ln(1 f)] ¼ nln(t t 0 )+nln(k), where t is the time, t 0 is the induction time (assumed to be zero in this case), k is the rate constant, n is a number related to the mechanism and f is the extent of the reaction. 29 The extent of the reaction has been de ned as V(t)/V inf (V inf equals the nal stable crystallite volume View Article Online Nanoscale in the speci c synthesis) with the volume calculated from the diameter estimated by the Scherrer equation. This approximation is valid in the beginning of the reaction, when there is no signi cant ripening. The 450 C, 500 C and 550 Cexperiments all exhibit two distinct linear regions, suggesting a change in mechanism during synthesis. A change in reaction mechanisms during hydrothermal processing is not uncommon and has been observed in other systems such as the hydrothermal reactions of layered double hydroxides. 30 Fits to the rst linear region yield the following values: n(450 C) ¼ 1.18(2), n(500 C) ¼ 1.51(1), and n(550 C) ¼ 2.5(1). Typically, values of indicate a diffusion controlled mechanism, indicate a zero-order, rst-order or phase boundary controlled mechanism, and indicate nucleation and growth control. 26,29 In the second linear region, the values fall between 0.8 and 1.0. The activation energy, E a, calculated by the Arrhenius equation k(t) ¼ Aexp( E a /(RT)) may be obtained as the slope of a linear t toln(k) vs. T 1 (Fig. 5d). For the initial nucleation and crystallisation of the nanocrystallites we obtain an activation energy of 66(19) kj mol 1, which is in good agreement with a similar study. 31 As the initial period is described by different growth mechanisms, it is difficult to assign this value to one speci c type of mechanism. The second linear region is represented by a much lower activation energy of 35(4) kj mol 1 which we can describe more precisely as a phase boundary type mechanism. A phase boundary mechanism exhibiting similarly sized activation energy has previously been observed for the transformation of anatase to rutile under solvothermal conditions. No emergence of a rutile phase has, however, been observed in this study. Fig. 6b shows the macrostrain versus size for the c-axis of the three high-temperature runs, calculated from the unit cell parameters as strain c ¼ (c i c in nite )/c in nite 100%, where c in nite is the unit cell c-axis value at in nite time. For the Fig. 5 Sharp Hancock plots of the data from the 450 C, 500 C and 550 C experiments and a rate equation fit to obtain the activation energies. This journal is ª The Royal Society of Chemistry 2013 Nanoscale, 2013, 5,

226 Published on 25 January Downloaded by Aarhus University Library on 25/07/ :16:48. Nanoscale Fig. 6 (a) c-axis macrostrain of the last three runs calculated as strain c ¼ (ci cinfinite)/cinfinite 100%. (b) a-axis macrostrain of the last three runs calculated as straina ¼ (ai ainfinite)/ainfinite 100%. 550 C synthesis, the reaction is so rapid that few data points are available for small crystallite sizes. For both 450 C and 500 C, a negative macrostrain of up to 1% for the c-axis is observed, and compared with literature values (maximum of 0.28% at 5 nm in ref. 32) the strain is very signi cant. The macrostrain observed for the a-axis (Fig. 6a) is similarly negative yet smaller than what is observed for the c-axis. Calculating macrostrain versus crystallite size from an in situ study holds the advantage of providing many data-points per experiment, as opposed to one data-point per synthesis when using the harvested product of a traditional ex situ autoclave synthesis. Furthermore, in ex situ studies it is very difficult to completely control reaction conditions and make different syntheses fully comparable. The macrostrain characteristics of anatase have been found to vary considerably depending on the synthesis route. In the literature this diverse behavior is explained by a variety of mechanisms based on local chemistry and structure. In particular, three effects are believed to play a role in determining the crystal behavior of small oxide nanoparticles: (1) the positive pressure exerted by the increasingly curved surface as crystallites become smaller will tend to compress the structure, View Article Online Paper thus generating a negative macrostrain. 33 The strength of this effect may be strongly modi ed by changes in solution chemistry, as it is a consequence of basic surface energy considerations. 34 (2) The curvature effect will be counterbalanced by the generation of surface dipoles generated from surface-ti dangling bonds coordinated to water in the rst hydration shell. 35 The coordination displaces the Ti-atoms towards the coordinated water molecules, distorting the surface Ti O octahedra of the anatase crystallites. This generates parallel dipoles perpendicular to the crystallite surface repelling each other, thus creating a negative pressure on the crystallites (positive macrostrain). (3) The third macrostrain effect is caused by Ti 4+ vacancies in the structure which also produce a negative pressure on small crystallites. 36 In anatase, the Ti O octahedron is compressed in the edge-sharing plane in order to more effectively screen neighbouring cations, while it is elongated along the c-axis due to the increased in-plane screening. When Ti 4+ vacancies are generated, the surrounding Ti O octahedra relax, leading to an increase in the a,b-parameter and a shortening of the c-parameter. With one effect predicting compression in both directions, one effect predicting expansion in both directions and one effect predicting expansion along c and contraction in the a,b-plane, it is obvious that different outcomes are possible. Table 1 lists the trends observed in the present study together with ve selected previous studies of anatase nanoparticles. Despite the different results, there is a consistency in results produced by similar conditions, and as an example all TTIP-based syntheses produce the same types of strain. The strong negative macrostrain observed in the present study for the c-direction suggests that the effectofcurvatureand/orti 4+ - vacancies dominates over the dipole-effect. The curvature effect should always be present to some extent for any nanosized crystallites. The presence of Ti 4+ vacanciesisindicated by the white color of the synthesized particles. 37 The presence of defects is reasonable since the in situ measurements are conducted far from equilibrium, which means that the structure has not relaxed. The different behavior of the a-axis agrees with the opposed characteristic of Ti 4+ vacancies along the a-axis. The present results are in good agreement with those reported by Zhang et al., who have used a similar synthesis route. 32 The differences in strain depending on synthesis conditions can be used as yet another handle to design titania nanoparticles not only with a speci c size, but also speci c strain properties. Table 1 Macrostrain and unit cell behavior in six different studies of anatase Reference Macrostrain (a-axis) Macrostrain (c-axis) Unit cell volume Synthesis route 38 Positive Negative Expansion Chemical vapor deposition 39 Positive Negative Expansion Combustion ame chemical vapor condensation 35 Negative Positive Expansion TiCl 4 in EtOH and benzyl alcohol 32 Slightly negative Negative Compression Heating of prehydrolyzed TTIP 40 None Negative N/A Heating of prehydrolyzed TTIP This work Slightly negative Negative Compression Heating of prehydrolyzed TTIP 2376 Nanoscale, 2013, 5, This journal is ª The Royal Society of Chemistry 2013

227 Published on 25 January Downloaded by Aarhus University Library on 25/07/ :16:48. Paper Conclusions The present in situ study reports on nanoparticle formation and growth in sub- and supercritical water isopropanol using a pulsed synthesis method. The pulsed synthesis method allows direct transfer of synthesis parameters from in situ experiments to subsequent laboratory scale production, but the robust reactor design also allows data measurement up to rather extreme conditions (P ¼ 250 bar, T ¼ 550 C). The synthesis parameters needed to produce a certain average size of anatase nanocrystals can be found from the size versus temperature/ time plot providing a strong tool for nanoparticle design. The present proof of principle study shows that one can greatly reduce the time and effort spent on optimizing parameters for a speci c synthesis. The in situ growth curves were tted to an Avrami growth model and, based on Sharp Hancock plots, an activation energy of 66(19) kj mol 1 for the initial crystallization was estimated. The in situ experiments also allow study of the macrostrain of titania anatase nanoparticles, where each synthesis run provides many data points under highly controlled conditions. The present results indicate a large negative c-axis macrostrain, which is in good agreement with previous ex situ hydrothermal experiments under similar conditions. Acknowledgements We gratefully acknowledge the ESRF for beam time and assistance during the experiment from Veijo Honkimäki. This work was supported by the Danish Strategic Research Council (Center for Energy Materials), the Danish National Research Foundation (Center for Materials Crystallography), and the Danish Research Council for Nature and Universe (Danscatt). Notes and references 1 D. C. Hurum, A. G. Agrios, K. A. Gray, T. Rajh and M. C. Thurnauer, J. Phys. 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229 Angewandte. Communications Crystal Growth DOI: /anie Understanding the Formation and Evolution of Ceria Nanoparticles Under Hydrothermal Conditions** Christoffer Tyrsted, Kirsten Marie Ørnsbjerg Jensen, Espen Drath Bøjesen, Nina Lock, Mogens Christensen, Simon J. L. Billinge, and Bo Brummerstedt Iversen* Cerium(IV) dioxide (ceria) based materials are attractive in many technological fields owing to their important properties such as ion conduction, reversible oxygen storage, and catalytic activity. [1] Ceria-based nanomaterials can be produced through different synthesis routes including phcontrolled precipitation, microemulsion, mechanochemical processing, and pyrolysis. [2a,b,c,d] In this context, hydrothermal and supercritical syntheses have attracted increasing attention as environmental friendly, readily adjustable one-step routes to the production of a wide variety of crystalline nanomaterials. [3] Nanomaterial properties often depend on their size regime, [4] requiring a detailed knowledge of the many diverse chemical processes and material changes taking place during the synthesis, when the soluble precursor complexes react and grow into stable nanoparticles of the product. However, the extreme conditions of elevated temperatures and pressure needed for hydrothermal/supercritical synthesis necessitate the use of thick-walled reaction chambers, making it difficult to study the chemical processes as they occur (in situ). This can be circumvented by highly penetrating probes such as high-energy X-rays. Here, we present an in situ study on the hydrothermal and supercritical synthesis of CeO 2 nanoparticles using a unique experimental setup that allows direct probing of the reaction mixture with synchrotron X-rays. [5] In situ X-ray scattering studies provide detailed information on the formation and growth of inorganic nanomaterials. [6a,b,c] Powder X-ray diffraction (PXRD) probes the average crystal structure as well as the microstructure of the [*] C. Tyrsted, K. M. Ørnsbjerg Jensen, E. D. Bøjesen, Dr. N. Lock, Dr. M. Christensen, Prof. Dr. B. Brummerstedt Iversen Center for Materials Crystallography Department of Chemistry and inano, Aarhus University Langelandsgade 140, 8000 Aarhus (Denmark) bo@chem.au.dk Prof. Dr. S. J. L. Billinge Applied Physics and Applied Mathematics Columbia University, New York, NY (USA) and Condensed Matter Physics and Materials Science Department Brookhaven National Laboratory, Upton, NY (USA) [**] This work was supported by the Danish National Research Foundation (Center for Materials Crystallography), the Danish Strategic Research Council (Center for Energy Materials), the Danish Research Council for Nature and Universe (Danscatt), and the US National Science Foundation. The Advanced Photon Source is supported by the US Department of Energy, Office of Basic Energy Sciences. Supporting information for this article is available on the WWW under sample, whereas total X-ray scattering and atomic pair distribution function (PDF) analyses make it possible to investigate structures without long-range order, such as discrete clusters in solution and small nanoparticles. Thus total scattering is ideal for in situ studies of precrystalline processes occurring during hydrothermal synthesis. The number of applications of total X-ray and neutron scattering are rapidly increasing, [7a,b,c] but few have attempted to target the highly challenging experimental conditions of hydrothermal and supercritical synthesis. [8a,b] Here, total scattering is used to provide previously unobtainable structural information about the initial transformation of molecular precursor complexes into pristine nanoparticles. In addition, in situ PXRD is used to follow the nanocrystal structure, size, and size distributions. Figure 1. A) A PDF for the precursor solution and B) PDF for CeO 2 nanoparticles 60 seconds after initiation of the synthesis. Molecular complexes present in C) solid (NH 4 ) 2 Ce(NO 3 ) 6 and D) the precursor liquid for CeO 2. E) Atomic arrangement in crystalline CeO 2 nanoparticles, 60 seconds after initiation of the synthesis. The initial transformation from aqueous precursor medium to crystalline CeO 2 nanoparticles was investigated at 200 8C using in situ total X-ray scattering. Figure 1A shows the pair distribution function (PDF) obtained for the dissolved Ce(NH 4 ) 2 (NO 3 ) 6 precursor prior to heating. The cut-off distance of the PDF correlations is approximately 7 Š indicating the presence of local ordering only. In contrast, the low r region of the PDF obtained for well-ordered CeO 2 nanoparticles 60 seconds after initiation of the synthesis is Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2012, 51,

230 Angewandte Chemie displayed in Figure 1B. A significant structural change occurs upon nucleation of CeO 2 as evidenced by the clear change in the shortest Ce-Ce distance (Figure 1A and B). The solidstate structure of the Ce(NH 4 ) 2 (NO 3 ) 6 precursor is wellknown and is comprised of monomeric Ce IV ions octahedrally coordinated to six bidentate NO 3 groups as shown in Figure 1C. [9] However, in solution it takes a different form: the PDF displayed in Figure 1 A reveals that it exists as a structural intermediate between the dissolution of the crystalline precursor and the nucleation of crystalline CeO 2 nanoparticles. The observation of a sharp Ce-Ce peak at around 4.16 Š makes this conclusion unavoidable and suggests a dimer structure for the complex. The structure of this unknown precursor complex was found by fitting the PDF and is shown in Figure 1D. The calculated PDF from this molecular complex (black line, Figure 1A) is clearly visible in the PDF signal and well modeled despite being just about 7 Š in diameter and extracted from a large solvent signal. The molecular complex corresponds to two Ce(NO 3 ) 2 6 octahedrons condensed to form a dimeric structure with the general formula [(OH) 6x (NO 3 ) 6(1 x) CeOCe(NO 3 ) 6(1 x) (OH) 6x ] 6, 2 revealing a partial reaction between dissolved Ce(NO 3 ) 6 complexes. The structure of the CeO 2 nanoparticles obtained 60 seconds after nucleation can be seen in Figure 1E for comparison. The gradual shift of the shortest Ce-O and Ce-Ce interatomic distances of the precursor complex can be observed in Figure 2A together with the corresponding distances for CeO 2 at the time of nucleation. After 3 seconds the dimer complex coexists with pristine CeO 2 nanoparticles exhibiting a considerable difference in the Ce-O and Ce-Ce distances between the two phases. As the solvent reaches the set temperature within the first couple of seconds and nucleation commences, the dimer structure seems to contract, possibly because of weak dimer interactions. During the Figure 2. A) Evolution in the shortest interatomic Ce-O and Ce-Ce distances, d(ce-o) and d(ce-ce), for the precursor complex and CeO 2. B) Normalized time-resolved evolution in the scale factor of the structural models for precursor and CeO 2 nanoparticles. C) Timeresolved evolution in the CeO 2 nanoparticle diameters (d dia ). D) Timeresolved evolution in the reduced pair distribution function. conversion of the dimer into ceria nanoparticles no continuous change in the bond distances is observed. Since the dimer is observed after the existence of nanoparticles, the assembly of dimers into larger clusters must be slow and ratedetermining, because the concentration of these clusters is so low that it cannot be determined experimentally. To explain the pathway of this dimer assembly into ceria nanocrystals seems to to be interesting for future theoretical modeling. The gradual conversion of the precursor material into CeO 2 is quantified in Figure 2B which shows the evolution of the structural scale factors for the precursor and the CeO 2 nanoparticles based on the structural refinement of the time-resolved PDF. [10] At 2008C the conversion of the precursor to the nanoparticles is completed after the first 10 seconds of the synthesis, and a slower evolution takes place over a much wider time-scale. The increase in the CeO 2 nanoparticle diameter after nucleation is shown in Figure 2C together with the time-resolved PDF in Figure 2D. To further study the growth of the nanocrystalline material after nucleation, in situ PXRD measurements were performed at a pressure of 230 bar and temperatures of 200, 300 (subcritical conditions), and 4008C (supercritical water conditions, T> 3748C, P > 221 bar). Figure 3A shows the evolution in the volume-averaged crystallite diameter of the CeO 2 nanoparticles, obtained from Rietveld refinement, and this diameter is shown to be heavily influenced by the synthesis temperature. Under supercritical conditions the crystallite size stabilizes at a diameter of about 16 nm, this diameter decreases to about9 nm at 3008C and about 4 nm at 2008C. Kinetic analysis of the growth curves was performed with a size-impediment model, (D(t) 2 = D 2 max (D 2 max D 2 0 )exp[ k(t t 0 )]). [11] The model parameters include the average grain size D(t), with D 0 and D max being the initial and equilibrium particle sizes, respectively. The growth rate is described by the k parameter, containing information about the specific interface energy and grain boundary mobility. The synthesis duration is described through time t and the onset time t 0. The growth rate can be converted to express the interfacial energy (g) and grain boundary mobility (M) through D 2 max k/2 = 4agM, where a is a geometric constant. [11] The resulting equilibrium grain sizes and growth rates are D(2008C) = 3.56(1) nm, D(3008C) = 8.81(3) nm, D- (4008C) = 15.68(3) nm, k(2008c) = 0.30(3) min 1, k- (3008C) = 0.10(2) min 1, and k(4008c) = 0.65(2) min 1. Using the approximations of constant interfacial energy (g) and equal geometric constants (a) for spherical particles, the mobility is given as M = D 2 max k/8constant, or M = D 2 max k/8, giving M (2008C) = 0.5(1), M (3008C) = 1.0(2) and M - (4008C) = 20.0(6). Thus, the in situ data suggest a highly nonlinear increase in the grain boundary mobility when the synthesis temperature is increased to supercritical conditions. The in situ PXRD data were in addition analyzed by whole powder pattern modeling (WPPM). [12] Figure 3B shows the evolution in the crystallite size distributions, based on data recorded after 10 s, 20 s, 5 minutes, and 20 minutes. As expected the size distributions broaden and shift towards larger crystallite sizes with increased synthesis time. The samples synthesized at 2008C retain a relative narrow size distribution relative to samples synthesized at Angew. Chem. Int. Ed. 2012, 51, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

