Classification of Perovskite and Other AB03-Type Compounds l

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1 Journal of Research of the National Bureau of Standards Vol. 58, No.2, February 957 Research Paper 2736 Classification of Perovskite and Other AB3-Type Compounds l Robert S. Roth A classification of A +2 B+'3 com pounds has been made on t he basis of ionic rad ii of the cons tituent ions. A grap h of t his type for t he perovski te compounds can be ~ivide d in~o orthor hombic, pseud ocubic, a nd cubic fi elds, wit h an area of ferro electn c and antlferroelectnc compounds s uperimposed on the cuhic fi eld. The structures of s ohd solu tons. be~ween vari ous perov s ki te compou nds cannot b e com pletely c<;)jt el ~ted on the bass <?f ths smple two-dim e nsional chart. Therefore, a n ew type of classficaton of t he perovsklte-type compounds has b een attempted, using a t hree-dimensiona l graph with pol ari ~ab ili ty of ions plotted as tile t hird dimension. This t hree-dimensional grap h h a s been appljed s uc cessfully to comp ounds of t he type A+2B H 3, w hich crystalli ze with perovski te-ty pe stru ct ures. n addi tion a classifi cation of d ouble oxides of t ri valent ions has s hown that all co mp ou nds of this typ~ hav ing the pcro vs ki te s tructw e can be divided into two groups, with rhombohedra l a nd orthorhombic sy mm et ry. No ideal cubi c perovski tes of the A+3B+3 3 compounds hav e been found. th en :fir ed in a conventional platinum-wound quench furnace, or refired in the original calcini ng furnace. A p artial sm vey of the reactions occmring in The quenching technique was used, whenever applibinary oxide mixtures of the types AO :B 2 and cable, because it h as been observed that sh arp er A 2 a:b 2 a h as b een condu cted as part of a program X-ray patterns ar c often obtained by very fast coo~ of fund amental research on cer amic dielectrics. n ing of the specimen. t is known that phase transladdition, binary, ternary, and quaternary reactions tions in the perovskite structures ar c usually comb etween end members of the AO B 2 compounds pletely reversible and cannot be frozen in by qu enchh ave also b een studied. Combinations of oxides in g. Thus the perovskite structm es discussed are giving the simple formul a type AB 3 were selected the room-temperatme stable forms, al though other because of current interest in ferroelectric ceramics. m aterials t reated in this manner would generally Previous publication h ave covered the data com- contain the high-temperature forms, if any. The piled on many of these systcms, such as CaO-Ti2 fmal firing temperature ranged from,25 to,55 [] 2 PbTiOa-PbZrOa [2], B eo with Zr2, Ti 2, and C and was m aintained constant for a given length of Ce' 2 [:3], MgO-CaO-Sn2 and Ti 2 [4], :M go-zr2- time. Equilibrium conditions were usually reached Ti 2 and CaO-Zr2-Ti2 [5], alkaline earth oxides in e s than 3 hr. Equilibrium was b elieved to h ave with Ge2 [6], PbTiOa-PbZrOa-PbO:Sn 2 and been reached when X-ray patterns of the specimen PbTiOa-PbHfO a [7], alkaline ear th oxides with U 2 showed only a sin gle phase or when the pattern of a [8], and divalent ions with Zr2 [9]. This paper is multiple-phase specimen showed no ch ange wi th sucdesigned primarily to present new data and a new cessive h eat treatment. The fired disks wer e exammethod of r epresen tation of these stru ctme types ined by X-ray diffraction, using a Geiger-count~r and to coordinate the information already published. diffractometer employing nickel-filtered copper rachation. The X-ray data reported can be considered 2. Sample Preparations and Test Methods to be accurate to ± O.OOl A when three decimal places are recorded, and to ±. AOwhen only two n gener al t he materials used were the highest decimal places are r ecorded. The r esults reported available purity of the component oxides, varying in this work are gener ally the d ata obtained at room from about to 99.9-percent pmity. The start- temperature from specimens treated in a m anner to ing m aterials, in sufficien t quantities to give either form a matured cer amic dielectric bodv. a.-g sample or a.-g sample, d epending on the n the case of specimens containing an ion that was availability of the raw materials, were weighed to apt to oxidize, a neutral atmospher e was m aintained th e nearest milligram, mixed together, and formed in the furnace. These ions were VH, UH, and Ce+3 ; into -in. or X-in.-diameter disks at a pressm e of the neutral atmosphere used was either helium or 5, bin.2 The pressed disks were fired for 4 hr argon. The fm naces used were similar to those at, C on platinum foil in an air atmosphere, previously mentioned, bu t modi:lied to maintain a u ing an electrically heated fm nace wound with neutral atmosphere. 8-percent-P t 2-percent-Rh wire. Th ese disks were then ground and r emixed, and 3. The Perovskite Structure Type ne\v d isks for st udy of the solid-state reactions, about X in. high, were formed at 5, bin.2 in either a The structures of the p erovskite-type compounds }~-in. or X-in.-diameter mold. The specimens were have b een studied by many workers. The exact nature of the structmes involved is still in doubt This work has been sponsored as part of a program for mprovemen t of Piezoelectric Ceramics by the omce of Orcinance Research of tbe Department in many cases. Conflicting r eports in the literature of the Army. make difficult the job of assigning the correc t struco Figures in brackets indicate the literatm e referen ces at t he end of this paper.. ntroduction 75

2 trn'e, or even symmetry, to any particular perovskitetype compound. The simplest case of the perovskite structure is that of a simple cubic cell with one ABX3 formula unit per unit cell. n this case the A ions are at the corners of the unit cell with the B ion at the center and the negative ions occupying the face-centered positons. The space group is ~-Pm3m and has the notation G-5 of the Strukturbericht []. As will be seen in the following discussion of actual perovskite-type compounds, very few binary oxides have this simple cubic structure at room temperature, although many of them assume this structure at elevated temperatures. Many modifications of this simple structure have been proposed to account for the X -ray patterns observed for different perovskite-type compounds. Among these modifications a simple doubling of the unit cell has been used []. A monoclinic modification suggested by N a'ay-szabo [2] for the type compound perovskite (CaTi 3) has been shown to b e actually orthorhombic by M egaw [ 3]. The latest modification of this structure was made by Bailey [4] and quoted by Megaw [5], using an orthorhombic modification with the b parameter approximately twice the pseudocubic cell edge and with the a and c parameters approximately..j2 times th e pseudo cubic cell. t will be seen that the X-ray patterns of a great many compounds can be indexed on the basis of this type of distortion of the perovskite structure. The compounds CaTi 3, CaZr3, and CaSnOa have been indexed previously on this basis and the d-spacings and (hkl) values published [4, 5]. However, it should b e noted that a discrepancy exists between the reported space group for CaTi 3, P cmn [5], and the published indexing of these patterns. Although CaSn3 contains no reflections that are not allowed by this space group, both CaTi 3 itself and also CaZr3 show diffraction peaks, which can only be indexed on the basis of forbidden reflections. These peaks are especially prominent for CaZr3 and indicate that perhaps a different space group is r equired for the CaTi 3type orthorhombic modifications of the p erovskite structure. n addition to those types of distortions that require a multiplication of the pseudo cubic cell, there are several other distortions in perovskitetype structures that require only a slight modification of one or two parameters, resulting in tetragonal, orthorhombic, and rhombohedral symmetries. t is these latter modifications that are of most interest in