Size effects. Lecture 6 OUTLINE

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1 Size effects 1 MTX9100 Nanomaterials Lecture 6 OUTLINE -Why does size influence the material s properties? -How does size influence the material s performance? -Why are properties of nanoscale objects different than those of the same materials at the bulk scale? -Why nanomaterials are unstable?

2 Size-dependent properties At the nanometer scale, properties become size-dependent. For example, (1) Chemical properties reactivity, catalysis (2) Thermal properties melting temperature (3) Mechanical properties adhesion, capillary forces (4) Optical properties absorption and scattering of light (5) Electrical properties tunneling current (6) Magnetic properties superparamagnetic effect 2 New properties enable new applications

3 Materials structures Most materials are made up of ordered crystals that meet at disordered boundaries; the crystals in nanomaterials are only ,000 atoms across. Amorphous or glassy materials are totally disordered; the only characteristic dimension is that of the atoms or molecules that make them up. They are an extreme from of nanomaterial. 3

4 4 Thermal property - Melting point

5 Thermal property - Melting temperature Melting Point (Microscopic Definition) Temperature at which the atoms, ions, or molecules in a substance have enough energy to overcome the intermolecular forces that hold the them in a fixed position in a solid At macroscopic length scales, the melting temperature of materials is size-independent. For example, an ice cube and a glacier both melt at the same temperature. 5

6 Thermal properties Nanocrystal size decreases In contact with 3 atoms surface energy increases melting point decreases In contact with 7 atoms Surface atoms require less energy to move because they are in contact with fewer atoms of the substance 6 Example: 3 nm CdSe nanocrystal melts at 700 K compared to bulk CdSe at 1678 K

7 7 Melting point as a function of size

8 Thermal transport Heat is transported in materials by two different mechanisms: lattice vibration waves (phonons) and Free electrons. In metals, the electron mechanism of heat transport is significantly more efficient than phonon processes. In the case of nonmetals, phonons are the main mechanism of thermal transport. In both metals and nonmetals, as the system length scale is reduced to the nanoscale, there are quantum confinement and classical scattering effects. 8

9 Quantum confinement The presence of nearby surfaces in 0-D, 1-D, and 2-D nanostructures causes a change in the distribution of the phonon frequencies as a function of phonon wavelength as well as the appearance of surface phonon modes. These processes lead to changes in the velocity with which the variations in the shape of the wave s amplitude propagate, the so-called group velocity. The phonon lifetime is modified due to phonon-phonon interaction and free surface and grain boundary scattering. 9

10 Thermal property - Conductivity where v is a particle velocity, l is a free path length, С = сn is a heat capacity of unit volume, c is a heat capacity of single particle, n is a number of particles 10

11 Mechanical Properties At the nanoscale, surface and interface forces become dominant. For example, These forces can exceed (1) Adhesion forces (2) Capillary forces forces that are normally (3) Strain forces dominant at macroscopic length scales 11

12 Mechanical properties Relative to microstructural (MSM) metals and alloys, the NSM contain a higher fraction of grain boundary volume (for example, for a grain size of 10 nm, between 14 and 27% of all atoms reside in a region within nm of a grain boundary); therefore, grain boundaries play a significant role in the materials properties. 12 Changes in the grain size result in a high density of incoherent interfaces or other lattice defects such as dislocations, vacancies, etc. As the grain size d of the solid decreases, the proportion of atoms located at or near grain boundaries relative to those within the interior of a crystalline grain, scales as 1/d. This has important implications for properties in ultra-finegrained materials which will be principally controlled by interfacial properties rather than those of the bulk.

13 Grain boundaries Crystals contain internal interfacial defects, know as grain boundaries, where the lattice orientation changes The misfit between adjacent crystallites in the grain boundaries changes the atomic structure (e.g. the average atomic density, the nearestneighbor coordination, etc.) of materials. At high defect densities the volume fraction of defects becomes comparable with the volume fraction of the crystalline regions. In fact, this is the case if the crystal diameter becomes comparable with the thickness of the interfaces. Non equilibrium materials 13 DEFECTS!!!