231 Angewandte. Communications Figure 3. A) Volume-averaged crystallite diameters determined by Rietveld refinement of data obtained for the synthesis of CeO 2 nanoparticles at T = 200, 300, and 4008C. The calculated data points have been binned in a three-to-one ratio to emphasize the growth curves. B) Crystallite log-normal size distributions determined by WPPM of data obtained for the synthesis of CeO 2 nanoparticles synthesized at 2008C (black line; 20 s, 1 minute, and 20 minutes), 3008C (red line; 10 s, 20 s, 5 minutes, and 20 minutes), and 4008C (blue line; 10 s, 20 s, 5 minutes, and 20 minutes). The frequency (Freq.) is defined as the percentage distribution at a given particle diameter. C) Change in the unit cell volume [(V(D) V min )/V min 100%] presented as a function of volume-averaged crystallite diameter for CeO 2 synthesized at T = 200, 300, and 4008C (D% = volume expansion and d dia = crystallite diameter) C, where the size distribution quickly broadens and reaches average sizes above 10 nm. The presence of a narrow crystallite size distribution at an early stage for T= 4008C corresponds well with an earlier study of small-angle X-ray scattering (SAXS) size distributions of CeO 2 synthesized in a continuous flow system at T= 375 8C, with an effective heating duration of about 5 seconds. [13] In the case of TiO 2,it has been shown that increasing the temperature rather than the synthesis time is most effective for improving the crystallinity of the nanoparticles. [14] If this is transferred to the case of ceria, it is likely possible to synthesize very small but highly crystalline CeO 2 nanoparticles with narrow size distribution in less than 20 s under supercritical conditions. Figure 3C shows the evolution in the nanoparticle unit cell dimensions based on Rietveld refinement of the PXRD data. In situ experiments are ideal for studies of sizedependent structural changes as they provide large numbers of directly correlated data, whereas ex situ data suffer from potential systematic differences between data points. The in situ data show a clear enlargement of the unit cell at low crystallite sizes (< 5 nm) whereas the unit cell dimensions are unchanged for sizes larger than 10 nm. Through modeling of the unit cell expansion (green curve in Figure 3C), [15] it is suggested that a unit cell volume expansion of 5% is achievable for 1.6(2) nm nanoparticles. The synthesis of nanoparticles with increased unit cell volumes is interesting as in the case of ceria-based oxygen conductors it has been speculated higher conductivities are achieved owing to a smaller migration enthalpy of the oxygen vacancies. [16a,b] In situ total scattering studies of the hydrothermal synthesis of CeO 2 nanoparticles gives unprecedented insight into the structure of the precursor complexes, which transform into pristine CeO 2 nanoparticles. The total scattering data reveal that a 1m aqueous solution of (NH 4 ) 2 Ce(NO 3 ) 6 consists of dimeric Ce IV nitrate complexes, which upon heating to 200 8C transform into CeO 2 nanoparticles in less than 10 seconds. In situ PXRD data show that highly crystalline 3 4 nm nanoparticles with narrow size distributions can be obtained in seconds for both hydrothermal and supercritical syntheses. The in situ data confirm a strong temperature dependence on the crystallite sizes which stabilize at about 4 nm at 200 8C, about 9 nm at 300 8C, and about 16 nm at 400 8C after 20 minutes of synthesis. The experimentally determined growth curves suggest a nonlinear increase in the grain boundary mobility when transcending from subcritical to supercritical synthesis conditions. A broadening in the nanoparticle size distributions is observed with increasing synthesis temperatures. The crystallographic unit cell was observed to be much increased for small nanoparticles with the bulk value being reached for particles > 10 nm. A maximum expansion of around 1.5% was seen for about 2.5 nm nanocrystals, and the data suggest expansions of up to 5% for particles below 2 nm. The present study provides direct evidence of the possibility to describe both atomic and microstructural changes during the hydrothermal synthesis of inorganic nanomaterials. The generality of the method renders these results a showcase from which important knowledge is obtainable for many different materials. The gained knowledge can in effect be used for the design of shape-tailored nanoparticles with specific properties. Experimental Section In situ measurements: A 1m Ce 4+ aqueous solution prepared from (NH 4 ) 2 Ce(NO 3 ) 6 (Sigma Aldrich, > 98 %) was used for the in situ syntheses in a custom-made capillary reactor pressurized to 230 bar and heated to temperatures of 200, 300, and 4008C. The in situ total scattering PDF experiments were performed at beam line 11-ID-B at the Advanced Photon Source in the USA. In situ PXRD experiments were performed at beam line I711 at MAX-lab in Sweden. The experimental setup used for both the in situ total scattering and PXRD measurements has been described in detail by Becker et al. [5] Data treatment: The integrated total scattering data were analyzed by the PDF method through the PDFgetX3 program (unpublished results). Prior to the Fourier transform, the data were corrected for background scattering using measurements in deionized water in the same capillary at the appropriate temperatures. The resulting PDFs were refined sequentially in PDFfit2 using PDFgui. [10] The structural refinement of CeO 2 is based on crystallographic data from ICSD [17] The structural refinement of the aqueous Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2012, 51,

232 Angewandte Chemie precursor solution is based on crystallographic data on solid cerium oxide nitrate (ICSD-75163). [18] Integrated PXRD data were modeled with the Rietveld method in FullProf Suite. [19] The instrumental contribution to peak-broadening was determined by refinement of a NIST LaB 6 pattern. The size broadening was described using a linear combination of cubic harmonics giving a Lorentzian description of the Bragg peak broadening. [20] The strain contribution to the Bragg peak broadening was taken into account by including a Gaussian profile parameter. Whole powder pattern modeling (WPPM) was performed using the program PM2K. [21] The instrumental profile components were determined by a Cagliotti function fit to the LaB 6 diffraction pattern. [22] The size contributing part was implemented as originating from a log-normal size distribution of nanoscale scattering domains. Dislocation strain contributions were taken into account through a Wilkens model using the edge and screw dislocation contrast factors and Burgers vector modulus for a ceria crystal structure. [21] Received: June 18, 2012 Published online: August 15, 2012 Ḳeywords: crystal growth hydrothermal synthesis nanoparticles X-ray diffraction X-ray scattering [1] A. Trovarelli, Catal. Rev. 1996, 38, [2] a) H. I. Chen, H. Y. Chang, Ceram. Int. 2005, 31, ; b) A. Bumajdad, M. I. Zaki, J. Eastoe, L. Pasupulety, Langmuir 2004, 20, ; c) T. Tsuzuki, P. G. McCormick, J. Am. Ceram. Soc. 2001, 84, ; d) S. J. Shih, K. B. Borisenko, L. J. Liu, C. Y. Chen, J. Nanopart. Res. 2010, 12, [3] a) T. Adschiri, K. Kanazawa, K. Arai, J. Am. Ceram. Soc. 1992, 75, ; b) P. Hald, J. Becker, M. Bremholm, J. S. Pedersen, J. Chevallier, S. B. Iversen, B. B. Iversen, J. Solid State Chem. 2006, 179, [4] V. H. Grassian, J. Phys. Chem. C 2008, 112, [5] J. Becker, M. Bremholm, C. Tyrsted, B. Pauw, K. M. O. Jensen, J. Eltzholt, M. Christensen, B. B. Iversen, J. Appl. Crystallogr. 2010, 43, [6] a) H. Jensen, M. Bremholm, R. P. Nielsen, K. D. Joensen, J. S. Pedersen, H. Birkedal, Y. S. Chen, J. Almer, E. G. Sogaard, S. B. Iversen, B. B. Iversen, Angew. Chem. 2007, 119, ; Angew. Chem. Int. Ed. 2007, 46, ; b) M. Bremholm, M. Felicissimo, B. B. Iversen, Angew. Chem. 2009, 121, ; Angew. Chem. Int. Ed. 2009, 48, ; c) N. Pienack, W. Bensch, Angew. Chem. 2011, 123, ; Angew. Chem. Int. Ed. 2011, 50, [7] a) S. J. L. Billinge, M. G. Kanatzidis, Chem. Commun. 2004, ; b) P. J. Chupas, S. Chaudhuri, J. C. Hanson, X. Y. Qiu, P. L. Lee, S. D. Shastri, S. J. L. Billinge, C. P. Grey, J. Am. Chem. Soc. 2004, 126, ; c) M. Estrella, L. Barrio, G. Zhou, X. Q. Wang, Q. Wang, W. Wen, J. C. Hanson, A. I. Frenkel, J. A. Rodriguez, J. Phys. Chem. C 2009, 113, [8] a) K. M. O. Jensen, M. Christensen, P. Juhas, C. Tyrsted, E. D. Boejesen, N. Lock, S. J. L. Billinge, B. B. Iversen, J. Am. Chem. Soc. 2012, 134, ; b) C. Tyrsted, B. R. Pauw, K. M. O. Jensen, J. Becker, M. Christensen, B. B. Iversen, Chem. Eur. J. 2012, 18, [9] T. A. Beineke, J. Delgaudi, Inorg. Chem. 1968, 7, [10] C. L. Farrow, P. Juhas, J. W. Liu, D. Bryndin, E. S. Bozin, J. Bloch, T. Proffen, S. J. L. Billinge, J. Phys. Condens. Matter 2007, 19, [11] H. Natter, M. Schmelzer, M. S. Loffler, C. E. Krill, A. Fitch, R. Hempelmann, J. Phys. Chem. B 2000, 104, [12] M. Leoni, T. Confente, P. Scardi, Z. Kristallogr. 2006, 23, [13] C. Tyrsted, J. Becker, P. Hald, M. Bremholm, J. S. Pedersen, J. Chevallier, Y. Cerenius, S. B. Iversen, B. B. Iversen, Chem. Mater. 2010, 22, [14] J. R. Eltzholtz, PhD thesis, Aarhus University (DK), [15] M. I. Ahmad, S. S. Bhattacharya, Appl. Phys. Lett. 2009, 95, [16] a) F. Zhang, S. W. Chan, J. E. Spanier, E. Apak, Q. Jin, R. D. Robinson, I. P. Herman, Appl. Phys. Lett. 2002, 80, ; b) B. C. H. Steele, Solid State Ionics 1984, 12, [17] S. Hull, S. T. Norberg, I. Ahmed, S. G. Eriksson, D. Marrocchelli, P. A. Madden, J. Solid State Chem. 2009, 182, [18] N. Guillou, J. P. Auffredic, D. Louer, J. Solid State Chem. 1994, 112, [19] J. Rodríguez-Carvajal, Physica B 1993, 192, [20] M. Järvinen, J. Appl. Crystallogr. 1993, 26, [21] M. Leoni, R. Di Maggio, S. Polizzi, P. Scardi, J. Am. Ceram. Soc. 2004, 87, [22] G. Caglioti, A. Paoletti, F. P. Ricci, Nucl. Instrum. Methods 1958, 3, Angew. Chem. Int. Ed. 2012, 51, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

233 Article pubs.acs.org/jacs Revealing the Mechanisms behind SnO 2 Nanoparticle Formation and Growth during Hydrothermal Synthesis: An In Situ Total Scattering Study Kirsten M. Ø. Jensen, Mogens Christensen, Pavol Juhas, Christoffer Tyrsted, Espen D. Bøjesen, Nina Lock, Simon J. L. Billinge,*,, and Bo B. Iversen*, Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University, DK-8000 Aarhus C, Denmark Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States *S Supporting Information ABSTRACT: The formation and growth mechanisms in the hydrothermal synthesis of SnO 2 nanoparticles from aqueous solutions of SnCl 4 5H 2 O have been elucidated by means of in situ X-ray total scattering (PDF) measurements. The analysis of the data reveals that when the tin(iv) chloride precursor is dissolved, chloride ions and water coordinate octahedrally to tin(iv), forming aquachlorotin(iv) complexes of the form [SnCl x (H 2 O) 6 x ] (4 x)+ as well as hexaaquatin(iv) complexes [Sn(H 2 O) 6 y (OH) y ] (4 y)+. Upon heating, ellipsoidal SnO 2 nanoparticles are formed uniquely from hexaaquatin(iv). The nanoparticle size and morphology (aspect ratio) are dependent on both the reaction temperature and the precursor concentration, and particles as small as 2 nm can be synthesized. Analysis of the growth curves shows that Ostwald ripening only takes place above 200 C, and in general the growth is limited by diffusion of precursor species to the growing particle. The c-parameter in the tetragonal lattice is observed to expand up to 0.5% for particle sizes down to 2 3 nm as compared to the bulk value. SnO 2 nanoparticles below 3 4 nm do not form in the bulk rutile structure, but as an orthorhombic structural modification, which previously has only been reported at pressures above 5 GPa. Thus, adjustment of the synthesis temperature and precursor concentration not only allows control over nanoparticle size and morphology but also the structure. INTRODUCTION It is well established that the material properties of metal and metal oxide nanoparticles are highly dependent on the particle characteristics such as size, shape, and aggregation structure. 1 4 In the development of advanced functional nanomaterials, finding a green and energy efficient synthesis pathway, which allows control over these characteristics, is therefore crucial. In this context, the hydrothermal method is promising, and during the past decades various inorganic micro- and nanoparticles of high crystallinity and homogeneity have been produced using this approach. It has been shown that many of the particle characteristics can be altered by adjusting simple synthesis parameters such as temperature, pressure, precursor concentration, and reaction time. 5 However, the mechanisms controlling particle formation and growth during hydrothermal synthesis are still not fully understood, and to produce nanoparticles with tailor-made characteristics, it is necessary to gain further insight into the processes. We have in a number of studies used X-ray scattering techniques to investigate in situ the hydrothermal synthesis of various inorganic compounds, that is, watching the formation and growth of nanoparticles as it takes place Here, we use in situ total scattering with a time resolution of few seconds in the study of the hydrothermal synthesis of SnO 2, a large gap n-type semiconductor. So far, only a few studies have used the total scattering technique to obtain information about chemical reactions as they happen, and none of these have taken place under hydrothermal conditions. Total scattering and pair distribution function (PDF) analysis, as opposed to conventional crystallographic diffraction methods, allow extraction of structural information from amorphous, nanosized structures as well as crystalline structures because information on both the short- and the long-range order can be obtained. 21,22 The PDF analysis therefore allows for deeper insight into processes taking place during crystallization. In recent years, SnO 2 nanoparticles have been studied extensively for several applications. In 1997, Idota et al. first introduced Sn-based anode materials for Li-ion batteries, 23 and, apart from being a promising anode material, SnO 2 is used in numerous other applications, for example, as a gas sensor, 28 Received: January 30, 2012 Published: March 15, American Chemical Society 6785 dx.doi.org/ /ja300978f J. Am. Chem. Soc. 2012, 134,