the study of ferroelectric forms of the p erovskite structure, especially in the two groups of mixed oxides under discussion, A +2B 3 and A +3B+3 3. Other ferroelectric perovskite compounds, like Na+ Nb H 3, have been suggested to have multiple-type unit cells [6] even larger than in the CaTi 3 type. A classification of the p erovskite-type structures on the basis of the radii of the constituent metallic ions has been attempted by several workers [7, 8, 6, 9]. t has been pointed out by Keith and Roy [9] that it is not-, advisable to attempt to classify more than one valence group of structure types on anyone diagram. n other words, separate diagrams are needed for the compounds of the type A+2B H 3, A+3B+3 3, A+lB H 3, etc. t seems quite probable that perovskite-type structures with F-l, or some other such ion, in place of - 2 would also require separate diagrams for a reasonable classification. These diagrams still do not lend themselves to absolute classifications, as some compounds simply do not seem to fit, t has been suggested by Roberts [2, 2] that the polarization of the constituent ions may play an important role in determining the symmetry formed by a given pervoskite structure. A classic example of polarization determining crystal type over and above ionic radii may be found in the phenacite-olivine structure types where the Zn+2 ion is found to be out of place in a radii classification [22]. t is this notion of polarization that is used in the present paper in an attempt to make a better classification and diagrammatic representation of the perovskite structures. 4. Results and Discussion 4.. Mixed O xides of Divalent and Tetra valent ons a. General For the purpose of convenience most of the data accumulated has been put in the form of tables, although some of the more controversial compositions are also discussed in the following sections. t is known that CdTi 3 crystallizes in both the perovskite- and ilmenite-type structures [23]. As the perovskite structure requires a relatively large A ion and the ilmenite structure a relatively small A ion, it can be seen that all AB 3 compounds with Ti and an A+2 ion larger than Cd+2 should have the perovskite structure, wher eas those with A+2 ions smaller than Cd+2 should have the ilmenite structure. n all such cases where compound formation takes place, this is found to be true. The values used in this study, for the radii of the metallic ions under consideration, are listed in table. The composition, structure type, and symmetry, where known, for the mixed oxides of divalent and tetravalent ions are listed in table 2. The parameters of the unit cell are given for all those materials studied. nformation obtained in the present study is shown in boldfaced type, and the author's comments on previous work are given in italics. n general, r eferences to other works are made only when the particular compound or mixture has not been studied in the present work or when results of other investigators disagree with the r esults found in the present investigation. b. Ce 2:Ti 2 A specimen of Ce2:TiOz heated in air has yielded an X-ray pattern of Ce2 plus a perovskite-type phase. t seems highly unlikely that either Ce2 or Ti 2 would reduce, in air, to the poin t of forming an A+ZB + 3 structure. t seems more likely that an A+3B+3 3 structure is the phase found in the X-ray pattern (see discussion of classification of mixed oxides of trivalent ions). 76

3 c. SrZrOs. Radii and polari zabi lity, where used, of metallic ions pertinent to this study TABLE on R adius [iz~~)~:f~~~ " Radi us on a ----'-----' , ,---- BaH Pb H Eu +~ 8'+2 Ca+Z Od +: b A _ A ' 7_ _99 49_ 34_9 ' 56_ _ \n+2 "Fr+ 2 Zn +2 A _ RO N i+2.72 _9 Mg+' Be+:? ' ~L"'l'i valont A +'.5 Fe+3 Sc+' n _64.8 c _ 82 _92 Oa+3 Or+3 y +3 ions Bi+3.96 _ Gd +'.62 S m+3 N d+3 +' La+3 'l'ctf'avnicnt ions Ot< SiH Gc H \[n H V" rri H a _7,6,42.53 _6. 7~.79 _ ,6: _68 Unless othel'wise i ndicated, rad ii of the ion s arc talrcn from A hrells [3. b'rho rad ius of Eu+2 h S beon adapted from the val ue given by (, rcen [3ll and corrected for rad ius of -'=.4A. o 'rhe radius of n+3 and 8c+3 are both givell as O.8l A by Ahrens [3], As this eannot be shown on the diagram, n+3 is used as,82 A and Sc+' as O.8 A. This is tbough t to be justified as the compounds of Sc+' are said to ba \' e Slightly sma ller parame ters than the corresponclin g eompounds of n+' [9], d Unless otherwise indicated, polarizability of the ions is taken from Roberts [2], ''bc pola)'izability of Od+' was estimated as exploinecl in tex t, TABLE Toler- 2_ Th e compound SrZrOa h as generally been regarded as a cubic perovskite [24, 6, 25]; although N arayszabo [26] has r eferred it, like CaTiO a, to the monoclinic system. Th e X-ray pattern of this compound shows diffraction lines other than those found in simple cubic structures, definitely indicating some type of distortion of the unit cell. n addition, the "cubic" peaks in the SrZrOa pattern have a tendency to split into two or more peaks (not Kal and K(2)' The Ka2 doublets cannot be clearly distinguished in the SrZrOa X-ray p at tern, although thcy are quite clearly shown in p attern s of the true cubic perovskite specimens like BaZrOa or SrTiO a. The split in the pseudocubic peaks resembles those found in PbZrOa for a pseudo tetr agonal distortion with cia, although there are a few possible di screpancies in intensity valu es. On the other hand, the distortion may be of the type found in CaTiO a. As observed in at least six differ ent specimens, the SrZrOa " pseudocubic" peak at a valu e of h2 + fc2 + l 2 = 6 is split into a close doublet with th e low-angle side of the doublet lower in intensity t han the hi gh-angle side. Th e same peak in PbZrOa has the in tensities of th e doublet rever cd. Although CaZrOa and CaTiOa h ave foul' peaks very close together in this r egion, the two on th e low-angle side ar c of lower intensity than the two on the high-angle side. Such discrepancies, noted above, make it impossible to ass ign SrZrOa to either the PbZrOa ' CaTiO a structure. Calculations of (hlel) valu es for bo th types of cells, as well as theoretical intensity values for each structure, would have to be made before a fmal decision could be made. Nhx ed oxides oj the type A + 2B +< 3 J leat treatment ance Composition factor for pcrovskile Structure type 'r em perature 'rime ( ) (h' ) Symmetr y Heferences and diseussion stl'uc t U'Ca Mixed oxides contai ning, BaOO' PbOO, SrOO,._ Aragonite. Orthorhombic Berman, a ncl Fronde! [39] do clo _ Palache, D o, do do _. Do,. do do Do _ Oalcite. RhombohedraL Do, clo do Do do _do Do.do do Do do clo Do do clo Do, do c _ Do, OaCO' _ OaOO' OdOO, _ j\[noo' ]>e 3 _ ZnOO'., j\ l go O, j\ixed oxides containing Si2 n asio, PbSiO, SrSiO,. OaSiO, _ OdSiO, M gsi 3.4 Unknown.. Present work. Specimen sllpplied by E. Levin oj NBS stuff_ Unlrnown Winchell [4]_ Pseudo wollastonite. Unknown Present work. Specimen supplied by E. T. Carlson oj NBS staff. Pse udowollastonite. U nknown. Prese nt work. Specimen supplied by -. S. Yod er oj Geophysc;ul Luboratory, Carnegie nst., Wushington, D_ C. Unknown. Silverman, Morey. and Rossini [4]_ Enstatite Orthorhombic Present work. X -ray data obtained from specimen of Bishopsville m eteorite supplied by FT, S. Yoder_ a= 8_222, b=8,8o, c= 6_82 ri, 77