14 Crystals always contain defects Vacancies are point defects in the crystalline structure of a solid that may control many physical properties in materials such as conductivity and reactivity. However, nanocrystals are predicted to be essentially vacancy-free; their small size precludes any significant vacancy concentration. This result has important consequences for all thermo mechanical properties and processes (such as creep and precipitation) which are based on the presence and migration of vacancies in the lattice. Point defects: 0.1 nm (10-10 m) 14

15 Impurity atoms 15 Material properties can be altered significantly through the addition of impurity atoms

16 Glossary Point defects - Imperfections, such as vacancies, that are located typically at one (in some cases a few) sites in the crystal. Extended defects - Defects that involve several atoms/ions and thus occur over a finite volume of the crystalline material (e.g., dislocations, stacking faults, etc.). Vacancy - An atom or an ion missing from its regular crystallographic site. Interstitial defect - A point defect produced when an atom is placed into the crystal at a site that is normally not a lattice point. Substitutional defect - A point defect produced when an atom is removed from a regular lattice point and replaced with a different atom, usually of a different size. 16

17 Summary of point defects (c) 2003 Brooks/Cole Publishing / Thomson Learning 17 (a) vacancy, (b) interstitial atom, (c) small substitutional atom, (d) large substitutional atom, (e) Frenkel defect, (f) Schottky defect.

18 Defects for plasticity Crystals all contain line defects known as dislocations Dislocations act as the main source of plastic deformation in crystalline materials 18

19 Plastic deformation (a) When a shear stress is applied to the dislocation in (a), the atoms are displaced, causing the dislocation to move one Burgers vector in the slip direction (b). Continued movement of the dislocation eventually creates a step (c), and the crystal is deformed. (Adapted from A.G. Guy, Essentials of Materials Science, McGraw-Hill, 1976.) (d) Motion of caterpillar is analogous to the motion of a dislocation. 19

20 Dislocations Dislocations are positioned closer together and dislocations movement in the net is hindered by interaction between them. Together with the reduced elastic strain energy, this fact results in dislocations that are relatively immobile and the imposed stress necessary to deform a material increases with decrease in grain size. 20 Dislocations have a less dominant role to play in the description of the properties of nanocrystals. The free energy of a dislocation is made up of a number of terms: (i) the core energy (within a radius of about three lattice planes from the dislocation core); (ii) the elastic strain energy outside the core and extending to the boundaries of the crystal, and (iii) the free energy arising from the entropy contributions. In mc the first and second terms increase the free energy and are by far the most dominant terms. Hence dislocations, unlike vacancies, do not exist in thermal equilibrium.

21 Increase in strengths and hardness The relation between yield stress and grain size is described mathematically by the Hall-Petch equation 21 where k y is the strengthening coefficient (a constant unique to each material), σ o is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), d is the grain diameter, and σ y is the yield stress.

22 Grain boundary strengthening Grain boundary strengthening (or Hall-Petch strengthening) is a method of strengthening materials by changing their average grain size. It is based on the observation that grain boundaries impede dislocation movement and that the number of dislocations within a grain have an effect on how easily dislocations can traverse grain boundaries and travel from grain to grain. So, by changing grain size one can influence dislocation movement and yield strength This is a schematic roughly illustrating the concept of dislocation pile up and how it effects the strength of the material. A material with larger grain size is able to have more dislocation to pile up leading to a bigger driving force for dislocations to move from one grain to another. Thus you will have to apply less force to move a dislocation from a larger than from a smaller grain, leading materials with smaller grains to exhibit higher yield stress.

23 Hall-Petch strengthening limit Hall-Petch Strengthening is limited by the size of dislocations. Once the grain size reaches about 10 nm, grain boundaries start to slide. 23

24 Ductility Deformation and fracture of ultra-high-fine materials: (a) Plastic flow localization; (b) nanockrack nucleation; (c) final failure Fracture surface of a 30 nm grain size electrodeposited Ni tensile specimen. 24

25 Deformation of nano-metal 25 from Kumar et al., Acta Materialia, 2003, v.51,

26 How to improve ductility? NC materials with high ductility: (a) a bimodal single-phase structure composed of nanograins and large grains; and (b) nano-composite consisting of nanoscale grains and dendrite like inclusions of the second phase (from I.A. Ovid ko, Rev. Adv. Mater. Sci., 2005, v.10, ). 26