234 Journal of the American Chemical Society photo catalyst, and thermoelectric material. 29 Several studies of the hydrothermal synthesis of SnO 2 have been published, and for many applications hydrothermally synthesized particles show superior properties to materials synthesized using high temperature methods. 31,36 38 Here, we use total scattering to reveal the mechanisms behind particle formation and growth. EXPERIMENTS AND DATA ANALYSIS METHODS The SnO 2 nanoparticles were crystallized from aqueous solutions of SnCl 4 5H 2 O (Sigma-Aldrich, 98%) of various concentrations (1, 2, and 4 M). The in situ total scattering measurements were performed at the 11-ID-B beamline at APS, Argonne National Laboratory, U.S. The experimental setup is sketched in Figure 1 and has been described in detail Figure 1. Experimental setup. The synchrotron X-ray beam is monochromatized, hits the nanoparticles inside the reactor, and gets scattered onto the 2D detector. The reactor is heated by a jet of hot air and pressurized by water. elsewhere. 39 The precursor is injected into the reactor, which consists of a thin fused silica tube measuring 0.7 mm in inner diameter and 0.09 mm in wall thickness, ensuring a high transmission of X-rays. The tube is mounted in the setup using Swagelok fittings, pressurized with deionized water, and heated using a jet of hot air coming from below the sample. At the same time as the experiment is initiated by turning on the heating, sequential X-ray exposures are started. The efficiency of the heater combined with the small volume of the capillary ensures very fast heating, and the desired temperature is reached within seconds after initiation of the experiment. For all experiments, the pressure was set to 250 bar, whereas the temperature was varied between 160 and 350 C. A Perkin- Elmer amorphous silicon detector measuring cm 2 was placed 226 mm from the sample. The X-ray wavelength was Å, and q-max was 21 Å 1. The time resolution of the data was 7 s. Article The raw total scattering data were integrated in Fit2D, 40 and the PDFs were subsequently obtained using PDFgetX3 (unpublished). Scattering from the capillary with deionized water at the appropriate conditions was subtracted from the integrated pattern before using data in the q-range from 0.6 to 19.5 Å 1 in the Fourier transformation. The PDFs were modeled to extract structural and microstructural parameters using SrFit (unpublished) and PDFgui. 41 Furthermore, the data were analyzed by Rietveld refinement using the FullProf Suite. 42 Synchrotron powder X-ray diffraction (PXRD) experiments were also performed at beamline i711 at MAXII, MAX-lab, Sweden, using the same experimental setup. For these experiments, the pressure was again fixed at 250 bar, whereas the temperature was varied from 160 to 250 C. Experiments using both 1 and 2 M precursor were done. The PXRD data were integrated using Fit2D 40 and treated by single peak fitting. The wavelength was 1.00 Å, and the detector-to-sample distance was mm. The detector was an Oxford Diffraction Titan CCD measuring 16.5 cm in diameter. The time resolution of the data was 4 s, and q max was 3.8 Å 1. Nanoparticles synthesized in the same reactor in our home laboratory using 2 M SnCl 4 5H 2 O (Sigma-Aldrich, 98%) at 250 C and 250 bar for 5 min were used for ex situ TEM characterization. The TEM characterization was done using a Phillips model CM20 TEM microscope working at 200 kv. Because of inhomogeneous heating of the capillary when moving away from the center of the tube, care has to be taken when comparing X-ray data collected from the center of the reactor with TEM data measured on material collected from the entire hot zone of the reactor. RESULTS AND DISCUSSION Structures in Aqueous Solutions of SnCl 4. Figure 2A shows room-temperature total scattering data from the precursor at different concentrations. It is clear that the concentration of SnCl 4 dramatically affects the scattering pattern. The structural differences can be understood by considering the reduced pair distribution functions (PDF) shown in Figure 2B. In the data for the 2 and 4 M SnCl 4 solutions, a large peak is present at r 2.4 Å along with several smaller peaks at 3.3 Å. These features agree well with the formation of [SnCl x (H 2 O) 6 x ] (4 x)+ complexes, which has been reported in NMR studies of SnCl 4 solutions. 43 Sn 4+ and Cl have Shannon ionic radii of 0.55 and 1.81 Å, respectively, giving Figure 2. (A) Raw total scattering data from 1 M (red), 2 M (green), and 4 M (blue) solutions of SnCl 4 5H 2 O at room temperature. The scattering pattern from the capillary filled with water is shown in black, almost overlapped by the pattern from the 1 M solution. (B) PDFs obtained from the data shown in (A). The scattering pattern from water has been subtracted prior to the Fourier transformation. (C) Fit of mer-[sncl 3 (H 2 O) 3 ] to data recorded of 2 M SnCl 4 at room temperature. The thick black curve shows the observed G(r), the red curve the model, and the blue the difference between the two. (D) mer-triaquatrichlorotin(iv). (E) Hexaaquatin(IV) dx.doi.org/ /ja300978f J. Am. Chem. Soc. 2012, 134,

235 Journal of the American Chemical Society Article Figure 3. (A) Raw total scattering data from 1 M (red), 2 M (green), and 4 M (blue) solutions of SnCl 4 5H 2 O after 6 min at 200 C. The black line shows the total scattering from the capillary filled with water at 200 C. (B) PDFs obtained from the data shown in (A), using the same color codes. (C) Fit to the G(r) obtained after 30 min at 250 C, 2 M. The observed G(r) is shown by the thick black line, with the calculated in red. The contribution from the [SnCl 3 (H 2 O) 3 ] + is shown in orange and from SnO 2 in green. The blue line in the bottom of the graph is the difference between the total calculated G(r) and the observed G(r). Sn Cl bond lengths of ca Å, 44 that is, close to the r-value for the most intense peak. A model describing the complex was applied as shown in Figure 2C. The NMR study of SnCl 4 solutions showed formation of several species with different stoichiometries such as [SnCl 4 (H 2 O) 2 ] and [SnCl 3 (H 2 O) 3 ] + in different quantities. 43 However, to reduce the number of parameters, only one complex was included in the final model, mer-[sncl 3 (H 2 O) 3 ] + (Figure 2D), which has the weighted average stoichiometry of the species reported in 2 M SnCl 4 solution. 43 To simplify the model, H 2 O was replaced by O. The refinement of the model gave Sn Cl and Sn O distances of 2.42 and 2.26 Å, respectively, which agrees well with single-crystal diffraction studies of cis-[sncl 4 (H 2 O) 2 ] reporting Sn Cl distances of Å and Sn O distances between 2.15 and 2.30 Å. 45 The shoulder at 2.02 Å does not originate from the aquachlorotin(iv) complex, but can be ascribed to the Sn O distances in [Sn(OH 2 ) 6 ] 4+ (Figure 2E), which is believed to form simultaneously with [SnCl x (H 2 O) 6 x ] (4 x)+ species. Sn 4+ is a Lewis acid, and hexaaquatin(iv) is therefore partially deprotonated, yielding an acidic solution and complexes of the type [Sn(H 2 O) 6 y (OH) y ] (4 y)+. No significant structural features from either complex are seen in the PDF from the 1 M solution. This is most likely due to the relatively low concentration of the precursor, which makes the scattering signal from Sn species insignificant as compared to that of the water in the capillary. Formation of SnO 2 Nanoparticles. In Figure 3A are shown the raw data collected after 6 min at 200 C, and Bragg peaks from crystalline SnO 2 nanoparticles are clearly visible. Figure 3B shows the PDFs obtained from the total scattering in Figure 3A. Here, all significant peaks above r = 3.5 Å can be ascribed to the rutile SnO 2 structure; however, for the 2 and 4 M experiments, the Sn Cl peak is still present, and it remains in the PDF throughout all experiments performed with the high precursor concentrations. The metal complexes present in the precursor solution are the building blocks for the SnO 2 nanoparticles, and the precise formation mechanism was elucidated by modeling the PDFs of mer-[sncl 3 (H 2 O) 3 ] + and the SnO 2 nanoparticles simultaneously, as is illustrated in Figure 3C. In the modeling of the timeresolved data, the scale factor for mer-[sncl 3 (H 2 O) 3 ] + was refined along with the bond distances and the anisotropic thermal parameters for the ligands. These were restrained such that the factors expressing the vibrations along the bond (longitudinal) were all constrained to take the same value, u l, and all vibrations perpendicular to the bond (transverse) were constrained to one value, u t. For the crystalline phase, the scale factor, the unit cell, the atomic positions, and the isotropic thermal parameters were refined. Additional examples of the fits are shown in the Supporting Information along with the resulting parameters. The time- and temperature-dependent scale factors obtained from the modeling are plotted in Figure 4A. In the beginning of Figure 4. (A) Normalized scale factors for the complex (open symbols) and SnO 2 (closed symbols). Black symbols show the data for 2 M and 160 C, blue 2 M and 200 C, green 2 M and 250 C, and red 2 M and 350 C. (B) G(r) calculated from the three first frames of the experiment done at 200 C and 2 M. (C) Formation mechanism for SnO 2 nanoparticles, where Sn 4+ is shown as red, and O 2 as blue. H + is not shown. [Sn(H 2 O) 6 y (OH) y ] (4 y)+ units cluster together and form SnO 2 nanoparticles of the rutile structure, where Sn is octahedrally coordinated. the reaction, the SnO 2 scale factor rapidly increases, but interestingly a similar decrease in the value for the aquachlorotin(vi) complex scale factor is not observed. This is also evident in the PDFs obtained for the first few frames after the initiation of the experiment, as shown in Figure 4B, where the intensity of the Sn Sn peak at ca Å increases significantly more than the Sn Cl intensity at 2.36 Å decreases. This shows that the SnO 2 nanoparticles do not form directly 6787 dx.doi.org/ /ja300978f J. Am. Chem. Soc. 2012, 134,

236 Journal of the American Chemical Society Article Figure 5. (A) G(r)s obtained from the frames recorded after 10 min for the experiments performed with 2 M precursor. The refined sp-diameter is marked by the black ticks. (B) The sp-diameters plotted as function of time for all experiments. The insert shows the size region from 3.5 to 4.5 nm. The growth curves from the three experiments done at 160, 180, and 200 C with 2 M are almost completely overlapping. from the Sn 4+ ions bound in the chloride complex, but from Sn 4+ ions coordinated in the hexaaquatin(iv) complex. The Sn O peak at 2.02 Å remains constant in intensity as SnO 2 nanoparticles form, and indeed the Sn O bond length in the crystalline SnO 2 refines to an identical bond length value. Overall, the data conclusively show that the SnO 2 nanoparticles must form from clustering of octahedrally coordinated aquahydroxotin(iv) complexes as illustrated in Figure 4C, and the formation mechanism can be written as: [Sn(H O) (OH) ] 2 6 y (4 y) + y (aq) SnO (s) + yh O(l) + (4 y)h O (aq) As the reaction progresses, that is, as the aquahydroxotin(iv) units form solid SnO 2, aquachlorotin(iv) slowly disproportionates, causing more and more tin to form SnO 2 as is seen in the gradual decrease of the mer-[sncl 3 (H 2 O) 3 ] scale factor. The Cl Cl peak at 3.32 broadens as the heating is initiated and can subsequently no longer be distinguished from the SnO 2 peaks. The broadening of the peak is due to strong thermal vibrations of the ligands transverse to the Sn ligand bond. This is discussed in further detail in the Supporting Information. Growth of Nanocrystalline SnO 2. The spatial extent of the correlations in the PDF provides information about the growth of the nanoparticles as illustrated by the G(r) in Figure 5A. The data shown were all recorded after 10 min with the 2 M precursor at different temperatures. It is clear that increasing the synthesis temperature extends the PDF oscillations to larger r-values. However, to get an estimate of the particle size, the instrumental resolution has to be taken into account, because this dampens the oscillations at high r and causes them to completely disappear above 60 Å. Therefore, both the instrument effect and the particle size were included in the model. Examples of the fits along with the resulting parameters and estimated standard deviations are given in the Supporting Information. The resulting spherical particle diameters (spdiameter parameter) are shown in Figure 5B. The results for the 2 M experiments clearly reveal that it is possible to control the particle size by means of the reaction temperature. This is seen when comparing the growth curves obtained from the 200, 250, and 350 C syntheses. However, below 200 C, the particle size is not temperature dependent and appears to be stable around 4 nm, as shown in the inset in Figure 5B. The effect of SnCl 4 concentration on particle size can be seen when comparing the growth curves from the + syntheses done using 1, 2, and 4 M at a reaction temperature of 200 C. With increasing precursor concentration, the particles grow larger, and to synthesize very small particles (<4 nm), the SnCl 4 concentration should be reduced to 1 M or less. Note that for the experiment done at 350 C with 2 M precursor, particle sizes well above the instrumental resolution limit are obtained, and for these values the uncertainties are significant. The growth mechanisms at different temperatures can be understood when considering the increase in particle volume along with the total amount of SnO 2 nanoparticles formed. The volumes of the particles, calculated as V = (sp) 3, are plotted with the scale factors in Figure 6. For the 180 C experiments, Figure 6. Normalized scale factor (black) plotted with the particle volume (red). (A) 180 C, 2 M; (B) 250 C, 2 M. the growth curves and scale factors follow exactly the same path; that is, the particles grow because more SnO 2 can be formed from hexaaquatin(iv). The same behavior is observed for 160 and 200 C (see Supporting Information). However, at 250 C, the scale factor first increases rapidly, and then stabilizes after ca. 5 min. After the stabilization of the scale factor, the particle volume continues to increase, indicating particle growth by Ostwald ripening. This explains the different 6788 dx.doi.org/ /ja300978f J. Am. Chem. Soc. 2012, 134,