4 TABLE 'r olerance Composition factor for perovskite 2. M ixed oxides of the ty pe A +2B H 3- Continued H eat treatment ' cmpcrature (O C ) Timc (hr) Struct ure type Symmetry R cferences and discussion structure a Mixcd oxidcs containing OeO, BaOeO'. P b OeO,_._... _ 8rOeO,. _.. CaOeO' CdOe3. ZnO:OeO' MgO eo' Be O:O e 2 7~.64 _::::::::::::: g6~~~ _... _.... _._... _. _.. _... _._ Pseudowollastonitc _ U known Roth [6j' P seudowollastonitc _ Unknown Ro(h [6. U nknown P seudo wollastonite _ U nknown U nknown U nknown No : co mpound Enstatite Orthorhombic.235_... _.. No inform ation Symmetry almost texagonal. H eated at 2. psi. Prese nt work. Probably nonequilibrium. Roth [6J. Roth [6]. Probabl y n oneqltilibr ium. Present work. Probably nonf.quilibrium. Present work. Speciment contains Zn2Ge4, willemite type. p l us Ge O,. qltartz type. Roth [6]. a =8.66. b=8.95!'. c=5.346 A. : compound between B eo and OeO, seem' unlikely; probably onlll Be,Oe4forms. Mixed oxides containing ]vno, o 84._ " {' Mixed oxides B a VO,.. 8rY,... _ CaVO'.. M go : VO '.... B eo :VO ' (H e lium )._...2 (H e lium)._.. e:~~-(~~~~~~:::::: _ _ pel'ovskite C UbiC W ard. Glsh ee. McCarrol. and Rid gely [42]. Pel'ovskite.._ C ubic_._.. _... _... Y ak el [43]. Symmetr y reported as cubic with doubled cell Bl conta inin~ VO, Unknown U nknown.. P erovskite _... Orthorhombic.,. _. P erovs kite_..... Cubic... _... _._. U nknown... _.. _... _... _ U nknown... _ _... Prese nt work. Present work. Presen work. a=5.326.)= c=5.352 A. W ard. G ushec. McCarrol. and Ridgely [42]. King and Suber [44. Kin g and Suber [44. Mi xcd oxides containing Ti 2 BaTiO,_ Pb'fiO,.._... _Q _.._. _... _ E uti 3.. SrTi3.. CaTiO,.._.. _ _._._ >.7.._ CdTiO,_.. } CdTiO,. Mnrri3 Ferri3 ZnO:TiO, e:~r:~'_~~::::::::::: _._._... _ _. CoTiO, _.... _. NiTiO,.. _... _.. M gti O,... _. B eo : TiO,_ _ _ _... _ Perovskite _... Tetragonal ca > L _._.. Present work. a = c=4.29 A. P erovs kite..... _. Tetrago nal ca> L _... Jalfe. toth. a nd Marzullo [7]. a = c= 4.36 A. P erovskite_._... Cuhic.. Brous. Fanku cb en. and Banks [45J. P erovskite _... Cubic.. Present work. a= 3.94 A. Perovskite Orthorhombic c Coughanour, Roth, Marzullo. a nd Sennett [4]. a = b= c=5.443 A. Perovskite._._... Orthorhombic_._... Present work. = 5.3. b=7.66. c=5.49 A. lmenite._. _... _.. Rhombo hedral Posn!ak a nd Barth [23]. me nite Rhomboh edral Present work. a=5.585 A, a=5t57'. lmenite. RhombohedraL. Wells [24]. No : co mpound Present work. Specimen contains ZnzTi4, spinel type. plus TiO,. rutile. menite _._... _. RhombohedraL. Prespnt work. X Ray pattern too diffuse to mea~ure parameters. menite._._.. RhombohedraL Present work. a =5.448 A. a=55. me nite RhombohedraL Presen t work. a=5.59 A, a =54 3'. No reaction _...._..._.. Lang.ltoth. and Fillmore [3]. Mixed oxides containing SnO, BaSnO'... _..92 PbO: SnO,._ _. _.. _ 85_..... _._ _... _.... SrSnO '_._... _.. 85 CaSnO'... _.8 CdSnO'._.. 8 MnO:8nO,. _.. _.74 ZnSn3 (?).. _._.72 : 8nO'.. _ Perovskite Cubi c _ Present work. a=,.4 A. No : compound Jall'e. Roth. and Marzullo [7]. Specimen con tains Pb2S n 4 unknown structure plus SuO,. No reaction Starting material PbO and SnO,. U nknow n _ Distorted fluorite- type stru cture, probably PbSn4. Starting material precipitated hy drated lead stannate. PbSnO' Unknown.. Coffen [46]. Starting material p recipitated hy drated lead stannate. P erovskite... TetragonaL._.... N aray Szabo [26]. Perovskite Cubi c Present work. Commercial specimen, unfir ed. a=,.34 A. Perovskite.... _._. C ubic_.._... M egaw [3]. Coffcen [46]. Perovskite..... _. CaTi3 type. Naray Szabo [26]. Perovskite Ort horhombic c Co ughanour, Hoth, Marzullo. a nd Sennett [4]. a=5.58. b= c=5.564 A. No compo und _ Preselt work. Specimen contained only Sn O,; CdO volatilized. A compound of CdSnO, probably exists belo w this tempera ture. Unknown... _.. _... _.. _... _... _.. _._.. Coffeen [46]. Decomposition of CdSnO, is abou t.77 C. Perovskite._._.... Ca'l'iO, type.. _. :-;raray Szabo [26]. No reaction Present work. MnO added as MnC3. Speci men contained SnO,. Mn3 4. Unknown._... _. _ _. Coffeen [4]. P ublished pattern litobably spinel plussno,. Present work. Specimen contained C2Sn 4, spi nel p lus SnO,. Coffeen L46]. Published pattern that of a mix t UTe oj spinel and SnO,. t~:~~::~::::::::: --.~ ~:~~\:~.~~~.~~::::: :::::::::::::::::::::::: 78

5 T,BLE 2. A!fixed oxides of the type A +2B3- Continuecl Composition '' olerancc factor for pcrovskito structure a J cat treatment 'r em perature (O C ) 'rime (lir) Structure type Symmetry References and d iseussion Mixed oxides contain ing Sn Oz- Continu cd NiSnO' MgSnO' BeO:SnO' _ oo , ~, S U nkno\vll Co ffeen [46J. lmenite Rhombohedral.. Cou ghanour, Uoth, Marzullo. and Sennett [4]. X-ray patern too diff"se to mea8<re ljarameters. No : compound _ Coughanour, Roth. Marzullo. and Senne tt [4]. Specimen contains ~lg2s n 4, spinel, p lus SoO,. No : compound.. Cougha nour, Roth, Marzullo. a nd Sennett [4]. Specimen contains Mg,SnO" spinel. pl"s SnO,. Unkno\vT. ColTeell [46]. No studies reported. Reaction "nlilaly from analogu to BeO sustems. Mixed oxides containing UfO,d PbRfO, _ SrH fo, _ CaUfO, _ erovskite P erovskitc Pero\'skite P seudotetragonai. Shirane and Peplnsky [47J. CaTiO, type Naray Swbo [26]. Unlikely tliat pure RfO, was available attliis tim. CaZrO, typc _ Curtis, Doney, and Johnso n [48J. BaZrO' PbZrO' SrZrO, CaZrO' CdO: Zr2 MnO:ZrO'_. ZnO: 7,rO,. CoO :Zr2 NiO:ZrO' TiO: Zr2 MgO:ZrO' BeO:ZrO..8S Mixed oxides contain ing Z'OJf,45 P crosvkitc. Cubic Present work. fl=4.9f A. P erovskitc l>scudotetragonal Jalre, Roth, and Marzullo [7J. a=4.56, c=4.9o A. Pcrovskite PseudotetragonaL. L~~~;;;;;;;;;;;;; Sawagllehi, Maniwa, and Tosh ino [49J. Perovskite PseudoietragonaL._ Sawaguchi, Shiranc, and 'akagi [5}.g,75.. P crosvkitc l>scudocubic Present work. a=4.99 A. Starting malerial commercial 8rZ'3, also contains excess Afonoctinic Zr2 plus unknown plase., 5._ ]>erovskitc Probably orthor hol- Pr cs~ nt work. a=5.792, b=8.89, c=5.88a. bic. c Perovskite Cubic _ Perovskite CaTiO, type.55_ P erovskitc Orthorholllbicc _ Perovskite CaTiO, type (orthorhombic).,4 No : compound,3 3 No reaction No reaction No rcaction ,42 (He liul) 3 No : compound,55 48 No : compound,8 O. 5 No reaction Slartina material SrCO, pt"s Monoclinic 2' no e.rcess phases. Wells (24J, Wooel [6J, Shirane and Hosbino [25J. Naray Szabo [26]. Coughanour, Roth, M.. trzullo, and S~ nn ett [5]. a= h=8.8, c=i.758 A. Naray-Szabo [26J. As many oftlte compo" nds listed in til is reference do no actuauy exist, CdZrO, cannot be accepted as a true compound wilhout jurtlier experimental evidence. Rolh [9J. Contains Cltbic Z'O, solid solution pl"s J" n,o. Present work. Dietzel and Tober [5l' Dietzel and Tober 5. Roth [9]. Contains cubic Z'O, solid solulion Jlus rr' io.. Specimen SlLJplied by F. Brown, Jet Propulsion L ab., Calif. nst. of 'Tech. Cougha nour, Roth, Marzullo, and Se nnett [5. Contains cnbic ZrO,soliri solution pt"s MgO. Lang, Uoth, a nd ~"' illlore [3]. Mixed oxides containing CeO, BaCoO' PbO:CeO' SrCeO' CaO :Ce2 CdO: Ce2 MgO:CeO. BeO:CcO' r~~ :~~~~~~~~~~~~~ r~~~ :::::::::::::: e :~~~:::::::::::::: r~~ :::::::::::::: {::::::::::::::::::: l~ :~~~::::::: ::: :::: No,8 P erovskite Pse udocubic Present work_ a=4.887 A. P erovskite Pseudocubic Present work. a=4.887 A. Possibly orthorhombic. h Perovskite CaTiO, type N aray-szabo [26]. Perovskite Cu bic Hoffman [52], Wells [24J, W ood [6J..5 No reaction Present work. Perovskite CaTiO, type Naray-Szabo [26J. Compound probably does not exist. 4 J>erovskite. _ Orthorhombic Present work_. a=5.986, b=8.5~l, c=j.25 A. Perovskite CaTiO, type ' aray-szabo [26]. No reaction Present work. No reactlon Keith and Roy [9J. Perovskite CaTiO, type N aray-szabo [26J. Compo"nd probably does not exist. No reaction _ Keiih and Hoy [9J. Perovskite CaTiO, typc _ Naray-Szabo [26J. Compound probably does not exist. reaction Present work. No reaction Keith and Roy [9J. Perovskite. Carri3 N aray-szabo [26J. Compound probably does not exist. Such a compound could only be an antiperovskite structllre..5 No conlpound Lang, Roth, a nd Fillmore [3J. Possibly a solid sol"tion of BeO in CeO,. 79