27 27 Nanostructured solids

28 Why nanostructured polycrystalline materials are unstable? GB consists of several types of extrinsic defects, namely, stationary dislocations with Burgers vectors normal to a boundary plane, gliding or tangential dislocations with Burgers vectors tangential to the boundary plane, and disclinations in triple junctions. Disclinations and grain boundary dislocations form elastically distorted layers (zones) near grain boundaries. 28 High density of defects -> High energy Nature -> seek to lower energy Grain growth occurs in materials to reduce the overall energy of the system by reducing the total grain boundary energy. Therefore, grain growth in NC materials is primarily driven by the excess energy stored in the grain or interphase boundaries.

29 Grain boundaries diffusion relative increasing of GB diffusion coefficient 29

30 Pileups in a grain and a layer of a nanolayer structure 30

31 31 Hardness

32 Nanoscale optical properties Bulk gold appears yellow in color Nanosized gold appears red in color The particles are so small that electrons are not free to move about as in bulk gold Because this movement is restricted, the particles react differently with light 32 Optical properties are connected with electronic structure, a change in zone structure leads to a change in absorption and luminescence spectra.

33 Visible electromagnetic spectrum CdSe Semiconducting Quantum Dots 33

34 34 Surface plasmon absorption Surface plasmon absorption of spherical nanoparticles and its size dependence. (a) A schematic illustrating the excitation of the dipole surface plasmon oscillation. The electric field of an incoming light wave induces a polarization of the (free) conduction electrons with respect to the much heavier ionic core of a spherical metal nanoparticle. A net charge difference is only felt at the nanoparticle surfaces, which in turn acts as a restoring force. In this way a dipolar oscillation of the electrons is created with period T. (b) Optical absorption spectra of 22, 48 and 99nm spherical gold nanoparticles. The broad absorption band corresponds to the surface plasmon resonance (from S. Link, M.A. El-Sayed Int. Rev. Phys. Chem. 2000, v.19, 409)

35 optical properties Transformation of absorption spectra of sodium from atom to solid 35 Absorption (fluorescence) spectrum of Na atom relates to the transition 2S 2P. The spectrum of Na3 cluster expands into the discrete molecular spectrum reflecting electron excitations and atom oscillations. Continuous spectrum of Na8 cluster reflects the processes of dissociations and defragmentation of cluster on atoms. Spectrum of nanoparticle reflects resonance absorption of cluster atoms. Spectrum of massive film reflects the interband transitions of electrons in metal. Optical absorption spectra of sodium: а) for atom, b) for cluster Na3, c) for cluster Na8, d) for nanoparticle of d<10 nm size (~10 6 atoms) in NaCl crystal, e) for thin film of d=10 nm width.

36 Blue shift Blue shift refers to a shortening of a transmitted signal's wavelength, and/or an increase in its frequency. The name comes from the fact that the shorter-wavelength end of the optical spectrum is the blue end, hence, when visible light is compacted in wavelength, it is "shifted towards the blue", or "blue-shifted". Blue shift phenomenon is a quantum size effect. W is a work function, EF is a Fermi energy, HOMO is the highest occupied molecular orbital, LUMO is the 36lowest unoccupied molecular orbital Transformation of zone structure of a solid under reduction of its size from macroto nano-scale down to a single atom, showing the increase of the band gap g E and the blue shift hω = E for nanoparticles and nanostructured state of matter.

37 The properties of MC and NC materials of the same chemical composition 37

38 In the quantum world, the rules are different. The classical world The quantum world 38

39 Quantum tunneling A nanoscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating a potential barrier or impedance higher than the kinetic energy of the particle. 39 Electron tunneling is attained when a particle with lower energy is able to exist on the other side of an energy barrier with higher potential energy.

40 Go through the wall Tunneling is the penetration of an electron into a classically forbidden region. A barrier, in terms of quantum tunneling, may be a form of energy state analogous to a "hill" or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without sufficient energy. 40

41 The principal of quantum tunneling Electrons exhibit wave behavior and their position is presented by a wave (probability) function. The wave function represents a finite probability of finding an electron on the other side of the potential barrier. Since the electron does not posses enough kinetic energy to overcome the potential barrier, the only way the electron can appear on the other side is by tunneling through 41 the barrier.

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