237 Journal of the American Chemical Society Article dependency of the particle size on temperature below and above 200 C. The data were also treated by Rietveld refinement, and details are given in the Supporting Information. In q-space, the particle growth can be studied by applying the Scherrer equation, 46 stating that the peak width is related to the volume weighted size of the coherently diffraction domains, that is, crystallites, although this becomes unreliable for very small particle sizes. The Rietveld fits improve when the particles are allowed to elongate along the c-axis; that is, the particles are not spherical. Despite underestimating the absolute crystallite size as compared to the PDF, the Rietveld refined anisotropy should be reliable. The refined volume weighted particle sizes are shown in Figure 7A and B. The aspect ratio between the sizes Figure 8. LSW fits to the data for the experiments from 160 to 250 C with 2 M. The data points are shown as black dots, with the fit as a red line. The expression D(t) D 0 =k (t t 0 ) 1/x was fitted for t between 1 and 30 min. D is the particle diameter in the a direction at time t, D 0 was chosen as the diameter at time t 0 = 1 min, while k and x were free variables. case, x should take a value of 3, and this is close to the results obtained here. From 160 to 200 C, the diffusion is expected to be limited by the amount of Sn 4+ found as [Sn- (OH 2 ) 6 y (OH) y ] (4 y)+. At higher temperatures, where the growth happens by Ostwald ripening, small particles need to be dissolved to provide precursor for growth of the larger nanoparticles. Structural Changes of SnO 2. Figure 9A and B shows the changes in unit cell parameters, c c final and a a final,asa function of the particle size obtained in the Rietveld refinement. Figure 7. (A) Volume weighted crystallite sizes along the crystallographic a/b direction, obtained from Rietveld refinement. (B) Volume weighted crystallite sizes along the c direction. (C) Crystallite aspect ratio (D a /D c ). All results shown are from the 2 M experiments, with the black lines being the results at 160 C, dark blue at 180 C, light blue at 200 C, green at 250 C, and red at 350 C. in the a/b- and c- direction is shown in Figure 7C. This plot shows that not only the particle size, but also the aspect ratio can be controlled by the synthesis temperature. Generally, the volume weighted crystallite sizes obtained from Rietveld analysis are smaller than the particle sizes obtained in the PDF analysis, but the time and temperature trends of the growth are similar. The growth mechanisms were further studied by doing kinetic analysis (Lifshitz Slyszov Wagner (LSW) theory) of the growth curves in the crystallographic a direction as shown in Figure 8. The expression D(t) D 0 = k (t t 0 ) 1/x was fitted to the growth curves for the 2 M experiments from 160 to 250 C between 1 and 30 min. D is the particle diameter at time t, D 0 is the diameter at time t 0, while k and x are free variables. The resulting values and fits are shown in Figure 8. x is dependent on the growth mechanism, and the LSW theory states that if the volume of the particles increases linearly with time, then the reaction is limited by diffusion of the precursor, and not by the reaction at the surface of the particles. 47 In this Figure 9. Changes in the unit cell plotted as function of particle size D a for the 2 M experiments. (A) Changes in the a-axis (a a final ). (B) Changes in the c-axis (c c final ). The black lines show the results from 160 C, dark blue are for 180 C, light blue for 200 C, green for 250 C, and the red is for 350 C dx.doi.org/ /ja300978f J. Am. Chem. Soc. 2012, 134,

238 Journal of the American Chemical Society Only changes in the parameters within each experiment are considered because the absolute values are somewhat uncertain due to the necessary lack of internal standard in the in situ experiments. As the particles grow, the unit cell decreases along the c-direction. This effect is much smaller in the a-direction, and the size-dependent structural changes are therefore anisotropic. Expansion of the bulk unit cell in nanoparticles is well-known for many metal oxide systems, and different explanations have been given, such as valence reduction, 48 stacking faults, 23 and surface defect effects. 49 The present in situ data are not of sufficient quality to probe in detail the origin of the unit cell size dependency as reliable values for the precise occupancies and atomic positions cannot be extracted. For further analysis of the size/structure effect, high-quality, lowtemperature ex situ X-ray and neutron total scattering data are needed. The PXRD experiments at MAX-lab provide additional information about the relation between nanosized particles and crystal structure. For the experiments using 1 M, the diffraction peaks are abnormally broad as is especially clear for the (110) peak at ca. 17 shown in Figure 10. For the 180 and 250 C particles. However, these studies only show formation of the α- PbO 2 polymorph, whereas the CaCl 2 structure has not earlier been reported as a stable phase due to size effect. The bulk phase and the first high pressure phase are closely related, as is seen in the unit cell parameters in Table 1, and Table 1. Structures of SnO 2 phase space group bulk phase P42/ mnm Article structure type lattice unit cell 55 rutile tetragonal a = Å, b = Å, c = Å phase II, HP Pnnm CaCl 2 orthorhombic a = Å, b = Å, c = Å phase III, HP Pbcn α-pbo 2 orthorhomic a = Å, b = Å, c = Å, phase IV, HP Pa3 distorted flourite cubic a = Å distinguishing between the two structures is quite difficult due to the large peak broadening and the lack of an internal standard. Therefore, only a crude model with few parameters was used to extract the phase fractions. The weight percent of the orthorhombic/tetragonal phase was therefore roughly estimated by simply fitting Gaussian curves to the (110) peaks and determining the ratio between the two intensities. The results are shown in Figure 11. For the 1 M, 160 C data, it Figure 10. Section of the PXRD frames collected 3 min after initiation of the experiments showing the (110) peaks of the SnO 2 structures. The data points are seen as black dots, and the fitted Gaussian curves are shown as red lines. For the experiments done with 1 M SnCl 4 at C, double peaks were observed, and these were fitted with two Gaussians, shown in blue and light blue. data, the line shape is clearly not symmetric. This could be due to the coexistence of two different polymorphs of SnO 2, the bulk tetragonal phase and an orthorhombic modification. The orthorhombic phase is a high pressure polymorph, and it has been reported to exist in the bulk phase above 5 GPa. 50 The high pressure polymorph has the CaCl 2 structure (space group Pnnm) and forms through a second-order phase transition from the tetragonal phase. At pressures above 12 GPa, this structure turns into another orthorhombic phase (α-pbo 2 structure), and at even higher pressures a cubic phase becomes stable. Earlier studies of tin oxide nanostructures have reported the formation of the high pressure polymorphs due to the large surface-tovolume ratio of the nanoparticles, elevating the pressure on the Figure 11. The ratio between the intensity from the tetragonal (110) peak and the sum of the tetragonal and orthorhombic peak intensities. is not clear whether one or two phases were present; the peak shows slight asymmetry, but it is not possible to get a stable fit using two Gaussian functions. Therefore, the 1 M 160 C data will not be considered any further. For all of the 2 M data, only the bulk tetragonal rutile phase was present. At 1 M and 180 C, the tetragonal phase fraction is 30%, whereas at 250 C, this fraction has increased to 50%. The fractions are constant throughout the experiments. This shows that by choosing appropriate hydrothermal synthesis parameters, not only the size and the morphology of the nanoparticles can be controlled, but also the specific crystal structure. CONCLUSIONS The PDF method applied to total scattering data provides information about noncrystalline compounds that cannot be obtained using conventional crystallographic techniques. This opens a huge uncharted territory for in situ studies of chemical 6790 dx.doi.org/ /ja300978f J. Am. Chem. Soc. 2012, 134,

239 Journal of the American Chemical Society Article reactions. On the basis of in situ total scattering experiments, the formation mechanism for SnO 2 nanoparticles from aqueous solutions of SnCl 4 was established. When dissolving the precursor, both [SnCl 6 x (H 2 O) x ] (4 x )+ and [Sn- (H 2 O) 6 y (OH) y ] (4 y)+ are present in the solution, but the SnO 2 nanoparticles crystallize uniquely from Sn 4+ ions coordinated to H 2 O/OH. The nanoparticle size and aspect ratio can be controlled by adjusting the precursor concentration, the reaction temperature, and time. The growth is found to be limited by diffusion of precursor to the growing nanoparticle, but only at temperatures above 250 C do the particles grow by Ostwald ripening. The c-axis of the unit cell is found to be dependent on the particle size, and it expands for small particle sizes. The a-axis is found to be almost independent of particle size. For very small particles (<4 nm), the high pressure orthorhombic polymorph of SnO 2 is observed (CaCl 2 structure). Thus, adjustment of hydrothermal synthesis parameters not only provides control over particle size and morphology, but also over the crystal structure. ASSOCIATED CONTENT *S Supporting Information Details and examples of the refinements of the PDFs (PDFgui and SrFit). Details and examples on the Rietveld refinement and size determination (FullProf). TEM image of SnO 2 nanoparticles. This material is available free of charge via the Internet at AUTHOR INFORMATION Corresponding Author sb2896@columbia.edu; bo@chem.au.dk Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by The Danish Strategic Research Council (Center for Energy Materials), the Danish National Research Foundation (Center for Materials Crystallography), and the Danish Research Council for Nature and Universe (Danscatt). MAX-lab and the Advanced Photon source, APS, are acknowledged for beamtime. Work in the Billinge group was supported by the U.S. National Science Foundation through grant DMR Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH Do rthe Haase (MAXlab), Kevin Beyer (APS), Peter Nørby (Aarhus University), Jacob Becker (Aarhus University), and Per Runge Christensen (Aarhus University) are thanked for assistance during the experiments. REFERENCES (1) Kim, C.; Noh, M.; Choi, M.; Cho, J.; Park, B. Chem. Mater. 2005, 17, (2) Ansari, S. G.; Boroojerdian, P.; Sainkar, S. R.; Karekar, R. N.; Aiyer, R. C.; Kulkarni, S. K. Thin Solid Films 1997, 295, 271. (3) Burda, C.; Chen, X. B.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, (4) Daniel, M. C.; Astruc, D. Chem. Rev. 2004, 104, 293. (5) Byrappa, K.; Adschiri, T. Prog. Cryst. Growth Charact. 2007, 53, 117. 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241 PHYSICAL REVIEW B 86, (2012) Lattice dynamics reveals a local symmetry breaking in the emergent dipole phase of PbTe Kirsten M. Ø. Jensen, 1 Emil S. Božin, 2 Christos D. Malliakas, 3 Matthew B. Stone, 4 Mark D. Lumsden, 4 Mercouri G. Kanatzidis, 3,5 Stephen M. Shapiro, 2 and Simon J. L. Billinge 2,6 1 Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University, Denmark 2 Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA 3 Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA 4 Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5 Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA 6 Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA (Received 14 May 2012; published 20 August 2012) Local symmetry breaking in complex materials is emerging as an important contributor to materials properties but is inherently difficult to study. Here we follow up an earlier structural observation of such a local symmetry broken phase in the technologically important compound PbTe with a study of the lattice dynamics using inelastic neutron scattering (INS). We show that the lattice dynamics are responsive to the local symmetry broken phase, giving key insights in the behavior of PbTe, but also revealing INS as a powerful tool for studying local structure. The new result is the observation of the unexpected appearance upon warming of a new zone center phonon branch in PbTe. In a harmonic solid the number of phonon branches is strictly determined by the contents and symmetry of the unit cell. The appearance of the new mode indicates a crossover to a dynamic lower symmetry structure with increasing temperature. No structural transition is seen crystallographically, but the appearance of the new mode in inelastic neutron scattering coincides with the observation of local Pb off-centering dipoles observed in the local structure. The observation resembles relaxor ferroelectricity, but since there are no inhomogeneous dopants in pure PbTe this anomalous behavior is an intrinsic response of the system. We call such an appearance of dipoles out of a nondipolar ground-state emphanisis meaning the appearance out of nothing. It cannot be explained within the framework of conventional phase transition theories such as soft-mode theory and challenges our basic understanding of the physics of materials. DOI: /PhysRevB PACS number(s): Pa, dd, Gk, Nx I. INTRODUCTION The unexpected appearance, on warming, of local Pb off-centering dipoles was recently reported in PbTe. 1 No structural transition is seen in the average rock-salt crystal structure but is apparent in the local structure on warming above 100 K: the local symmetry is lowered, losing its centrosymmetry, upon warming. We refer to this as emphanisis meaning the appearance of something from nothing since it is fundamentally different from a normal ferroelectric transition where dipoles exist at low temperature but become disordered and fluctuating at high temperature. Here the dipoles appear upon warming from a ground state with no dipoles. In the original study 1 the dipoles were deemed to be fluctuating, but this could not be determined from the experiment itself. A recent inelastic neutron scattering (INS) study 2 noted the anharmonicity of certain phonons down to low temperature in PbTe. Here we present a detailed temperature-dependent INS study of the phonons in the temperature range where the local dipoles appear. 1 Below room temperature our results are in good agreement with earlier work on PbTe, 3,4 and we also see the significantly anharmonic signal of the zone center transverse optical (TO) mode reported by Delaire et al. 2 However, the main result of this work is the characterization of the anharmonic features at 6 mev as a new mode with a highly anomalous temperature dependence, growing rapidly in spectral weight with increasing temperature above 100 K, at the expense of the normal TO mode that is the incipient ferroelectric mode. 4 The new mode and the original TO mode coexist over the entire temperature range measured to 600 K, resulting in an additional phonon branch in the Brillouin zone indicative of a broken symmetry, though none is seen in the average structure. The new mode is broad with a short lifetime, but dispersive. It also hardens with increasing temperature. Since it appears over the same temperature range where local dipoles appear in the structure 1 we associate its appearance with the appearance of these objects that break the local, though not the average, centrosymmetric symmetry. Such behavior, observed in a pure binary alloy system, has not been described before and challenges our current understanding of the physics of materials. II. RESULTS We first consider the lattice dynamics at room temperature and below, and compare our measurements to earlier results in the literature 2 4 to establish the quality of our sample and data. Figures 1(a) 1(c) show representative room temperature INS constant Q scans, at three points in the Brillouin zone, collected on the HB3 triple axis spectrometer at Oak Ridge National Laboratory (ORNL). Details of the data collection are described in the Materials and Methods section below. As illustrated in the inset to Fig. 1, the points in reciprocal space are (a) (033), which is a zone boundary K point 5 in a position such that the instrument is sensitive to transverse polarized modes, 6 (b) ( ), which is a zone boundary L point sensitive to longitudinal modes, and (c) (133), which is a Brillouin zone center (Ŵ point) where both longitudinal and transverse modes can be measured. Certain phonon branches are expected based on the earlier work of Cochran et al., 3 the energy transfers of which are indicated by red dashed lines /2012/86(8)/085313(7) American Physical Society

242 KIRSTEN M. Ø. JENSEN et al. PHYSICAL REVIEW B 86, (2012) FIG. 1. (Color online) INS spectra of a PbTe single crystal at 288 K at different Q points in reciprocal space: (a) (0 3 3) zone edge, (b) ( ) zone edge, and (c) (1 3 3) zone center. The red dashed lines indicate the phonon energies measured by Cochran et al. (Ref. 3) for comparison. The inset in (c) is a schematic of the plane of reciprocal space that the triple axis spectrometer was set to work in. The grey dots are the reciprocal lattice points, and the lines are Brillouin zone boundaries. The red, pink, and blue dots are the Q points for the data shown in (a) (K point), (b) (L point), and (c) (Ŵ point), respectively. (d) (f) show false color plots of the intensity (color axis) vs energy transfer, E = hω, and temperature of the same modes shown in the panels above. (g) (i) show representative fits of Lorentzian peaks (in red) to the TO mode at the [133] zone center spectra: (g) 2 K, (h) 134 K, and (i) 231 K. The vertical dashed lines are the extracted mode energies ω. (j) ω 2 vs T for all the temperatures fit in the temperature range below 300 K with a straight line fit to the data shown in red. in Fig. 1. There is good semiquantitative agreement with the earlier results. Figures 1(d) 1(f) shows a false-color plot of the scattered intensity as a function of temperature and energy transfer, E = hω, for the same three Q points. The K-point modes in Fig. 1(d) do not change energy at all vs temperature, neither do they broaden significantly. This is expected in a harmonic system, but even in a quasiharmonic approximation where lattice expansion is taken into account it is common to see softening with increasing temperature. 7 The longitudinal acoustic/longitudinal optical (LA/LO) doublet at the L point shown in Fig. 1(e) does appear to broaden with increasing temperature though the peak contains two components that are both softening with increasing temperature. Fits to the line shapes suggest that there is little broadening of the individual lines. Qualitatively, the softening of these modes may be explained by a quasiharmonic analysis. We now consider the zone-center TO mode in Figs. 1(c) and 1(f). This mode is the soft mode that indicates an incipient ferroelectric phase transition in PbTe. 4 The mode softens with decreasing temperature (the opposite of the L-point modes and opposite to early density functional theory (DFT) calculations 8 ) but never reaches zero frequency. A softening to zero frequency would indicate the soft-mode transition temperature 9 and a structural phase transition. It is immediately apparent that the mode is anomalously broad as pointed out recently. 2 The zone edge modes in Figs. 1(a) and 1(b) have a FWHM of around 1.5 mev which is close to the calculated energy resolution of the instrument, as described in Materials and Methods below. However, the high-energy tail on the zone center TO mode is of the order of 5 mev. The temperature dependence of this scattering feature is shown in a false-color plot in Fig. 1(f). This feature in the scattering is seen to broaden dramatically with increasing temperature and is highly asymmetric and non-gaussian. 2 To study the temperature dependence of this mode in greater detail we have fit curves to the spectra at each temperature. We focus initially on the low-temperature region, T<300 K. We would like to see if our data reproduce the earlier results of Alperin et al. 4 Reasonable fits could be made to the scattering features by fitting a Lorentzian peak on a linear