6 TABLE Composition Tolerance factor for perovski te structure a. 2. lt[ixed oxides of the type A+2B 3- Continued H eat treatm en t Temperature (OC) Timc Structure type Symmetr y References and discussion (h') J\' ixcd oxides containing lt2 i BaU O,. 82, (Argon)... 5 SrUO,.. 75, (Argon)...5 CaUO '. 7 MgO:UO '- BeO :U O, t~~~(~~~~~~~~::::,8 (Argon).5,8 (Argon).5.5 Perovskitc Pseudocubic Lang. Knudsen. Fillmore. and Roth a~4.387 A. Similar to BaCeO, with small splitting of diffraction peaks. Perovskite ~ Orthorhombic c Lang. Knudsen. Fillmore. and Roth a~ 6.. b~8.6, c~6.7 A. Perovsk ite _ Orthorhombic c Lang, Knudsen, Fillmore, and Roth a ~5.78, b~8.29. c~5. 97 A. Alberman. Blakely. an d Anderson [27J.; Lang, Knudsen, Fillmore, and Roth ~r~:m:f~: : : : : : :~~;;~:::::::: ::::::::: [8J. very [8]. [8J. [8J' Lang, Knudsen, Fillmore, and Roth [8. Mixed oxides containing T ho,' BaThO,.. 8 :::::::::::::::::::: :::::: ~~~~~~~n~:::::::::::: g~~\'b~'ty;e:::::::::: ~~~a~~s'zlt~ [~~ells [24J. Wood [6J. a As the radii givpn by Ahrens [3] a re closer to Pauling radii than to Goldschmid t radii. the values listed for tbe tolerance factor are, in general, slightly smaller th an thosc calculated by other authors (Keith and Roy [9J. Wood [6]), using modified Gold schmidt radii. b Probably onl y CaO can form a perovskite componnd with MnO, (Ward. Gushee. McCan'ol, a nd Rid gely [42]). t secms unlikely that CaMnO, has a s imple cu bic structure. and it is tentatively left on the border between orthorhombic and pseudocubic ty pes. c This structure is related to cubic porovskite as follows: a~.j2a'. b~2a', c~..fia', d Due to the lan tbanide contraction. HfH ]]as a radius only sligh tly smaller than ZrH, and tbe compounds containi ng HfO, are pro bably m ostly isostrnctural with t.he corresponding ZrO, compounds. e 'ho oseudotetra!:onal structure w ith ca< l is actuall y orthorhombic with a=.jz,a', b=2.j?,a.', and c=2c'. f N o compounds of the imenite structure type have been found with Zr2, or, indeed, with an y BH ion larger than 8n, g Strong anomaly of the dielectric constai,t at abollt 23 C, antiferroelectric below this tempcrature. h The exact nature of the distortion h as not been determined. as the amount of distortion i, small. T hcre are definite splits ill the diffraction lines as well as excess peak s other than those fot' a Simpl e cubic structure. ; No work bas been reported on U O, systems with N io, Co O. Zn, MuO. CdO. or FeO. ; P u blished X-ray pattern is that of a mixture of UO, solid solntion and pero vs kite com pound. Pattern published for Ca,UO, is act ually the perovskite-ty pe compound. k Perovskites of the followin g ox ides with '' ho, have heen listed by Naray-Szabo [26J: BaO. PbO. SrO, CaO, CdO. and l\ lgo. Of these reported compounds, proba bly only BaT ho, really ex ist s (Keith and R oy [9]). Although no ThO, compounds were examined in the present work, it seems likel y t hat BaTh O, wo uld have the sam e type of structure as is found in BaCeO, and BaU O,. d. CaU 3 in a total increase in the tolerance factor. However, a replacem ent of 5 percent of UH by U+6 and Ca+Z increases the tolerance factor to only.726. Thus it can be seen that the lower limit of.77 for the tolerance factor in A+2B 3 perovskite structures is not absolutely correct. The compound CaU 3 also h as a CaTi 3 structure. However, a 5:5 molecular mixture of CaO and U 2 does not yield an equilibrium perovskite compound. The forma tion of the perovskite compound in the CaO-U 2 system takes place only in the presence of excess CaO. This phenomena h as been discussed by Alberman, et al. [27] and by L ang, et al. [8]. The perovskite compounds of the type A+2B H 3 have been assigned a minimum tolerance factor (t ) of.77 by Keith and Roy [9]. The tolerance factor for the perovskite structure, as described by Goldschmidt [7], is e. BaGeOa The AB 3 silicate compounds cannot form p erovskite-type structures, as the silicon ion is much too small, always OCCUlTing in tetrahedral coordination. The B ion must occupy an octahedral position with respect to oxygen, even in the most distorted structutes, in order to be classified as a perovskite. As the germanium ion is larger th an the silicon ion and is known to OCCUT in octahedral coordination, a study was made of the reaction of Ge 2and various divalent metallic oxides. The only known case of octahedrally coordinated Ge H is one of the polymorphic forms of Ge2. Ge2 can be readily formed in the rutile-type structure by h eating the quartz-t ype polymorph at 7 C and 2, psi. 3 An attempt was made to form a titanate-type BaGe 3 (with th e germanium ion in octahedral coordination) by h eat ing the pseudowollastonite form to 7 C at 2, psi, but no ch ange in the crystal structure was observed. Differential thermal analyses of BaGeOa indicated a phase transformation at about 34 C. 4 where t = tolerance factor for perovskite structure, RA= ionic radius of larger cation, RB = ionic radius of smaller cation, Ro= ionic radius of oxygen (=.4 A). This tolerance factor for CaU 3 is equal to.7 and is th e only known A +2B 3 perovskite-type compound with t considerably less th an.77. Some Ca+2 may actually substitute for U in the B position, accompanied by a partial oxidation of UH to UH, to give a structutal formula Ca(Ut4U~ ~_X) Ca ~ h-x») 3. Such a structural substitution r esults ' A specimen of rutile-type GeO, was prepared n this manner by A. Van Valkenburg a nd E. Bunting of the Bmeau stafl. ' :- 4 The diflerential tbermal analysis was performed by E. Newm an of the Bureau stafl. 8

7 This phase transformation is apparently very disj'uptive, as a pressed pcllet of BaO:Ge2 results in finely divided white powder of crystalline BaGe3 when heated to, C and furnace cooled. A -per cent addition of F c2 3 to BaGe3 results in an intact ceramic sp ecimen with an entirely different X -ray pattern, which may represent a stabilized form of high-temperat ure BaGe 3. Si A classification of structure types based on the {)onstituent ionic radii can be made for all the compounds of th e A+2B H 3 typ e. However, the properties of the solid solutions formed by a mixture of two or more compounds cannot always be correlated by a simple radii classification. n an attempt to xplain some of these discrep ancies a third property, polarizability of the consti tuent ions, has been used. t is exceedingly diffi cult, in the presen t state of knowledge, to arrive at correct valu es for the polarizability of a given ion in a given structure type. Th e values used here have bee n taken mainly from the l'esults published by Roberts [2, 2 ] and arc listed in table. However, a Roberts did not give a val ue for Cd+2, this ion was assigned a value that would fit the observations of other workers. Both P auling 28] and Kettelaar [29] indi cate that the polarizability of t he Cd+ 2 ion in a given stru cture type is between those of Ba+2 and of Sr+2. Therefore, the values given by K ettelaar [29] for B a+ 2, Cd+2, and '+2 wwe compared, proportionately, to those given by Roberts for the Ba+2 and Sr+2 ions in th e perovkite s tructure, and a value of approximately.56 A3 was assigned to the Cd+3 ion. A b asic division of s tructure types can be made on a two-dimension al chart of AB 3 compounds, wh er e the radius of the A+2 ion is plotted as the ordinate and the radiu s of the B +~ ion as the ab scissa. n figure and table, all values of the radii, except for Eu+2, arc taken from Ahrens [3] an d r eprese nt the ionic size for sixfold coordination. As pointed o ut by 'ivood [6], a correction for coordination would tend to move boundary lines but not to distort the picture of the basic classification. The value for Eu+2 has been taken from Green [3] and corrected for a r adius of - 2 of.4 A. n general, a division {)an be made between structur al types containing large and small A+2 ions. The boundary of this division usually fall s near a value of. A, and often the Ca+2 (.99 A) or Cd+2 (.97 A) compounds occur in both structure types. For the carbonates, all {)ompounds containing divalent ions larger than Ca+2 h ave the aragonite structure, whereas those with ions smaller than Ca+2 h ave the calcite structure. the case of the silicates and germanates, the p seudowollastonite structure type occurs for most of the compounds containing large divalent ions, wher eas the enstatite structure is found for the small ions like M g+2 (.66 A ). Except for the Ba and Sr vanadates described in table2, all other compounds:described in this study 8 M+n4 J4 T4 s~ Hf,Z~4 C~ y4 nt4.35 '--""e-.--.-"'ti-"t"'7rr--+-it-'+-'"r---r-l..lt'--'l v: v,.25 ARAGONTE <.5 PSEUDO WOLLASTON TE e o e S rv 3 <J) z 9.5 +"u..95 :> " 7' } CALCTE LMENTE i [ : : NO CO MPOU ND l :. : O X - X..J e e.65 a r------r L _ ~~K~~W~ J <J) a: PEROVSK TES.J - e , N 4.2. Classification of AB 3 Compounds Containing Double Oxides of Divalent and Tetravalent ons ~4 e.3!l O X!: J OJ.5 NO COMPOUND X " ENSTATTE: X.8 X X.9. RADUS OF 8+ 4 ONS. A F GURE. Classification oj the A +2B+'O,-lype com po unds according to the constittent ionic mdii.. Co m pound s sludied in t he present wo rk th at have t he stru cture ShO\\Ol by t he areas bou nded by dashcd Jincs; ~. compo ullds not st udied in t he prescn t WO k that arc ass umed to have the foi tr uct urc s hown by the areas bound ed by das hed lines ; co mpounds with complex or unknown s truct ure type; X. pasi tion of co llposi Lion~ s tud ied in the prf'scnt work that do not form A compo u nd s ;, the presence of a co mpou nd of F e'i 3, and tho a. bsence of a com)ounci at th e composition Zn O:Ti2 are indicated t.oge ther, as Zn H and Fe H lave approximately the same l'adills..j can be divided into perovskite and ilmenite stru cture types. The boundary between the two types occurs at a value ncar that of the Cd+2 ion and is shown as horizontal for the purpose of convenience. As no ilmenite compounds arc known with a B+ ion large t' than the radius of SnH (.7 A), the lower ri ght cornel' of figure is shown as an area of no compound formation. n all cases the boundary lines b etween stl'uctme types arc only an approximation, as not cl ough information is available on mixt ures of compounds of two differ ent stru ctu re types. n gen eral, there is only limi ted solid solu tion, if any, between compounds of diierent structure types, althou gh there is consider able or compl ete solid solution between compounds of a given type. An exception is found in som e mixtures of compounds on adj acent sides of th e boundary b etween orthorhombic and cubic (or tetragonal) perovskite compounds. A classification of those compounds h aving perovskite-type structures is shown in figure 2. The A +2B a p erovskites can be divided into two general types, those that are cubic or have distortions requiring an elongation of one or more parameters, and those that have di stortions that r equire some multiplication of the busic p erovskite unit cell. The latter type is mainly represented by the CaTiOa orthorhombic structure, those perovskites with relatively larger BH iolls and smaller A+2 ion s. An intermediate group are those compounds labeled pseudo cubic which, although not cubic, have not b een definitely iden tified as to structure type. This group sep arates the cubic from th e orthorhombic perovskites in figure 2. Sup erimposed upon the cubic group are tho se compounds that ar e tetragonal (cja> ) or pseudo-tetragonal (c Ja < ), ferro electric and an tiferroelectric, r espectively. An area showing

8 t4 T Hf Zr Sn Ce Th U Ti.9 \ TETRAGONAL C ---' ~.8, vi', z.5 <f) x \\ ~ N. RHOMBO'\HEDRAL,,,,- \ \ \ \ ' " PSE UDOTETRA GONAL ~ 'y a <,, Y a l l '' :::i.6 CUBC OR PSEUDOCUBC ~.5 <! r.7 - o,, ) o >- "- ::> +:" pt+2, <r 2 " H Zr.3 'i'<! Sn..--,---;----'----,' '-'-,--,---,..--,-----, --' ORTHORHOMBC.5 o a.!l,, ~~ eo.::::::::::' X X ,. ca+ 2 Cd+ 2 Co+ 2.3'=---'-,----:'::-----'----'------'--'----'-,-----'----' B RADUS OF 8+ 4 ONS, A RADUS OF 8+ 4 ONS, A F GURE 3. Graph of A +2 ions for of ionic radii of B ions and polarizability some of the componnds of the A +2B +< 3 perovskite stn,cture type. 2. Classification of the perovskite A +2 B 3-type compounds according to the constituent ionic radii. FGURE, Compounds studied in the present work that have the structure shown by the areas bounded by dasbed lin es; e" com pound s not studied in t he present work t hat arp ass umed to have the structure sho\\'n by t he meas bounded by dashed lines;. compo unds studied in t he present work t hat do not have t he perovskite type struct urc; X, position of compositions studied in the present work that do not form A+2B H 3 compounds. As the compound CaMn3 has not been studiea in the present work ancl con flictin g reports on its symmetry exist, it is tentatively left on the borcier between orthorllombieand pseudocubic types anci is shown by q uestion mark over symbol., Compounds having ferroelectric or antiferroelcctric structure types;., compounds hav ing cubic or pscuccubic stru ctw'c types; X, position of composition that docs not form A+2BH 3 compound. three-dimensional model is shown in figure 4. The field of ferro electricity and antiferl'oelectricity then becomes a volume instead of an area, and the symmetry of solid solutions is correlated by connecting a straight line between the end-member compounds plotted in three dimen sions. This straight-line relationship probably only holds true for solid-solution series that do not cross the eubieorthorhombic boundary. Other solid-solution series probably can only be shown by a curved line connecting the end-member compounds. t is recognized that the polarizability of the B ion also plays an important part in determining the symmetry of a perovskite compound. Theoretically the third dimension should be some weighted average of the polarizability of both the A+2 and BH ions. However, as the exact nature of such an average cannot be calculated at the presen t time only the values for the divalent ions are used. n figure 2 the area of ferro electricity and antiferroelectricity, represented by the field of tetragonal (cia> ), rhombohedral and pseudo tetragonal (cla< l), can now be considered to b e a two-dimensional proj ection onto a basal plane of a volume of such structures formed by plotting polarizability as the third coordinate. t should be possible to correlate the solid solutions of other perovskite compounds of this group on the basis of the proposed diagrams. However, it should be remembered that the boundaries shown arc only approximate; no account is taken of the polarizability of the BH ion, and the compounds distant from each other in ionic radii, or whose solid-solution series cross symmetry boundaries, do not n ecessarily have a lineal' relationship. n the system BaTi3-CaTi3 [33], the tetragonal solid solu tion extends further than would b e shown by a st.raight line connecting the two compounds in figures 2, 3, and 4. The reason for tlls is either that the BaTi 3 posit.ion is not shown high enough in the th ese compounds can be drawn sa tisfactorily, as indicated in figure 2. However, if the structures of various solid solutions are discussed in terms of this diagram it is found that there are certain discrepancies in the boundaries of the ferroelectric field. t is true that a complete series of solid solutions exist between BaTi 3 and PbTi 3, all of which are ferroelectric-tetragonal (cia> ). However, complete solid solution also exists between BaTi 3 and SrTi 3, only in this case the solid solutions revert to cubic symmetry (at room temperature) with a relatively small content of SrTi 3. These properties are in contradiction to the ferroelectric field shown in figure 2. The properties of the solid solutions between PbTi 3, PbZr3, and PbHf 3 can be explained by introducing a rhombohedral field b etween the tetragonal fields, figure 2. ~h.e discrepancies can be partially explained by uthzmg the theory of polarizability of th e ions. gnoring the polarizability values for the tetravalent ions because not enough values are available to make a decent analysis of the results, a three-dimensional plot can be made with polarizability of the divalent ions as the third coordinatc. A partial cross section o~ this type of diagram is shown in figure 3. n this dagram the polarizability of the divalent ions is plotted against the radius of the tetravalent ions. The diagram correlates the solid solutions of Ba Pb, and Sr titanates. The rhombohedral field ha~ b een so drawn in figures 2 and 3 to indicate the ferro electric phase observed by Shirane and Hoshino [32, 25] in solid solu tions of PbZr3 and BaZr3. The symmetries of the ferroelectric solid solu tions can best be seen if a three-dimensional model is constructed with polarizability as the third dimension. A diagrammatic representation of such a 82