243 LATTICE DYNAMICS REVEALS A LOCAL SYMMETRY... PHYSICAL REVIEW B 86, (2012) the imaginary part of the dynamic susceptibility according to 6 S( Q,ω) = χ ( Q,ω) ( ). 1 e hω k B T FIG. 2. (Color online) Plots of the INS spectrum at Q = (133). From the bottom (pale blue) the temperatures shown are 28, 99, 203, 299, 410, 486, and 601 K (topmost curve). Datasets are offset with respect to each other by 75 intensity units for clarity. The two arrows are guides to the eye, indicating the positions of the TO and the new mode at the highest temperature. Both modes soften upon cooling. sloping background, and from this we extracted the mode frequency. Three of these fits are shown in Figs. 1(g) 1(i). The temperature dependence is shown in Fig. 1(j). For a mean-field, second order phase transition, the soft mode theory predicts that the frequency of the soft mode approaches zero as (T T c ) 0.5, 9 soaplotofω 2 versus T will be linear and intercept the abscissa at transition temperature T c. It is clear that the zone center mode softens upon cooling according to mean-field soft mode theory but still has a positive frequency at T = 0: PbTe is an incipient ferroelectric but, in the absence of alloying with Ge, 10 does not undergo a ferroelectric phase transition upon cooling. There is excellent agreement with the earlier work. 4 Extrapolating the line to the abscissa we obtain a putative phase transition temperature of 151 K. This is a little more negative in temperature than Alperin et al. 4 ( 135 K) but in good general agreement, and it establishes the purity of our crystal. Having established that data from our sample are in good agreement with earlier work, we move to the main result of the current study. In Fig. 2 we show the temperature dependence of the zone center TO mode feature over a wide temperature range extending to high temperature. Over a narrow temperature range beginning above 100 K a new peak grows up rapidly but smoothly from the high energy tail of the TO mode, gaining spectral weight at the expense of the TO mode, but coexisting with it. Above room temperature the new peak becomes very strong, dominating the original TO feature. It indicates the presence of a new mode in the system that appears upon increasing temperature, which is highly anomalous. The neutron scattering dynamic structure factor S( Q,ω) is the normalized inelastic scattering intensity and is related to For a particular phonon mode in the sth branch at position Q = G q in reciprocal space, where G is a reciprocal lattice vector and q is a vector that lies within a single Brillouin zone, χ ( Q,ω) is proportional to F ( Q) 2 /ω qs, where F ( Q) isthe phonon dynamic structure factor. It is proportional to the Bragg scattering structure factor for zone center acoustic modes, but in general depends on the polarization of the vibrational mode and the atomic displacement vectors of the eigenfunction. To obtain a quantity proportional to χ ( Q,ω), we multiply the measured intensity by the Bose-Einstein factor C = (1 e hω k B T ). This removes the temperature dependent effects of phonon occupancy and allows us to track the changes in the phonon energy spectrum directly. The thus normalized data sets from Q = [331] were then fit with two damped harmonic oscillator functions to extract the different phonon dynamic susceptibilities. An additional Gaussian function was introduced to fit the intensity from the tail of the Bragg peak. Details of the fitting are in the Materials and Methods section. Representative examples of the fits to the data at various temperatures are shown in Figs. 3(a) 3(f). The growth of the susceptibility of the new mode, at the expense of the TO mode, with increasing temperature is clearly apparent, as evident in Fig. 3(g). As well as growing, the new mode sharpens and hardens with increasing temperature. Rapid growth of the new mode spectral weight begins at around 100 K. The behavior is reminiscent of the power law growth of an order parameter in a Ginsburg-Landau theory of a conventional second order phase transition 9 except in that case the order parameter grows upon cooling through the phase transition, not on warming as here. The temperature dependence of the mode susceptibility is reminiscent of the growth in the amplitude of the off-center Pb displacements observed in the atomic pair distribution function (PDF), 1 as shown in the inset. We have investigated the dispersion of the new mode in the [h11] direction away from the zone center using the ARCS chopper spectrometer at ORNL. As is evident from Fig. 4, the mode clearly disperses to higher energy transfer moving away from the zone center, similar to the TO mode, and hardens with increasing temperature. Small features in the h = 5.2 spectra at an energy transfer around 5 mev are acoustic phonons, which cannot be resolved at lower momentum transfers, and should not be confused with the new mode which is dispersing towards higher momentum transfer. The observation of additional modes implies a symmetry breaking in the system. The most trivial possibility is the appearance of a localized mode due to the presence of point defects in the material. Such modes are extremely weak and nondispersive but can become apparent, even for modest defect densities, when they interact with dispersing crystal modes. 11 This explanation can be ruled out by the temperature dependence. 100 K is too low a temperature for any significant thermally activated defect formation, and it is difficult to explain the power-law behavior of the susceptibility in this scenario. Also, the new mode is dispersive arguing

244 KIRSTEN M. Ø. JENSEN et al. PHYSICAL REVIEW B 86, (2012) FIG. 3. (Color online) (a) (f) Dynamic susceptibility obtained from the measured INS spectra (symbols) at representative temperatures with fits to the data shown as a pink line. There are two damped harmonic oscillator components, one for the TO mode (red) and one for the new mode (green). A Gaussian function was added to fit the intensity from the tail of the Bragg peak (orange). The horizontal blue line is a constant background component. (a) 2 K, (b) 98 K, (c) 203 K, (d) 299 K, (e) 482 K, and (f) 601 K. (g) shows the temperature dependence of the integrated weight in the new mode from the fits (black symbols). The inset shows the Pb off-centering displacement measured from the PDF measurement on PbTe reported in Ref. 1. against this explanation. Similar arguments argue against another possibility which is the formation of thermally induced intrinsic local modes. 12 These are localized phonon modes that form due to nonlinear effects in a strongly driven system of oscillators 13 and have been postulated to form due to thermal excitation in soft ionic systems. 12 An anharmonic coupling between the LA and TO modes has also been postulated to explain the breadth of the TO mode in PbTe, 2 but this does not explain the characteristic temperature dependence, and the clear observation of two distinct coexisting components in the vicinity of the TO mode. Also the LA mode is at zero frequency and far from the TO mode at the zone center where our data were measured. The most striking correspondence of the new mode is with the temperature dependent appearance of Pb off-centering structural dipoles in the local structure reported from PDF measurements. 1 This observation was rationalized on thermodynamic grounds as the entropically stabilized appearance of a paraelectric phase above an undistorted nonferroelectric ground state. In this picture, the emergent dipoles break the local symmetry by removing the center of symmetry on the Pb site, even though there is no change in the long-range symmetry. This will result in short and long Pb-Te bonds, changing mode frequencies associated with the TO vibrations which are the intra-unit cell anti-phase vibrations of Pb and Te, just as observed here. If each off-center Pb atom is fluctuating independently, this would result in a flat nondispersing mode. The observation of dispersion implies that off-centered Pb ion displacements are correlated over some range of space, resulting in polar nanodomains similar to those observed in relaxor ferroelectrics FIG. 4. (Color online) Neutron scattering intensity vs energy transfer from single crystal PbTe measured on the ARCS spectrometer. Curves in each panel are cuts along [h11] for 5 (zone center)<h<5.2 showing the dispersion of the modes. (a) 100 K, (b) 200 K, (c) 300 K, (d) 400 K, (e) 500 K, and (f) 600 K. At high temperature the intensity is almost exclusively coming from the new mode which is seen clearly dispersing to higher energy with increasing h

245 LATTICE DYNAMICS REVEALS A LOCAL SYMMETRY... PHYSICAL REVIEW B 86, (2012) FIG. 5. (Color online) Elastic diffuse scattering around the [h00],[0kk] plane of reciprocal space measured using the Triple axis spectrometer: (a) 16 K, (b) 482 K, (c) difference between the scans in (b) and (a): I(482) I(16). (d) and (e). As (a) and (b) but the intensities have been corrected to account for the change in phonon occupation of the acoustic modes that are within the energy resolution of the measurement. (f) The difference between the scans in (e) and (d). below the Burns temperature. 14 The new mode seen here is highly reminiscent of modes appearing in INS measurements of relaxor ferroelectrics that were attributed to polar nanodomains. 15 However, the crucial distinction here is that PbTe is a pure material. In relaxors the polar nanodomains are stabilized by nanoscale chemical disorder whereas here they must be intrinsic. A physical explanation may lie in the partially localized optical phonon modes recently postulated by DFT and molecular modeling 16 that result from partial covalency of the Pb and Te that competes with the electrostatic Madelung potential which prefers the high symmetry rock-salt structure. More work on the temperature dependence and the dispersion of these modes is needed to establish the true origin of this behavior. We would like to establish if there is a static component to the short-range ordered nanoscale distortions by searching for diffuse scattering around the zone center in the elastic channel (ω = 0). Indeed, we find there is a small increase in scattering at the base of the (111) Bragg peak at high temperature, which could be elastic diffuse scattering, as evident by comparing Figs. 5(a) and 5(b). The Bragg peak is evident as the strong scattering signal in dark red centered at (1.0,1.0,1.0). Another strong feature at (1.25,1.3,1.3) is a spurious feature of unknown origin. Powder diffraction lines are also evident coming from the aluminum cryostat windows, and for the line going through the Bragg peak, possibly some crystal mosaicity. The spurious features disappear (or rather appear with negative differential intensities) in the difference plot in Fig. 5(c) which shows the difference between the intensities at high (b) and low (a) temperature. We see some diffuse scattering intensity appearing at high temperature in this elastic measurement, suggesting that the high temperature broken symmetry phase has a static component. This extra diffuse scattering component shows up as positive intensity around the (111) point in Fig. 5(c), whereas the Bragg features have a negative difference (dark blue) due to Debye-Waller effects. However, the most likely origin of the observed increase in elastic diffuse intensity is the finite energy resolution of our measurement resulting in a temperature dependent signal coming from the increase in population of the acoustic phonons that lie within the energy resolution window. Figs. 5(d) and 5(e) show scans that have been approximately corrected for phonon effects by dividing the region around the Bragg peak by the Bose factor appropriate for the phonon modes in the resolution window. This correction accounts for all of the observed diffuse scattering at high temperature in Fig. 5(c) [see Fig. 5(f)] suggesting that there is no elastic diffuse scattering signal from the dipoles and therefore they have no static component but are completely dynamic in nature, again consistent with the DFT prediction. 16 The chemically simple binary PbTe compound continues to turn up surprises that challenge our understanding of condensed matter systems. We know of no other example of the appearance in a pure material of a new phonon mode with increasing temperature, and the characteristic temperature dependence of its dynamic susceptibility argues strongly that this is an intrinsic response of the system. The inelastic scattering is sensitive to the local symmetry which is broken at high temperature where the new mode is seen to coexist over a wide range of temperature with the original TO mode of the undistorted structure. A picture emerges of nanoscale regions where the local dipoles appear at high temperature and are

246 KIRSTEN M. Ø. JENSEN et al. PHYSICAL REVIEW B 86, (2012) correlated and fluctuating. This lowering of local symmetry with rising temperature, betrayed by the emerging modes seen here and in the PDF, 1 may explain the long known anomalous temperature dependence of the semiconducting energy gap in PbTe. 16,17 Unlike in conventional semiconductors where the energy gap is known to increase with falling temperature due to the reduction of the intensity of thermal vibrations, that of PbTe increases with increasing temperature up to as high as 600 K. It is this anomalous dependence that permits PbTe to exhibit delayed cross gap carrier excitations thereby sustaining a very high thermoelectric power factor at high temperatures. Coupled with the increased anharmonicity and phonon scattering from the same origin resulting in a very low thermal conductivity, this may help to explain the one two punch that propels PbTe to the top of its thermoelectric class. 18 III. MATERIALS AND METHODS A. Sample preparation Stoichiometric amounts of Pb (rotometals, at 99.9% purity) and Te (plasmaterials, at % purity) were flame sealed in an evacuated (<10 4 mtorr) fused silica tube. The mixture was heated to 1050 C at a rate of 100 C/h for 4 h and cooled down to room temperature at a rate of 20 C/h. For the single crystal growth, 20 g of PbTe were remelted using the Bridgman method. A 13 mm fused silica tube was loaded with PbTe and lowered at a rate of 2.6 mm/h through a single zone vertical furnace that was set at 1050 C. A cylindrical shaped crystal of 13 mm in diameter and 60 mm in height was used for the inelastic neutron scattering experiment. The quality of the single crystal was evaluated using neutron Laue diffraction at SNS. B. Triple axis inelastic neutron scattering experiments The inelastic neutron experiments were performed at the HB3 triple axis instrument at the high flux isotope reactor (HFIR) located at Oak Ridge National Laboratory. All the experiments were performed with a fixed final energy E f = 14.7 mev using pyrolytic graphite (PG) as a monochromator and analyzer and a PG filter after the sample to eliminate higher order contamination of the scattered beam. The neutron beam collimation was before the monochromator, sample, analyzer, and detector, respectively. This yielded an energy resolution of 1.06 mev full width half maximum (FWHM) for zero energy transfer, increasing to 1.62 mev FWHM at ω = 12.0 mev energy transfer. The sample was mounted to the cold-tip of a closed cycle He-4 based refrigerator (CCR). Data scans were made as a function of energy transfer at constant Q points in reciprocal space at 35 different temperatures between 2.5 and 600 K. C. Triple axis inelastic neutron scattering data curve fitting Here we describe the method used to extract the dynamic structure factors of the modes at the (133) zone center from the TAS data. First the data are normalized to obtain the dynamic susceptibility χ ( Q,ω) as described in the main paper. Based on earlier work we expect two zone-center modes to be present at finite energy transfer (the acoustic modes are hidden under the elastic line at ω = 0): the TO mode at around 4 mev and the LO mode around 14 mev. As the LO mode does not overlap with either the TO or the new mode, we do not take this into account in the fit, which only includes the region from 1 12 mev. The TO mode is then fitted with a function representing a damped harmonic oscillator, 6 with an additional constant background in the fit. Furthermore, a Gaussian function is added to take care of the tail of the Bragg peak which is present even after the normalization with the Bose factor. We then add an additional damped harmonic oscillator to account for the new mode. The spectra were then fit as a function of temperature sequentially with the starting model for each fit using the parameters obtained from the previous temperature point. Certain constraints were introduced in order to aid convergence, namely, the widths of TO and new mode curve and the background level were allowed to change by only ±20%, between subsequent runs. D. Triple axis elastic diffuse scattering measurements Elastic scans were also taken on a grid of points in the Brillouin zone at 16 and 482 K to search for diffuse scattering from static disorder. The range 0.8 <h<1.5 was scanned in the [h00] direction and 0.8 <k<1.5 in the[0kk] direction to capture the region around the (111) reciprocal lattice point. This is a zone center and the PbTe Bragg peak is evident in Fig. 5(a) at the (111) point. There is an additional Bragg feature at around ( ). We are not sure of the origin of this feature and think it is a spurious peak. It does not show any interesting temperature dependence and we neglect it in the analysis. In addition there are a number of powder Bragg lines evident. One goes through the (111) point and suggests some sample mosaicity. The other powder lines probably come from the aluminum sample environment. In Figs. 5(d) and 5(e) we have applied a simple correction to account for the increased occupancy of acoustic phonons that lie within the energy resolution of the measurement. Based on the dispersion curves measured by Cochran et al., we estimate the range of Q that is affected by phonons within the energy resolution (of around 1 mev). We assume that the average phonon energy in that region is 0.5 mev and so correct the intensities in this range of Q by the Bose factor appropriate for a mode of that energy and the temperature in question. This is a highly simplified correction and is intended to estimate the scale of intensity coming from the increase mode population at high temperature rather than being a highly accurate correction. We see that this simple correction accounts for essentially 100% of the diffuse scattering seen at higher temperature in the elastic channel. E. Chopper spectrometer inelastic neutron scattering experiments Inelastic neutron scattering measurements were also performed using the ARCS direct geometry time-of-flight chopper spectrometer at the spallation neutron source (SNS) at the Oak Ridge National Laboratory. Single crystal measurements were performed with an incident energy of E i = 30 mev with the sample mounted approximately in the (hk0) scattering plane of the instrument. The sample was mounted to the cold tip of a closed cycle He-4 based refrigerator (CCR). Data were acquired by rotating the sample about the vertical axis by 40 degrees and collecting data in degree increments. Empty