9 prepared in this study, do indeed seem to indicate tetragonal :ymmetry. However, as 8rZr3, which z is also in trus pseudo cubic area, is defini tely not Q Bo tetragonal, some doubt still exists as t o the true +< symmetry of this portion of the diagram. t is quite lj.. likely that all of the area covered by the pseudo cubic >field in the present diagram docs not have the same Cd t::: -l symmetry. Perhaps the area grades from tetragonal S, id through orthorhombic into still other symmetries. < N t is apparent that much more work remains to be Co n: < done on the symmetry of solid solutions of this type -l before a finished diagram can be presented... Theoretically figures 2 find 4, especially the threedimensional diagram (fig. 4), should be usable to ''" predict the symmetries of the solid solu tions of any rs' two or more compounds. However, it must be " Pb~ remembered that th e positions of th e boundaries, as shown, arc only approxima te because of lack of exs, ~ perimenlal data on solid solu tions. Therefore, at :::;) Q present, the usc of figure 4 is limited to selecting Lhe most probable of several possible symmetries. n t<-" many cases, several possibililies may seem Lo be equally probable and exp erimental evidence will be Mn V Ti Sn H Zr Ce U Th r equired before a fmal decision can be made. The RADUS OF 8+ 4 ONS, A diagram should prove of considerable help in interfg U RE 4. Th'ee-di mensional graph oj the perovskite-type preling inconclusive dala th at might olherwise A +2B 3 compounds lsing ionic mdii of the A+2 and B receive an incorrect or indefinite interpretalion. tans as two coordinates and the polw'izability oj the A +2 ions The present diagram.s, figures 2, 3, and 4, h ave as the third coordinate. been constructed from t h e data observed in ceramic O. Position of compound s of the orthorhom bic perovsk ite struct ure ty pe; ::;, bodies at room temperature. The appearance of positon of compollllcis of the cubic or psellcl ocllbi c pero l's ki te stru cture t ype;, positon of compolllhl s hav ing ferroe lectri c ' antiforroclcctric pcl'o vs kito t hese diagrams would be quite din'erent if constructed structure types. Coarse shacling indicat es bound ary hetween or t horhombic and pseudocubi c for other temperatures. For instance, at about structure typos ; Jncdium shad lng, bound ary enclosing compounds of ferroelectric 5 C the diagrams would show no fwld of ferroand antifcrroelcctric structure types; crosshatch shading, bound ary between pcro vs ki tc and SrV 3 s tructure types. The bound ary between cubic and electric-antiferroclectric compounds and solid solupseuclocubic pcro vs kite t y pes has not been sho\\' n on this diagram for Lho sake of clarit y. tions. Between - 3 C and C BaTi 3 would be orthorhombic instead of tetragonal, and t h e orthofield of ferroelectricily because no account is taken rhombic field, which h as been left ou t in the present of the polarizability of the TiN ion, or that the solid- diagrams, would playa much more irnportant role solution symmetries of additions of CaTi 3 to BaTi 3 in the diagrams. However, at still lower temperacannot be shown on a straight-line basis because of tures the rhombohedral symmetry of BaTiO 3 wou~d the large difference in ionic radii and polarizability. probably increase the arefi of rhombohedral sohd Probably both effects arc applicable in this case. solu tions at the expense of the orthorhombic field. The rhombohedral area has been indicated in t seems certain, however, that if enough information figures 2 and 3 because such a symmetry has actually on various compounds and solid solutions were availabeen found in this study. However, the orthorhom- ble, a diagram of this sort could b e prepared for a~y bic field suggested by McQuarrie and Behnke [33] given temperature, which would explain th e sohd for the solid-solution series BaTi3-BaZr3 and solutions of the perovskite compounds at that tembati3-cazr3 has not been included, as th e X-ray perature. powder patterns of this orthorhombic phase can only be indexed as pseudocubic and the symmetry 4.3. Mixed O xides of Trivalent ons is inferred from dielectric data. This orthorhombic a. General field seems very logical and probably should be included somewhere in the diagrams. Mixed oxides of the trivalent ions are known to McQuarrie [34] has reported a tetragonal phase form perovskite-typ e structures [26, 9]. Very occurring in the CaTi 3-8rTiOa system, between 55 recently a patent has b een granted B. T. Matthias mole percent 8'Ti 3 and 85 mole percent 8rTi3. on an electrical device embodying ferroelectric This tetragonal phase i not shown in figures 2 and lanthanum-containing substances. The compound 4, although it falls in the pseudocubic area separating LaA 3 (and LaGa 3) was claimed to have ferrothe cubic 8rTiO r type structure from the ortho- el ectric properties, although no proof of such ferrorhombic CaTi 3 type. These diagrams predict el ectricity or any description of the electrical propert hat, if this s:'} stem forms a complete series of solid ties was given [35]. The question as to whether or solutions, there should be a fi eld of symmetry other not th ese rare-earth aluminates arc ferroelectrics is than cubic and orthorhombic. X-ray patterns of very important. n agreement with single-crystal specimens prepar ed by M cquarrie, as well as several results of Matthias [35], rather low dielectric conpb '" < vl N '" 83

10 stants at room t emp erat ure wer e found for ceramic specimens of r elatively high porosity (2 t o 4% ). The X-ray patterns of these rare-earth aluminates have rhombohedral symmetry, as shown in table 3. The composition, structure type, and symmetry, where known, for t he mixed oxides of trivalen t ions T ABLE Compos ition 3. TolerH eat treatment ance lactor lor , perov'l'ernprratul'o Time skite () (hr) stru cture a are list ed in table 3. As for t able 2, parameters are given only for materials studied in the presen t work, and r esults of previous investigations are listed only when controversial subj ects are inv olved ' the par ticular composition h as not b een studied ll the present work. M i xed oxides of the ty pe A +3 B +3 3 StrLlctm e type Symmetry R eferences and d isclls'5i o n :Mixed oxides con tainin g Ah3,55 LaAO, P crovs kite Rhomboh edral.94 CeA 3. 9 d A3 SmAO,.9.89 B i, " Ah 3.87 P ero vski tc. CaTi 3ty pc P erovskite Nearly cubio P e rovs kitc.._._. Rhombohedral b P cro vski tc. ' r etragonal _ P erov:-:kitc. U n kn own c _ Pe rov sk~te _ Rhomboh edral b {P ero vskl te R hombohedral Pcro vski tc. Pro bably rhom bohedral. P erovski te 'f etragonal d. _ P erovskh e plu s garnel Orthorhombic (' plus cubic. t~:~~;~~~;~::::,55,55,5,55 YA ,835, Perovsk ite. CaTiO, t y pe 'rh3 type Cllbie Corwldum Rhombo hcdral Corundum R holll bohedral Coruudum _ Hholll bohedral il,3 P erovs kite pi us garnel Orthorhombic e plus c ubic. P ervos kite plus garne L Orthorhombi c e plus cubic. Garnet plus perovskitc. Cubic plus orthorhombi c. e Garnet solid solution Cu bic _ Y CrO, t y pe _ T et ragonal Low High n' 3: Ah 3 F e' 3: Ah O, Cr' 3:AhO, Oa' 3: Ab 3 Ah O, b 5 Prese nt work. a=3.788 A. «=9 4'. D istortion so slight that symmetry is assigned m ainly on tlte basis oj com parison 'with oth er alumina comp oun ds. Naray -Szabo [26]. Keith and R oy [9]. Prese nt work.,, =3.766 A, «=9 2'. Zacha riasen [53!. Keith a nd Ro y 9]' Prese nt work.,, =3.747 A. cx=923'. Keith a nd R oy [9]. Keith a nd R oy 9]. P robably has Sltme y pe oj struct"re as La-Ce and Nd A3. )laray-szabo 26]. Prese nt work. A p proxim ately 5 percent oj each p hase p resent (perovsl:ite p ltase, a=5.76, b =7.355, c=5.37 A). Present work. A mount oj perovskitepllase has decreased w ith respect to {Jarnet phase. Present work. A mount oj perovskile phase has dec reased witlt res pect to {Jarnet phase. Present work. Very smalt amount oj ])erovsliite Jhase Jresent. Keith a nd Roy [9]. Keith a nd R oy l9]. T etra{jonal Y CrO,-type structure ljrobubly is actually an orth orhombic perovskile stmct ure (see labte 4). ;\aray-sza bo [26]. Kcith an d R oy [9]. Keit h a nd Roy [9]. Keith a nd R oy l9]. Keit h a nd Roy [9]. Corundulll Rhomboh edral Present work. a= 5.3, a =55 J9'. Nli xed ox id es containing GaZ3 e~~~:::::::::::: LaOaO'.89 CeOaO'. 