247 LATTICE DYNAMICS REVEALS A LOCAL SYMMETRY... PHYSICAL REVIEW B 86, (2012) sample can measurements were performed for all data acquired at ARCS and subtracted from the data shown in the manuscript. The resulting large five-dimensional data sets show the scattering intensity throughout much of ( Q,ω) space. The data are projected into a 4D space, and 3D slices and 2D cuts are made to extract features of interest using the DCS-mslice program within the DAVE 19 software package. ACKNOWLEDGMENTS We would like to thank Simon Johnsen for help with growing the crystal and Nicola Spaldin and Petros Souvatzis for helpful discussions. Work in the Billinge group was supported by the Office of Science, US Department of Energy (OS-DOE), under Contract No. DE-AC02-98CH Work in the Kanatzidis group was supported as part of the Revolutionary Materials for Solid State Energy Conversion, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC The neutron scattering measurements were carried out at the HFIR and SNS at Oak Ridge National Laboratory was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. 1 E. S. Božin, C. D. Malliakas, P. Souvatzis, T. Proffen, N. A. Spaldin, M. G. Kanatzidis, and S. J. L. Billinge, Science 330, 1660 (2010). 2 O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M.-H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. D. Lumsden, and B. C. Sales, Nat. Mater. 10, 614 (2011). 3 W. Cochran, R. A. Cowley, G. Dolling, and M. M. Elcombe, Proc. R. Soc. London 293, 433 (1966). 4 H. A. Alperin, S. J. Pickart, J. J. Rhyne, and V. J. Minkiewicz, Phys. Lett. 40, 295 (1972). 5 M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group Theory Application to the Physics of Condensed Matter (Springer-Verlag, Berlin, 2008). 6 G. Shirane, S. M. Shapiro, and J. M. Tranquada, Neutron Scattering with a Triple Axis Spectrometer (Cambridge University Press, Cambridge, 2002). 7 B. T. Fultz, Prog. Mater. Sci. 55, 247 (2010). 8 J. M. An, A. Subedi, and D. J. Singh, Solid State Commun. 148, 417 (2008). 9 A. D. Bruce and R. A. Cowley, Structural phase transitions (Taylor and Francis, London, UK, 1981). 10 W. Jantsch, in Dynamical Properties of IV-VI Compounds, edited by H. Bilz, A. Bussmann-Holder, W. Jantsch, and P. Vogl, Springer Tracts in Modern Physics (Springer Berlin/Heidelberg, 1983), Vol. 99, pp R. M. Nicklow, W. P. Crummett, and J. M. Williams, Phys.Rev.B 20, 5034 (1979). 12 M. E. Manley, A. J. Sievers, J. W. Lynn, S. A. Kiselev, N. I. Agladze, Y. Chen,A.Llobet, anda.alatas,phys.rev. B79, (2009). 13 D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57, 43 (2004). 14 G. Burns, Phys. Rev. B 13, 215 (1976). 15 S. B. Vakhrushev and S. M. Shapiro, Phys. Rev. B 66, (2002). 16 Y. Zhang, X. Ke, P. R. C. Kent, J. Yang, and C. Chen, Phys. Rev. Lett. 107, (2011). 17 R. N. Tauber, A. A. Machonis, and I. B. Cadoff, J. Appl. Phys. 37, 4855 (1966). 18 Z. H. Dughaish, Physica B 322, 205 (2002). 19 R. T. Azuah, L. R. Kneller, Y. Qiu, P. L. W. Tregenna-Piggott, C. M. Brown, J. R. D. Copley, and R. M. Dimeo, J. Res. Natl. Inst. Stand. Technol. 114, 341 (2009)

248 Article pubs.acs.org/crystal Rapid Hydrothermal Preparation of Rutile TiO 2 Nanoparticles by Simultaneous Transformation of Primary Brookite and Anatase: An in Situ Synchrotron PXRD Study Jian-Li Mi, Casper Clausen, Martin Bremholm, Nina Lock, Kirsten M. Ø. Jensen, Mogens Christensen, and Bo B. Iversen* Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University, DK-8000 Aarhus C, Denmark ABSTRACT: The formation mechanism and crystal growth of TiO 2 in hightemperature high-pressure fluids were studied using HCl or H 2 SO 4 as additives. In situ synchrotron radiation powder X-ray diffraction reveals that phase-pure rutile TiO 2 nanoparticles can be formed using HCl as additive, whereas phase-pure anatase TiO 2 is obtained when H 2 SO 4 is used as additive. The supercritical (or near-critical) conditions provide a fast, one-step synthesis of rutile TiO 2 nanoparticles and when using a 1:1 volume ratio of isopropanol water as solvent at a temperature of 300 C and a pressure of 25 MPa particles with an average particle size of about 22 nm are obtained in 20 min. A detailed analysis by sequential Rietveld refinements shows that the formation of rutile TiO 2 occurs by a combined transformation of anatase and brookite TiO 2. Analysis of the unit cell dimensions of the nanoparticles shows a lattice expansion with decreasing particle size for anatase prepared with H 2 SO 4 medium and this may explain the stability of anatase particles that are significantly larger than their critical size. INTRODUCTION TiO 2 is an intensively studied material of growing interest in a variety of applications such as photoelectrochemical solar energy conversion and environmental photocatalysis of water splitting to generate hydrogen and treatment of polluted water. 1 The properties of TiO 2 depend strongly on particle size, crystal structure, morphology, and crystallinity. 2,3 Controlled and tailored preparation of TiO 2 nanoparticles is of great importance for the effective utilizations of such nanoparticles. TiO 2 has three polymorphs in nature, namely rutile, anatase, and brookite. 4 The anatase and rutile phases both have tetragonal structures, whereas brookite has an orthorhombic structure. All three crystal structures consist of (TiO 6 ) octahedra, which share either edges or corners. At ambient conditions rutile is the thermodynamically stable phase, whereas anatase and brookite are metastable. On the nanoscale anatase has been found to be more stable due to surface effects. The critical size for anatase-to-rutile phase stability has been predicted to be <14 nm. 5 However, the relative stability of anatase and rutile also depends on the synthesis technique and it is experimentally possible to obtain much larger anatase particle sizes. For example, Li et al. have found that the critical size for the transition of anatase to rutile is >32 nm. 3 Complete control over the synthesis of anatase TiO 2 has been achieved by pulsed supercritical synthesis where particles having any desired size between 7 and 35 nm can be prepared. 6 Nanostructured materials with small crystallite sizes and high surface areas are of great interest for improving optical, electrical, and catalytic properties. Rutile TiO 2 can be obtained via calcination of anatase TiO 2 or amorphous TiO 2 at high temperatures. However, the thermal treatments induce significant grain growth and the resulting rutile crystals are always large. Therefore, low temperature wet chemistry such as hydrothermal and sol gel methods have been used for preparation of nanostructured rutile TiO 2. 7 Previous studies show that different TiO 2 phases can be formed by using different acid media. It has been found that H 2 SO 4 or acetic acid can be used to form anatase, whereas HCl or HNO 3 acid media result in phase transformation from anatase nanoparticles to rutile nanoparticles. 8 However, under conventional hydrothermal conditions long aging time is necessary to obtain phase pure rutile TiO 2. Therefore, it is desirable to find new fast and convenient synthesis methods to produce rutile TiO 2 nanoparticles. A supercritical fluid is a fluid that is heated and pressurized above its critical point. 9 Supercritical fluids exhibit unique properties with gaslike transport properties in diffusivity, viscosity, and surface tension while also maintaining liquidlike properties such as high-solvation capability and density. Synthesis in supercritical or near-critical solvent is an efficient approach to produce highly crystalline nanoparticles with a narrow size distribution. 9 In our previous studies, we have applied supercritical synthesis to produce anatase TiO 2 and shown that the method allows quick synthesis with wellcontrolled size and crystallinity of the nanoparticles. 10 Here, we report that rutile TiO 2 nanoparticles also can be synthesized under supercritical or near-critical conditions. Considering the Received: August 25, 2012 Revised: October 23, 2012 Published: October 24, American Chemical Society 6092 dx.doi.org/ /cg301230w Cryst. Growth Des. 2012, 12,

249 Crystal Growth & Design synthesis of rutile TiO 2, the phase transformation of anatase to rutile in the solid state has been well studied. 5,11 However, understanding of the formation and growth mechanism of rutile TiO 2 in near-critical hydro/solvothermal conditions is still lacking. It is clearly of interest to develop a fast synthesis route of rutile TiO 2 under supercritical/near-critical condition and to investigate the reaction processes. In recent years, in situ X-ray studies have been used to investigate a wide range of chemical reactions, 12 and in our group we have focused on studying nanocrystal growth processes under near-critical or supercritical conditions. 13 The present work is focused on fast synthesis of rutile TiO 2 nanoparticles in near-critical condition and the reaction is followed by in situ synchrotron radiation powder X- ray diffraction (SR-PXRD). The data provide clear insight into the phase formation and particle growth processes of TiO 2 in different phases. EXPERIMENTAL SECTION All chemical reagents used in the experiments were analytical grade. A sapphire capillary was used as a high-pressure cell to study the formation and growth of TiO 2 crystallites by timeresolved in situ SR-PXRD. A solution of 2.0 M titanium tetraisopropoxide (TTIP, Ti(OCH(CH 3 ) 2 ) 4 ) was prepared by dissolving TTIP (>97%) in isopropanol. This solution was added dropwise into an equal volume of 2.0 M HCl (or 1.0 M H 2 SO 4 ) aqueous solution under continuous stirring, and a sol was obtained. The sol precursor was injected into the sapphire capillary, and subsequently, the sapphire capillary was sealed, pressurized with a HPLC pump, and heated using a hot air flow. 14 The experiments were performed at a temperature of 300 C and a pressure of 25 MPa. The in situ SR-PXRD data were collected at beamline I711, MAX-II, MAX-lab, Sweden, using monochromatic X-rays with a wavelength of Å (E = 12.4 kev). The data was collected on a Mar165 CCD detector with a time resolution of 5 s between each frame, of which 1 s was detector dead time for readout. The SR-PXRD data were refined using the Rietveld method implemented in the FullProf program 15 and corrected for instrumental broadening using data measured on a LaB 6 standard. A Thompson- Cox-Hastings pseudo-voigt axial divergence asymmetry profile function and a background modeled with linear interpolation were used. RESULTS AND DISCUSSION Part a of Figure 1 shows the time evolution of the PXRD patterns for the sample, which is prepared in HCl medium. During the first 70 s, the PXRD patterns show the amorphous phase but then the anatase and brookite phases form rapidly. At the same time, the TiO 2 rutile phase starts to form slowly. The intensities of the diffraction peaks of the anatase and brookite phases increase rapidly in about 20 s after being detected and subsequently decrease with prolonged reaction time. However, the intensities of the diffraction peaks of the rutile phase increase continuously and become almost constant after a reaction time of 8 min. When H 2 SO 4 is used as medium, anatase TiO 2 starts to form quickly after a reaction time of 30 s as can be seen in part b of Figure 1, and diffraction peaks from other phases are not observed. The results indicate that in the HCl medium, rutile TiO 2 is formed at the expense of the anatase and brookite phases, rather than by formation directly from the amorphous phase or by phase transformation only from anatase, and this will be further discussed below. Parts a and b of Figure 2 show representative PXRD data with observed, calculated and difference patterns of the sample prepared in HCl medium at reaction times of 3.3 and 19.8 min, respectively. At a reaction time of 3.3 min, the diffraction pattern shows a mixture of rutile, anatase and brookite phases, whereas at a reaction time of 19.8 min, almost single phase rutile is obtained with only about 1 wt % anatase left. The high quality of the data allows us to refine all the three phases, and excellent agreement is observed between the calculated and observed patterns. The particle size was obtained from the peak broadening. The anisotropic particle shape can be modeled by a linear combination of spherical harmonic function. 16 β h λ λ = = almpylmp( Θh, Φh) D cos θ cos θ h lmp Article Figure 1. Time evolution of the in situ SR-PXRD patterns for the synthesis of TiO 2 in HCl (a) and H 2 SO 4 (b) media, respectively. where β h is the size contribution to the integral breadth of reflection h, and Y lmp (Θ h,φ h ) are normalized real spherical harmonics. The refined coefficients a lmp were used to calculate the volume-weighted particle size along different crystallographic directions. An anisotropic refinement of the 19.8 min data shows that the rutile particle has sizes of 23(1) and 20(1) nm along the a and c directions respectively indicating isotropic growth. Therefore, a simplified model having only an isotropic size was used. The same method was used for the anatase and brookite particles. The refined parameters and crystallographic details from the Rietveld analysis of the SR-PXRD data for the sample prepared in HCl medium at reaction times of 3.3 and 19.8 min are listed in Table 1. Note that in our previous studies we have shown that the sizes of the nanoparticles calculated from PXRD data agree very well with the transmission electron (1) 6093 dx.doi.org/ /cg301230w Cryst. Growth Des. 2012, 12,