86 NdOaO'. 85 t~~----:~:::::::::: Sm' "Oa' 3.84 t:::::::::::::::::: Y,3 : Oa' 3.8 Oa' 3 _ t::::::: :::::: :::::.7 P erovs kit e. Orthorhombic tl _ Prese nt work. Very slight distorlion. a=5 494, b=7.769, c=5.579 A. P erovskitc Keith a nd Ho y l9]. Pcrovski tc Keith a nd R oy [9]. T his compound is probabty also orthorhombic. P erovskite Orthorhombic e Prese nt work. Distortion greater than in L ao a O,. a=5.424, b=7.74, c=5.~9 6 A. Pero vs ki tc Hhom bohedral or Keith a nd R oy l9]. monocli nic. OarneL _ Keit h and Hoy [ 9]. Specimen heated to moderate temperature. Unknown Keith and R oy [9]. Specimen heated to hiylt temperat"re. 8rneL Keit h a nd R oy [9]. Specimen healed to moderate temperature. Un kn O\V'l. Keit ll a nd R oy l9]. Specimen heated to high temperature. Corundu m Hb omboh edral Ke ith a nd R oy [9]. \ixed ox ides conta in ing en Ol L acro'.88 CeCr O' _ NdC r SmCr O' _. 84 YCr3.8 t:::::::::::::::: F e,o" C'2, As recei v'cd c.,o, Perovskite Cll bic )laray-szabo [26]. Perovsk ite Keith and R oy l9]. "Slight distortion probably mon oclinic. Jt Orthorhombic. P erovskite Cubic Wold a nd Ward 38]. " P ossibly very slightly ciist.ortcd.' P erovsk ite M onoclinic or orth o- Yakel [43]. rhombic. P erovsk ite Nearlye ubic Keith a nd Hoy [J9]. P erovskite R hom bohedral or Keit h a nd Roy [9]. Probably ortilorlombic. monocli nic. YCrO, type T etragollal _ Kei t h a nd R oy [ 9]. r crovski tc :M oll ocl inic _ Loo b y and Ka tz [36]. P robably an orthorhom"ic perovsliite oj Ca'i'iO, tpe. YCr O, ty pe. 'l'etragonal Keit h a nd Ro y [9]. All the YC r3-type stru,ctllres are probabt!j orthorhombic perot;skites oj CaTiO, type. Cornndu m Rh om bohedral Keit h and Hoy l9]. Corundu m Rhomboh edral Prese nt work. a=5.s8 A, cx=54 5'. 84

11 TABLE 3. Nlixed oxides of the type A +3 B Continued Composiiion Tole.. ance factor fo.. pcrovskite struc Lurca ] f eai t.. eatment rrimc (h.. ) Structure type Symmei.. y References and discuss ion ~ix ed oxidcs containing Fe,O, LaFe 3 _ Ce'e 3 _ N de'e 3 Sml"eO, _. GdFe3 _ YFeO, _ n, 3: Fe' 3 Fe'O' _ R O. i7 i l C~~'-~~::::::::::: Perovskite Orthorhombic e Pe.. ovskite_....._. Ca''iO, typo _ Pe.. ovskite....._.... Pcrovskite... Cubic.. Perovskite P.. obably monoclinic. YCr3 type... Tetragonal. YC.. 3 typo... 'l'etra;ronal.. Pe.. ovskite_... P erovskite. O.. thorhombic '.. Orthorhombic e " YC.. 3 typo T etragonal.. ''23.. CubiC.. Coru ndum._. Rh om bohed.. al Present work. =6.545, b=7.85j, <=5.562 A. Naray-Szabo [26J. Keith and Roy [9]. "Ve.. y slight disto.. tion, possibly lllonoclin ic." Orthorhombic. W. L. Roth ll], Yakel [4 ]. Unit cell twice that oj simple perovskite. Keith and Roy [9]. Orthorhombic Kei th and Roy [9J. Probably orlhorhornlic perovskite. Keith and Roy [9J. Probably orthorhombic perov.kite. Gellc.. 54]. Same space group listed as given by lvegaw [[5J Jor CaTiO,. Prese nt work. =5.279, b=7.g9, c=5.58.'. Largest distortion fronl, cubic symm,etry oj any oj tile Jervoskites in the present study. Kcith and Roy [i9]. ll YCr3-t.ype straclures are probably orthorhombic perovskites. Keith and R oy [9]. Keith and R oy [9J. :r. ixed ox ides co ntaining SO,3 LaSc 3. _... _. CeSc3.. NdScO,... Y,O, : Sc,O,_.... n, O, : So,O,... _ Sc,O,... _._... _. 82 i 9 i il Y Cr3 TctragonaL _ Keith and Roy [9J. ljcrol)skite. YCr3. _..._... TctragonaL..._.._.. Kei th and Roy [9]. perovskile. YCrO'..._... T eiragonal... Keith and Roy [9]. perovskite. '', 3... _..._..._. Cubic..._._... K eith and Roy L9]. ' [',,..._.._..._. ubic._..._..._.. K cith a nd R oy [l Oj' '',,_._._.... C ubic_..._..._. K eit h and R oy [9. Probably orthorhombic Probably orthorhombic Probably orthorhombic ~ix cd oxides containing n23 La n3.. _... _.. Nd n3..._ Smln3_.._... Y, a: ln' 3... n' i il f::: ~~~~~~~~:~~~~~ ::: :: ::: ;~:::~::~c~:_:.:_~~~~ ~~~ ~::~:f::~~~i :~;,~~,~_:: : Present work. ( =5.728, b=8.27, c=5.94. A. Keith and Roy [9J. Probably orthorhombic perovskite. P ad urow and Sc hustcrius [55J. rhombic).,35.5 Pcrovskitc _ Orthorhombic e Present work. a=6.627, b=8.2, c=5.89. A. Orthorhombic e Prese nt work. ( =5.589, b=8.82, c=5.88. A. C ~~~~ ~:::::: : :::::: :~. ~f;o;~ ~~~~ ~~:::::::::: C ubic._. K cit h and Roy [L9J. Probably a mistake on the chart as no mention is made oj th is composi tion in the tet of the )('Jer. '',, C ubic... Padurow a nd Scllllsterius [55J. {::::::::::::::::::: '', _ C ubic.._ Kcith and Roy [t9j. As reccivecl.. ''23 Cubic Prcsent work. a=.7. A. Oxides of rare-earth iype L ay 3 y ' 3 L a23: Sm2 3 Sm'3 _ ='d, 3 _ CO' 3 La23 O. i.7l i5 i i l i. il As received,2.. Perovskiic_. Pseudocubic (ortho- P adurowand Sc husier ius [55]. rhombic). '',,_._.. Cubie...ceith and Hoy 9j' '',, _... Cubic.. Keith and Roy 9. '',,.._... Cubic.. Keith and Roy [9. La2 3 H exagonal Present work. a =3.88, c= A. La'3.._. l exagonal... Keith and Roy [9J. La2 3 HexagonaL Prese nt work. a=3.45, c=6.3g. A. " U n les~ otherwise indicated, rad ii of ihe ions are iaken from Ahrens [3J. b This type of rhombohed ral d istortion of the perovskite siruciure is similar io that reported by Askhao, F ankuchen, and Ward [7] for LaCo 3. r A symmetrical doublet was report.ed for the () reflectio n. 'rhis doublet was also observed in present work for powdered m at.rriul ; however, intact specimen showed twice the in tensity for lower-angle pea k, indicating rhombohedral symmetry wit ll <»9. d Thc siructure suggested for BiAlO3 is similar to t hat of PbSnO,. As the Jattcr compound does not exist, the compound BiAO, cannot be accepted without further experimental confirmation. _ e 'Phis structure js related to cubic perovskitc as follows: a~,j2a', )~2a', c~ -J2a'. f Tempcraturcs above,55 C werc obtaincd by cmploying a gas-fircd co mmercial furnace capable of practlcal opcration up ( aboui,85 C. 85

12 b. YAO a Y 2 a:a 2 a heated at,835 C 5 for h' contained even less of the perovskite structure. t seems that attainment of equilibrium between the garnet and perovskite structures in Y AOa is a slow process, and one of these structures might be only a metastable phase and have no true cquilibrium position. A detailed analysis of the phase equilibria throughout the Y 2 a-a2 a system would be necessary to answer this problem completely. The compound YAO a was assigned to a new structure type, YCrOa, b y Keith and Roy [9]. However, the compound YCrOa has been called a perovskite by Looby and Katz [36]. The X -ray pattern for the YCrOa-type structure in YAO a specimens can definitely be indexed as a perovskite type, as can be seen in table 4, and is similar in all respects to the CaTi 3-type structure. This structure has the additional advantage of having a much smaller unit cell. Actually the distortion from a cube is no greater than that found in CaZrOa or CaSnOa and does not deserve a new structure-type designation. Therefore, the orthorhombic-type structure, originally assigned to CaTiO a, may now be considered to be the more appropriate structure for the compounds referred by Keith and Roy [9] to the YCrOa type. Y AO a has been reported to form a garnet (solid solution) type structure by Kcith and Roy [9] who state that the garnet structure is a low-temperature form and the perovskite (YCrOa) type structure is the high-temperature form. This observation does not agree with the evidence found in the present study (see table 4 ). A : mixture of Y 2 a and A 2 a heated for h' at,5 C contained about 5 percent of the garnet-type structure and 5 percent of the perovskite-type structure. vvhen this specimen was reheated at,55 C for 9 h' the amount of the perovskite-type structure had greatly decreased relative to the garnet type. A second specimen of T ABLE 4. As very little is known quantitatively about the polarizability values of the trivalent ions in