250 Crystal Growth & Design Figure 2. Observed, calculated, and difference patterns of SR-PXRD for the sample prepared in HCl medium at reaction times of 3.3 (a) and 19.8 min (b). The green markers indicate the Bragg reflections for the rutile, anatase, and brookite. Table 1. Refined Parameters in the Rietveld Analysis of the SR-PXRD Data for the Samples Prepared in HCl Medium at Reaction Times of 3.3 and 19.8 Min reaction time (min) no. of data points no. of refined params no. of reflns R P (%) R WP (%) R F (%) (rutile) R F (%) (anatase) R F (%) (brookite) 2.91 a (Å) (rutile) 4.602(1) 4.613(2) c (Å) (rutile) 2.971(1) 2.975(1) a (Å) (anatase) a 3.787(2) c (Å) (anatase) 9.484(4) rutile (wt%) 75(1) 99(1) anatase (wt%) 10(1) 1(1) brookite (wt%) 15(1) 0(0) a The cell parameters of anatase were refined for the data before 5 min and then fixed with the obtained values from the 5 min data for subsequent other frames. microscopy (TEM) studies exemplified e.g. with anatase TiO 2 nanoparticles 10 and Zirconia nanoparticles. 13h Part a of Figure 3 shows the time evolutions of normalized scale factors of rutile, anatase, and brookite phases for the sample prepared with HCl medium. The time evolution of the Article scale factor for each phase reflects the changing amount of the phase during the reaction. As can be seen, the amounts of anatase and brookite increase abruptly during the first frames after initial detection, and then decrease simultaneously at a reaction time of about 90 s. The brookite phase disappears after 10 min. The amount of rutile phase increases with reaction time and reaches a constant value after 10 min. Part b of Figure 3 shows the time dependence of the weight fractions for the three phases. The weight fractions are 1(1) %, 48(2) %, and 51(4) % for rutile, anatase, and brookite respectively at a reaction time of 70 s when the crystallites were initially observed. After 10 min, the weight fractions are 99(1) %, 1(1) %, and 0%, and they remain unchanged until the last frame at 19.8 min. To obtain the absolute normalized scale factor representing the total crystalline products within the probed volume, we divide any of the individual scale factors for the three phases by their respective weight fractions. Part c of Figure 3 shows the time evolution of the absolute scale factor of the total crystalline products, indicating a quick crystallization process from the amorphous phase. Part d of Figure 3 compares the normalized formation rates of the rutile phase and the total crystalline product obtained by differentiating the rutile curve in part a of Figure 3 and the curve in part c of Figure 3, respectively. The formation rate of the total crystalline product shows that the crystallization transformation from amorphous phase happens very fast in 20 s but that the formation of rutile TiO 2 lasts until a reaction time of about 8 min. This indicates that both anatase and brookite are formed directly from the amorphous phase, whereas rutile is formed by a reaction between anatase and brookite. It is worth noting that, when brookite is consumed after 6 min, the formation of rutile slows down significantly. The above results show that the brookite phase plays an important role for the formation of rutile TiO 2 with HCl medium. At the initial formation of rutile, the particle size of anatase is only 3 nm and even after ripening the size of anatase crystallites is only 12 nm as shown in part a of Figure 4. The transformation from anatase to rutile in such small particles appears to be due to the presence of another metastable phase, namely brookite. The initial nucleation of rutile possibly occurs at the interface between the anatase and brookite crystals due to a high interfacial energy. It has been reported that the presence of brookite phase will enhance the anatase-rutile transformation during heat treatment, 17 which corroborates the present results. Brookite has also been proposed as an essential intermediate phase in mechanically induced anatase to rutile phase transformation. 18 Our results show that brookite is not acting as an intermediate in the phase transformation from anatase to rutile since both phases nucleate in similar amounts and then decrease simultaneously. Part a of Figure 4 displays the time evolutions of particle sizes of rutile, anatase and brookite for the sample prepared with HCl medium. Because of the small and decreasing weight fraction of brookite, it is not possible to determine the particle size of brookite beyond reaction times of 4 min and similarly for anatase, where rather large error bars of particle size are obtained. The particle size of rutile TiO 2 increases with reaction time until 5 min, and it is larger than those of anatase and brookite. It is known that the transition to rutile is accompanied by significant grain growth. The final particle sizes of rutile and anatase TiO 2 of about 22 and 12 nm are obtained for the sample prepared in HCl medium. The fact that the particle size of rutile is much larger than for anatase and brookite could be 6094 dx.doi.org/ /cg301230w Cryst. Growth Des. 2012, 12,

251 Crystal Growth & Design Article Figure 3. (a) Time evolution of normalized scale factors of rutile, anatase and brookite phases for the sample prepared in HCl medium, (b) time evolution of weight fractions for each phase, (c) absolute scale factor for the total crystalline products, (d) normalized formation rates of the rutile phase and the total crystalline product obtained by differentiation of the curves in (a) and (c). taken as an indication that the anatase and brookite particles fuse to form the rutile nanoparticles. It has been suggested that HNO 3 or HCl might contribute to the reorientation of anatase to produce rutile crystals which is possibly via a dissolution precipitation mechanism. 7a However, our results clearly show that under these conditions it is more likely a solid state reaction mechanism with combination of anatase and brookite nanoparticles to form the rutile phase. Even though the formation process of anatase and brookite crystallites is rapid, it is found that the particle growth of anatase and brookite continues for a much longer time which is attributed to Ostwald ripening. For rutile, the particle growth ceases almost at the same time as the formation stops. This further indicates that the formation of rutile is a solid state reaction mechanism involving a reconstructive process. Parts b and c of Figure 4 show the time dependences of cell parameters of rutile and anatase prepared with HCl medium. The cell parameters are fixed in the refinements for anatase after 5 min and for brookite for all the data. Both the rutile and the anatase phase show contractions of the cell parameters along both a and c direction with decreasing particle size. It is known that cell parameters deviate from bulk values when the particle size decreases to nanoscale due to the microstrain. The cell parameters of the rutile phase are a = 4.572(1) Å, c = 2.960(1) Å and a = 4.613(2) Å, c = 2.975(1) Å for the reaction times of 2 and 19.8 min corresponding to the particle sizes of 16(1) nm and 22(1) nm, respectively. This is equivalent to a lattice contraction of 0.9% along a direction and 0.5% along c direction. Part a of Figure 5 shows the time dependences of the normalized scale factor and particle size of anatase TiO 2 prepared using H 2 SO 4 as medium. An anisotropic refinement shows that the 10.4 min particles are 17(1) and 18(1) nm along the a and c directions, respectively indicating that the particles are almost isotropic. A particle size of 18 nm is obtained after 10 min reaction. The anatase phase prepared with H 2 SO 4 medium is much more stable than that prepared with HCl medium, even though the anatase crystallites are larger. In addition, the particle growth of anatase is much faster in H 2 SO 4 medium. As seen in part a of Figure 5, the particle growth almost stops once the crystallization is finished, and the ripening growth is not obvious in this case. When comparing part c of Figure 4 and part b of 5, it is seen that the microstrain characteristics are fundamentally different for the anatase nanoparticles prepared with H 2 SO 4 medium compared with those prepared with HCl medium. Thus, in H 2 SO 4 medium the cell parameters increase at small particle sizes, whereas they decrease in HCl medium. The microstrain characteristics of anatase previously have been found to vary considerably depending on the synthesis route. For example, Zhang et al. 19 have determined the cell parameters as function of particle size of nanocrystalline anatase prepared by hydrolysis of titanium ethoxide or titanium isopropoxide, and the results show lattice contractions along both the a and c axes. In contrast, Swamy et al. 20 have shown a small lattice expansion at reduced crystallite size (expansion of cell parameter a and the unit cell volume, and contraction for cell parameter c). This has been explained as a Ti deficiency, which leads to lattice expansion, whereas the contraction of the anatase lattice is due to surface stress. The microstrain was also found to vary with the shape anisotropy of nanocrystalline anatase. 21 In our experiments, the anatase nanocrystallites prepared with HCl medium show lattice contraction with reduced crystallite size, whereas the anatase nanocrystallites prepared with H 2 SO 4 medium have lattice expansion. Cell parameters of a = 3.806(1) Å and c = 9.565(2) Å are observed at 10 min for 6095 dx.doi.org/ /cg301230w Cryst. Growth Des. 2012, 12,

252 Crystal Growth & Design Figure 4. (a) Time evolutions of particle sizes of rutile, anatase, and brookite TiO 2 for the sample prepared with HCl medium, (b) cell parameters for rutile TiO 2, (c) cell parameters for anatase TiO 2. the anatase particles prepared with H 2 SO 4 medium. Compared with the cell parameters of a = 3.794(2) Å, c = 9.491(7) Å for the anatase particles observed after 5 min in HCl medium as well as most reported anatase cell parameters, 20 the elongation of the cell parameter along the a axis is moderate, whereas the value is much larger along the c axis. It has been suggested that Article anatase nanoparticles are formed due to the lower surface energy as compared to other phases when the particles are sufficiently small. On the other hand, a lower surface energy significantly accelerates the nucleation kinetics of the formation of anatase. 22 Zhang et al. has suggested that the surface free energy of nanocrystalline anatase has a strong size dependence with a maximum value at around 14 nm, where the particles have lattice contractions along both the a and c axes. 19 Even though the detailed mechanism for the variation of the microstrain with particle size is still unknown, the abnormal microstrain behaviors of anatase nanoparticles prepared in H 2 SO 4 medium may explain the stabilization of the anatase particles at a size much larger than the expected critical size. CONCLUSIONS The formation and growth of TiO 2 nanoparticles in near-critical solution were studied by in situ SR-PXRD. The synthesis method provides a fast route for preparation of rutile TiO 2 nanoparticles. The formation of rutile TiO 2 is a result of a solid reaction with phase transformation from anatase and brookite to rutile. The anatase nanocrystallites prepared with HCl medium show lattice contractions with reduced crystallite size, whereas lattice expansion is observed for the crystallites prepared with H 2 SO 4 medium. The different microstrain characteristics of anatase nanoparticles prepared under different conditions may explain the different properties in phase formation, phase stability, and crystal growth. AUTHOR INFORMATION Corresponding Author * Bo@chem.au.dk. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the Danish National Research Foundation (Center for Materials Crystallography), the Danish Strategic Research Council (Center for Energy Materials), and the Danish Research Council for Nature and Universe (DanScatt). The authors are grateful for the beamtime obtained at the beamline I711, MAX-lab synchrotron radiation source, Figure 5. (a) Time dependence of the normalized scale factor and particle size of anatase TiO 2 prepared using H 2 SO 4 as medium. (b) Anatase cell parameters as a function of time for synthesis with H 2 SO 4 medium dx.doi.org/ /cg301230w Cryst. Growth Des. 2012, 12,

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254 FULL PAPER DOI: /chem Watching Nanoparticles Form: An In Situ (Small-/Wide-Angle X-ray Scattering/Total Scattering) Study of the Growth of Yttria-Stabilised Zirconia in Supercritical Fluids Christoffer Tyrsted, [a] Brian Richard Pauw, [a, b] Kirsten Marie Ørnsbjerg Jensen, [a] Jacob Becker, [a] Mogens Christensen, [a] and Bo Brummerstedt Iversen* [a] Abstract: Understanding nanoparticleformation reactions requires multitechnique in situ characterisation, since no single characterisation technique provides adequate information. Here, the first combined small-angle X-ray scattering (SAXS)/wide-angle X-ray scattering (WAXS)/total-scattering study of nanoparticle formation is presented. We report on the formation and growth of yttria-stabilised zirconia (YSZ) under the extreme conditions of supercritical methanol for particles with Y 2 O 3 equivalent molar fractions of 0, 4, 8, 12 and 25 %. Simultaneous in situ SAXS and WAXS reveals a quick formation (seconds) of sub-nanometre amorphous material forming larger agglomerates with subsequent slow crystallisation (minutes) into nanocrystallites. The amount of yttria dopant is shown to strongly affect the crystallite size and unit-cell dimensions. At yttriadoping levels larger than 8 %, which is known to be the stoichiometry with maximum ionic conductivity, the strain on the crystal lattice is significantly increased. Time-resolved nanoparticle size distributions are calculated based on whole-powder-pattern modelling of the WAXS data, which reveals that Keywords: nanoparticles supercritical fluids X-ray diffraction yttria zirconia concurrent with increasing average particle sizes, a broadening of the particlesize distributions occur. In situ total scattering provides structural insight into the sub-nanometre amorphous phase prior to crystallite growth, and the data reveal an atomic rearrangement from six-coordinated zirconium atoms in the initial amorphous clusters to eight-coordinated zirconia atoms in stable crystallites. Representative samples prepared ex situ and investigated by transmission electron microscopy confirm a transformation from an amorphous material to crystalline nanoparticles upon increased synthesis duration. Introduction [a] C. Tyrsted, Dr. B. R. Pauw, K. M. Ø. Jensen, Dr. J. Becker, Dr. M. Christensen, Prof. Dr. B. B. Iversen Center for Materials Crystallography Department of Chemistry and inano Aarhus University, 8000 (Denmark) bo@chem.au.dk [b] Dr. B. R. Pauw RIKEN SPring-8 Center Sayo, Hyogo (Japan) Supporting information for this article is available on the WWW under Nanoparticles form a cornerstone of nanoscience and nanotechnology, and their effectiveness in a variety of applications is governed by the specific nanoparticle characteristics. Therefore, control of nanoparticle structure, size, size distribution, crystallinity, morphology and surface chemistry are the key points in many studies. [1] A wide range of synthesis methods have been developed to produce nanoparticles of ever increasing chemical complexity. [2] Among these, hydroor solvothermal reactions have become widespread since this approach provides considerable control over nanoparticle properties. [3] In recent years, synthesis in supercritical fluids has been introduced, thereby providing even greater control of nanoparticle characteristics, and this approach furthermore reduces reaction times to minutes or seconds. [4] The main body of work leading to the understanding of the chemical processes involved in nanoparticle formation and growth is based on characterisations of the products obtained after varying synthesis parameters (pressure, temperature, concentrations, ph, etc.), that is, ex situ investigations. [5] These methods have provided valuable knowledge. However, a complete understanding of the mechanisms involved during synthesis remains elusive since ex situ samples will never be fully comparable to in situ conditions. An in situ experiment is a single controlled experiment that yields a large mass of data all in exact timely correspondence to each other, whereas multiple ex situ experiments can always be questioned as to whether they are truly comparable with each other. Furthermore, the retrieval of ex situ samples at different time intervals is time consuming. In situ studies are, therefore, required to probe the reactions as they occur. X-ray and neutron studies have become common characterisation tools in the field of in situ studies, largely due to the increased availability of synchrotron X-ray and neutron sources. [6] These sources allow for continuous probing of the Chem. Eur. J. 2012, 18, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 5759

255 reaction mixture by allowing the X-ray or neutron beam to penetrate the synthesis reactor walls. Powder X-ray diffraction (PXRD), or wide-angle X-ray scattering (WAXS), is probably the most widely used in situ method in studies of solid-state reactions and formation of crystalline compounds. [7] Although this technique provides excellent information on the average crystal structure of the nanoparticles, and can provide a measure of crystallite size (and sometimes even size distribution [8] ), it does not contain information on the amorphous structure of the particles in the initial stages of the reaction, nor does it provide information on the agglomeration behaviour of the crystallites. The small-angle X-ray scattering (SAXS) signal contains information on the length scales of morphological features contrasting in electron density, such as particles and crystallites present in reaction mixtures. From this signal, depending on its quality, information on the size and size distribution of the particles and crystallites can be inferred. Thus, SAXS is a valuable addition to the WAXS information when studying nanoparticle syntheses in liquids. [9] A further level of information can be unlocked when the interatomic interactions in the amorphous state can be studied, something which is not possible when looking at the WAXS/PXRD and SAXS information. The interatomic interaction information can elucidate the true chemistry behind the initial reactions, which at its core involves rationalisation based on atoms, molecules and chemical bonds. This atomistic insight can be obtained for amorphous phases by measuring the total scattering from the sample and calculating the pair distribution function (PDF). [10] PDF studies have seen an immense growth owing to the availability of high-energy synchrotron radiation, and in situ total-scattering experiments are gaining in popularity. [11] Here we present for the first time a combined SAXS/ WAXS/total-scattering in situ study under the extreme conditions of supercritical fluids. The combined use of these three experimental techniques will eventually pave the way for comprehensive studies of a wide range of reactions and thereby give an unprecedented understanding of nanoparticle formation and growth. The aim to simultaneously and in situ utilise several complementary scattering techniques and to exploit their unique strengths requires that certain compromises have to be made. The individual experiments are, therefore, not optimised towards one single technique, and the data quality should not be compared to that obtained in individually optimised ex situ experiments. It is the combined use of several complementary in situ techniques that is required to obtain a complete picture of inorganic nanoparticle synthesis. As a proof of principle we have studied one of the most important nanoparticle systems in materials science: yttria-stabilised zirconia. Zirconia, either pure or doped, is one of the most utilised ceramic materials, in part owing to its toughness, thermal stability, low thermal conductivity and low electrical conductivity. [12] Zirconia doped with yttria (yttria-stabilised zirconia, or YSZ for short) has for decades been the chosen electrolyte material for solid oxide fuel cells (SOFC), because of its high ionic conductivity at elevated temperatures combined with relatively low material costs. [13] AY 2 O 3 molar fraction of 8 % in YSZ exhibits the highest ionic conductivity. [14] The operational temperature of this compound in SOFCs is usually C to reach an ionic diffusivity high enough for practical application. Significant efforts are therefore being directed towards reducing the operational temperature, while retaining a high ionic diffusivity. One method of achieving this is to manufacture electrolyte films from extremely small and densified nanoparticles, as the ionic diffusivity at the grain boundary of the nanoparticles is higher than regular lattice diffusion in larger, coarse-grained polycrystalline particles. [15] Large-scale synthesis of zirconiabased nanoparticles is possible through supercritical synthesis while still retaining small particle sizes and narrow particle-size distributions. [16] However, tuning of the physical parameters of these supercritically synthesised YSZ nanoparticles requires further insight into the reaction mechanisms, which can be provided by the application of in situ experiments. [16c,17] Results and Discussion SAXS: The SAXS data indicate a fast precipitation of material from the precursor medium after initiation of heating. This is evident from Figure 1A, which shows a rapid increase in the SAXS signal (invariant) that stabilises within the first 60 s. The SAXS invariant, determined from the fitting parameters, is a measure of the total amount of phaseseparated material (crystalline or amorphous) present in the irradiated sample volume. The individual phase-separated material grows rapidly in size and reaches an equilibrium value within 20 s as shown in Figure 1B. In other words, the nucleation and precipitation of the solid yttria-stabilised zirconia takes approximately 20 s under the present conditions. After this time the main changes appear to be localised mainly within the phase-separated material. The evolution in characteristic particle length in Figure 1B is shown as the Debye term- and structure-factor-derived correlation lengths. The different sizes resulting from the different contributions in Figure 1B indicate an agglomeration of smaller domains, with the characteristic length of the individual domains given by the Debye correlation length and the characteristic length of the agglomerates given by the structurefactor cut-off length. Although these characteristic lengths Figure 1. Time evolution of A) the SAXS invariant and B) the correlation lengths as given by SAXS for 0YSZ (&), 4YSZ (*), 8YSZ (~) and 12YSZ (^) Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2012, 18,

256 Watching Nanoparticles Form FULL PAPER are only qualitatively related to the particle and agglomerate dimensions, the reaction dynamics and the relative agglomerate size can be determined. Thus, for the final state, the agglomerate size (with a characteristic length of 22 Š) is about four times the size of the individual constituents (which have a characteristic length of about 6 Š). Figure 3. Time evolution of unit-cell axes in the A) a,b unit-cell direction and B) c unit-cell direction. C) Unit cell axis ratio between the pseudofluorite a f unit-cell direction and the c unit-cell direction. Data points corresponds to 0YSZ (&), 4YSZ (*), 8YSZ (~) and 12YSZ (^). Figure 2. Time evolution of A) the scale factor, B) particle size in the a,b unit-cell direction and C) particle size in the c unit-cell direction, obtained from Rietveld refinement of WAXS data for 0YSZ (&), 4YSZ (*), 8YSZ (~) and 12YSZ (^). WAXS: The scale factor from the Rietveld refinement of the WAXS data (a measure of the amount of crystalline material present in the X-ray beam, shown in Figure 2A) indicates a slow formation of crystalline material, taking up to 15 min to reach a stable value for all samples. Crystallitegrowth curves obtained from Rietveld refinement are shown in Figure 2B and C for the particle sizes in the a,b and c unit-cell direction, respectively. All particles exhibit a prolate morphology with the particle size in the c direction being larger than the size in the two equivalent a and b unit-cell directions. Near the end of the synthesis duration, the particle-size aspect ratio c/achtungtrenung(a,b) reaches a value of around 1.2 for all samples except 0YSZ (see the Supporting Information). The overall nanoparticle sizes given for these syntheses are comparable to those previously published in ex situ solvo- and hydrothermal synthesis studies. [18] As evident from the final sizes given in Figure 2B and C, there is a close correlation between the doping concentration and the size of the crystalline region in the particles, that is, the decrease in particle dimensions follows the increase in yttria content (0, 4, 8 and 12 %). The highly elongated morphology of the 0YSZ particles is most likely due to uncertainties in the Rietveld refinement arising from its difficulty in describing the coexisting monoclinic and tetragonal phases. Evolution of the crystallographic unit-cell dimensions can be followed for the a,b unit-cell axes (Figure 3A) and the c unit-cell axis (Figure 3B). Even though the pure ZrO 2 (0YSZ) synthesis yielded a phase mixture of the monoclinic and tetragonal crystal structure only the tetragonal unit cell is displayed here to facilitate comparison with the other syntheses. The a,b unit-cell axes of the tetragonal unit cells expand, whereas the longer c unit-cell axis contracts upon the nucleation and growth of all samples (0YSZ, 4YSZ, 8YSZ and 12YSZ). The change in the final unit-cell dimensions appears to be correlated with the degree of doping, just as was found for the particle sizes. The a,b unit-cell axis decreases and the c unit-cell axis increases in length upon increased yttria doping levels. Figure 3C shows the ratio p between the c unit-cell axis and the a f unit-cell axis (a f = ffiffiffi 2 a) of the cubic pseudo-fluorite structure. This depiction can be used to distinguish between the different possible tetragonal polymorphs (t, t and t ) of the crystal structure and estimate how close the unit cell resembles a cubic fluorite structure. [18b, 19] The final ratios for 0YSZ and 4YSZ reach a value around 1.01, which corresponds well with values found for the t tetragonal form. The more heavily doped samples (8YSZ and 12YSZ), on the other hand, show an increased tetragonality with ratios higher than Figure 3C shows that this aspect ratio decreases during growth for all syntheses. The increase in the final c/a f ratio with increased yttria content is the opposite of the trend found in a previous study concerned with larger particles (20 nm). [19] This observed difference could be an effect related to the very small crystallite sizes in the present study in which these changes in the crystal structure may affect the minimisation of the crystallite surface energy. [20] The data also show that the smaller the particles the stronger the effect of yttria doping is on the lattice strain (a(t) a(1)). The ion mismatch between Zr and Y appears to have the largest effect on the crystal lattice when the particles are very small. When the particles reach their stable diameter of about 4 nm the unit cell no longer changes dimensions. Figure 3 shows that the lattice strain in the small particles becomes Chem. Eur. J. 2012, 18, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

257 B. Brummerstedt et al. very large when the yttria-doping degree exceeds 8 %. This could be an important factor by determining that 8 % is the optimum doping level for the ionic conductivity of YSZ nanocrystals. In addition to the Rietveld refinement of the WAXS data, we performed whole-powder-pattern modelling (WPPM) of the same data to obtain an estimate of the crystallite size distributions. The results are plotted in Figure 4 showing the Figure 5. TEM images of 8SZ samples synthesised ex situ under conditions similar to the in situ experiments with synthesis durations of A) 20 and B) 10 min. Figure 4. Time evolution of the crystallite size distribution for A) 4YSZ, B) 8YSZ and C) 12YSZ found from whole-powder-pattern modelling of WAXS data. average size of the particles increasing as the synthesis time proceeds, as also proposed by SAXS and Rietveld refinement of the WAXS data. The WPPM technique, however, furthermore shows that the size distribution of the crystallites broadens with increased synthesis time. This is an important characteristic of the particles, not provided by the structural Rietveld refinement. It is noteworthy that for the high yttria content (12YSZ) the particle-size distribution initially is narrow, but then it reaches a fairly constant shape, which is merely shifted to larger average values as time goes. This specific effect may be due to the highly amorphous nature of the material, or inadequacies in the model. Transmission electron microscopy (TEM) was performed on a number of 8YSZ samples synthesised ex situ under conditions similar to the in situ experiments (250 8C, 230 bar). Figure 5 shows TEM pictures of two 8YSZ samples kept at synthesis conditions for 20 and 10 min, respectively. The sample heated for 20 min (Figure 5A) clearly shows a large collection of nanoparticles with an approximate diameter of 5 nm, in good agreement with size estimates from in situ WAXS. The sample heated for 10 min (Figure 5B), on the contrary, displays a precipate of amorphous material with dark contrast areas, a possible indication of initial crystallisation of nanodomains. Electron diffraction (not shown) confirmed that the particles viewed in Figure 5A exhibited a crystalline structure whereas no diffraction pattern was observed for the precipitate shown in Figure 5B. The combined results from SAXS and WAXS analysis strongly suggest that synthesis starts with a fast precipitation of globules of precursor or amorphous nanoparticles, which crystallise at a lower rate. This is supported by ex situ TEM measurements showing crystalline nanoparticles at a synthesis duration of 20 min and amorphous precipitate at a synthesis duration of 10 min. Ex situ syntheses may not directly represent those from in situ experiments as there are likely to be small fluctuations in the heating zone along the length of the capillary. For TEM analysis, separation of synthesised material placed at different positions in the capillary is not possible. The nearly equal agglomerate sizes found from SAXS for different yttria contents, and the corresponding difference in particle sizes found from the Rietveld refinements, implies a growing difficulty for the particles to fully crystallise upon increased yttrium doping. This is also reflected in the large lattice strain observed for small particles with high yttria content. Total scattering: PDF analysis, based on total-scattering experiments, has become an increasingly valuable tool for analysing different complex materials. [10,21] There are previous reports on in situ total-scattering studies of nanostructures, [11b, 22] but the present analysis is to the best of our knowledge the first time-resolved in situ total-scattering study of chemical synthesis under supercritical conditions. Three supercritical YSZ syntheses with compositions 0YSZ, 4YSZ and 25YSZ were investigated with the PDF analysis technique. The shown data are so-called reduced pair distribution functions, and are not applicable to coordination shell calculations (see the Experimental Section for details). Figure 6 shows the time evolution in the short (<10 Š) PDF Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2012, 18,

258 Watching Nanoparticles Form FULL PAPER Figure 6. Time-resolved evolution of the reduced PDF for A) 0YSZ, B) 4YSZ and C) 25YSZ. There is a time gap of around 50 s between each vertically shifted curve, starting at the bottom. The inserted black markers at around 3.6 Š correspond to the a,b unit-cell axes lengths and the black markers at 5.3 Š correspond to the c unit-cell axis length found from Rietveld refinement. correlations for the three syntheses. The first four bond lengths are assigned according to results from the Inorganic Crystal Structure Database (ICSD; no and no ). [23] The total-scattering data, which are the starting point of the PDF analysis, have also been examined using Rietveld refinement. The evolution in the tetragonal unitcell dimensions found from Rietveld refinement are plotted as black markers on the correlation peaks in Figure 6. The shortest Zr Y distance ( 3.6 Š) corresponds to the a,b unit-cell axes size (see Figure S7 in the Supporting Information). The a,b unit-cell axes expand during growth for all three samples, which confirms the results from the WAXS data. The c axis should, according to Rietveld refinement, decrease during growth for all samples. This behaviour is displayed differently in the PDF curves in which we see a gradual emergence of a correlation peak in the distance corresponding to the length of the c axis ( 5.15 Š). This overall behaviour corresponds well with the PDF analysis conducted on the transformation from amorphous to crystalline ZrO 2 by Zhang et al. [22b] The amorphous state of zirconia has local ordering that gives rise to distinct correlations up to around an interatomic distance of 5 Š. The PDF analysis therefore indicates an amorphous state prior to crystallisation as was also suggested by the SAXS/WAXS experiments. Figure 7. Structural models corresponding to A) the coordination between two precursor molecules and B) the coordination in the crystalline state. Plots (C) and (D) show a direct comparison of the reduced PDF from the start (black curve) and end (grey curve) of the synthesis for C) 0YSZ and D) 4YSZ. Theoretical calculations [24] have proposed that clustering of yttria/zirconia precursor molecules starts with edge sharing of octahedrons, with metal atoms coordinated to six oxygen atoms in the form of hydroxides (Figure 7A). From the information provided, the equilibrium distance between the metal atoms can be determined to be 3.32 Š for complex [(OH) 4 Zr-O 2 -Zr(OH) 4 ] 4 and 3.38 Š for complex [(OH) 4 Y-O 2 -Zr(OH) 4 ] 5. [24] The earliest PDF curves with distinguishable correlation peaks give a Zr Zr distance for 0YSZ of 3.33 Š (Figure 7C) and a Zr Y distance for 4YSZ of 3.40 Š (Figure 7D), matching well with the theoretically predicted values. The agreement between experimental and calculated results therefore suggests that the amorphous phase originates from the agglomeration of the cluster species shown in Figure 7A. As the distance between the two metal atoms slowly increases, the remainder of the correlation peaks appear corresponding to the bonds between two ZrACHTUNGTRENUNG(or Y) O 8 arrangements, which are part of the tetragonal crystal structure (Figure 7B). The small differences in peak Chem. Eur. J. 2012, 18, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

259 B. Brummerstedt et al. positions between the PDF patterns of 0YSZ and the PDF patterns of 4YSZ can be explained by coexistence of the phases in 0YSZ. The crystallinity of the 25YSZ sample is very low throughout the entire synthesis, and for this material there is, therefore, no transition from the PDF patterns of the amorphous structure as shown in Figure 7C. If we expand the PDF to longer correlations it is possible to follow the evolution in crystallite size (Figure 8). When reaching distances larger than the crystallite size the correlation peaks should disappear or fade. The crystallite sizes found from applying the Scherrer equation [25] to the highangle scattering data (plotted as black markers in Figure 8) fit reasonably well with this fading of the PDF for the more mature crystallites but exaggerates the sizes for the initial crystallite growth. The crystallite sizes for 25YSZ (Figure 8C) are considerably smaller than for the other samples, which is also supported by the sizes determined by the Scherrer equation. This again documents that crystallisation is more difficult when ion mismatch is introduced with yttria doping. The PDF analysis technique is, as shown, able to provide unique information about the initial reaction steps during the synthesis of zirconia nanoparticles. Such information has previously almost exclusively been available from theoretical modelling, but the PDF data provide experimental structure evidence to test theoretical predictions on nanoparticle nucleation and growth. There is good agreement between the changes in crystallite size and crystal structure found from the PDF evolution and the results from the Rietveld refinements of the WAXS data. The existence of amorphous particles before crystallisation, as indicated by SAXS, is also in excellent agreement with the PDF analysis. Conclusion True tailoring of nanoparticle characteristics and properties requires detailed understanding of the formation and growth of nanoparticles. The present study combines three powerful and complementary in situ techniques, SAXS, WAXS and total scattering, for the first time to give a comprehensive insight into the nanocluster formation, precipitation, crystallisation and growth. As a proof of concept the formation of yttria-stabilised zirconia in supercritical methanol was studied. The in situ SAXS and WAXS data show that YSZ formation in supercritical methanol is comprised of a fast (on the order of seconds) precipitation of agglomerated amorphous material followed by slow crystallisation (lasting minutes). This was, furthermore, supported by ex situ TEM investigations. The degree of crystallisation, the crystallite size and the unit-cell dimensions were shown to depend strongly on the yttrium-doping content. Introduction of increasing ion mismatch in the form of increasing yttria content makes the formation of the crystal lattice increasingly difficult. In particular, it was observed that yttria doping larger than 8 % introduces a strong lattice strain in small particles (<4 nm). The very first seconds of the nanocluster precipitation were followed in situ by using PDF analysis and it was shown that octahedrally coordinated precursor molecules form the initial amorphous phase. The structure of the amorphous phase gradually evolves into the crystalline tetragonal structure of the mature nanocrystallites. The in situ approach provides experimental data to test theoretical modelling of nanoparticle-formation reactions, and a combination of theory and in situ SAXS/WAXS/totalscattering experiments can possibly lead to the true design of nanoparticles with tailored properties. Experimental Section Figure 8. Time-resolved evolution of the reduced PDF for A) 0YSZ, B) 4YSZ and C) 25YSZ showing longer correlations. There is a time gap of around 50 s between each curve shifted vertically, starting at the bottom. The inserted lines correspond to the volume-averaged particle sizes found through applying the Scherrer equation to the raw scattering data. In situ synchrotron data were collected at beam line 1-ID-C at the Advanced Photon Source, Argonne National Laboratories (IL, USA), using a custom-built sample stage. [26] The X-ray wavelength was fixed at Š (70.01 kev), and a cm 2 General Electric a-si detector [27] was used. The resolution of the detector was pixels, which resulted in a pixel size of microns per pixel. The detector time resolution for the SAXS/WAXS experiments was 1.1 s per frame, recording 240 frames in sequence, followed by a readout period of 70 s. For these experiments, the sample-to-detector distance was 2590 mm, which allowed for a significant part of the SAXS and WAXS regions to be mea Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2012, 18,