perovskite compounds, this factor has not been used in the present work to describe the classification of these structmes. All the compounds studied are indicated in figme 5 according to the radii of the constituent A and B ions. As a complete diagram would list each compound twice, the B ion, for convenience, is always taken as the smaller ion. t can be seen from this diagram that all of the compounds in the upper left of the diagram, l arge A +3 and small B +a ions, form perovskite-type structmes. This group is followed by a belt of T2a-type structures, most or all of which probably represent solid solutions rather than true compounds. The lower left corner, containing small ions in both the A and B positions, shows a field of corundum (or ilmenite) type structures, probably solid solutions. The upper-right corner, in which both A and B are large ions, contains a field of La2 a-type structmes, probably solid solutions rather than compounds. This diagram does not differ appreciably from that of Keith and Roy [9]. However, the perovskite field is enlarged to accept all those compounds classified by Keith and Roy as of the YCr3 structure. n addition, a line is drawn to separate the field of rhombohedral perovskites from the r est of the perovskite compounds, which apparently all have the CaTiOa-type structme. t should be emphasized here that no compounds of the A+3B +3 3 type are known to have a simple cubic perovskite-type structure. One discrepancy in figme 5 might be found for the LaCo 3 compound reported by Askhan, Fankuchen, and Ward [37]. Co+a is listed by Ahrens [3] as having a radius of.63 A, essentially the same as that of Cr+3. This would place the compound L aco 3 wcll within the field of orthorhombic pcrovskites, instead of in the rhombohedral field as it should be. A possible expl anation of this discrepancy, other than assuming incorrect radii or resorting to nonstoichiometry, is the possibility of having large polarizability in the lanthanum cobaltate compound. The compound occw"ring in the specimen of Ce2: Ti 2, mentioned earlier, can be explained by this diagram if it is assumed that both Ce and TiH have been reduced to the trivalent state. Ti+3 has a radius of approximately.76 A [3] and the compound X-my powder dip'mction data for YAlOa Ke ith and Roy [9] Present work kl 4.4. Classific ation of ABO a Compounds Containing Double Oxides of Trivalent ons b d d hkl Relative intensity (' Observed Calculated A A l A ] i J2 2l J ]] l 2 (Ah3) J a This pattern is actuall y from a s peci men of 3Y,,,5Ah3 stated as having tbe YCr3 type of structure similar to the : specimen. b X-ray diffract ion lines due to tbe garnet solid-solution phase have b een omitted., Observed intensity of tbe difraetion peaks relative to the stron ges t peak. ' T emperatures above,55 were obtained by employing a gas-fired comm ercial furnace capable of practical operation up to a bout,85 C. 86

13 -- ---, d'.2 RHOMBOHED- ( RAL. ql.oo.,.n,,. -- Tl 2 3 «;.8 ::> " )!(J X.. fl)f!.,9 i5<n - o ORTHORHOMBC Z +«La" DO PEROVSKnE CORUNDUM,6.54' ':<----,.5~--;.6!-;;-~.7~ ---,.8;,,;----,.9,;;,;--".,;;,;----;,7r. O;----;.~ 2;--'.-i: 3~ At' RADUS OF B+3 O NS. A FGURE 5. Classification of the A +3B +3 3-type compounds according to the constituent ionic mdii,. Rhombohedral p~rovsk i t~. a > 9o; D. orthorhomb ic pero vs ki te (,,'' i3 type); 6. '', 3structure typ~ ; O. corundum structll'e type; La, 3structure type; compound s not studied in t he prcscnt work that are assunll'd to ha,'c t be struct ll'e shoml by the arcas bounded by das hed lines. two. Sup erimposed on t h e field of cubic compou nd s is an area of ferrociectric structures. A threedirnensional graph, using the polarizability of the divalent ions as Lhe third dimension, shows that thi area is really a proj ection onto a basal plane of a volume in space encompassing ferroelectric and antiferroelectric compounds and solid solutions. A two-dimensional plot using ionic radii has also been constructed for double oxides of th e trivalenl ions. This graph shows p erovskite compounds bordered by Tl2 3-type structures with corundum and La2 3 structures at th e ex trem e borders. The perovskite compounds can be divided into two types. Oxides of the larger rare-earth ions with Al 2 3 form rhombohedral perovskites with alpha sli ghtly greater than 9. The rest of the p erovskites, including the so-called YCr3-type compounds, ca n all be related to an orthorhombic CaTi3-type stru cture. No ideal cubic perovskiles are found for Lhe A +3B +3 3-type compound s. F erroele clricil,v in Lhis graph may be represen ted by Lhe l'hornbohcdl'al area and possibly other compounds acljacelll to Lhis field. Thanks are due Lo L. 'V. Coughanour and B. CeTi3 fall s \\Toll within th e fleld of orthorhombic perovskites, as shown in flgure 5. The rare-earth Jaffe for providing man~' of Lhe specimens, to S. vanadates r eported by Wold and Ward [38] can be Marzullo for measurin g their physical pl'opel'lies, to classified in this groupin g as probably orthorhombic, G. F. RYllders for preparing Lhe specimens co ntainas V+3 is listed by AlJ'ens [:3] as having a radius of in g vanadium, and Lo the slaff of the Mineral Prod.74 A. u cts Division of the N alional Burea u of Sta ndards F erroelectrieity in this diagr am is represented, for many helpful discussions. possibly, by the LaA 3 and LaGa3 compounds. 6. References t seems likel~t th at if L aal 3 is ferro electric, then all those rare-earth aluminates shown as being rhombo[] L. V. Coughanour, R. S. R olh, a nd V. A. D eprosse, J. hedral are also ferroelectric. t is not known whether Research NBS 52, 37 (954) RP2'7. any of th e other orthorh ombic perovskites like [2] B. J affe, R. S. Roth, and S. Marzullo, J. Appl. Phys. 25, LaGa3 arc ferroelectric, but no other r eports of 89 (954). [3 S. M. L ang, R. S. Roth, and C. L. Fillmore, J. Research ferj'o electricity have bee n found for this type of comnbs 53, 2 (954) RP2534. polmc. Assuming, however, that both LaA 3 and [4] L. W. Coughanour, R. S. Roth, S. :v:arwllo and F. E. LaGa3 are ferroelectric [:35] and that each h as a Sennett, J. R esearch NBS 54, 49 (955) RP2576. different symmetry type, a very interestin g poss i[5] L. W. Coughanour, R. S. Roth, S. Marzullo, and F. E. Sennett, J. R esear ch NBS 54, 9 (955) RP258. bility arises for piezoelec tric ceramics. t is known [6) R. S. Roth, Am. Min. 4,332 (955). that close proximity to a morpho tropic boundary [7] ]3. Jaffe, R. S. R oth, a nd S. Marzull o, J. Res earch NBS betwee n two ferroelectric solid-solution phases en55, 239 (955) RP2626. hances the electrical properties of a ceramic [7]. [8] S. M. L a ng, F. P. Knudsen, C. L. Fillmore, and R. S. R oth, NBS Circ. 568 ( 956). Therefore, as solid solutions of LaA 3 and LaGa3 [9 R. S. Ro th, J. Am. Ceram. Soc. 39, 96 (956). should cross a morpho tropic boundary, interesting [ P. P. Ewald a nd C. H ermann, Stru cturbericht, Z. Krist. piezoelectric properties might be obtained. (93-928). [] V. L. Roth, Proceedings of the 2Lh Annual Pi ttsburgh Diffraction Con ferenco (954). [2]. Naray-Szabo Naturwiss. 3, 466 (943). [3) -. D. M egaw,!>roc. Phys. Soc. 58, 33 (946). [4] P. Bailey, Thes is, Bristo l (952). l5] H. D. M egaw, Acta Cl'yst. 7, J87 (954). [6] E. A. Wood, Acta Cr ys L. 4, 353 ( 5). [7) V. M. Goldschmid t, S krif ter No rske Vid ensk aps-aka d. Mat. N aturvid. Kl. No. 2 (926). [8) W. H. Zachariasen, Skriftel' N ors ke Videnskaps-Akad. M at. N at urvid. K!. NO. 4 (928). [9 M. L. K eith a nd R. Roy, Am. Min. 39, (954). [2] S. Rober ts, Phys. R ev. 76, 25 (949). [2] S. Roberts, Ph ys. R ev. 8,865 (95). [22] R. C. Eva ns, An ntrod uc tion to Cr ystal Chemistry (Cambridge U niv. Press, London, 948). [23] E. Posnjak and T. F. W. Barth, Z. Krist. 88, 27 (934). [24 A. F. Wells, Structural norganic Chemistry (Oxford Univ. Press, Am en House, London, 95). 5. Summary The structul'es of Lhe perovskite compounds of the type A +2B 3 can be corrciated by plotting a threedimensional graph with the ionic radii of A+2 and B H as two of the coordinates and the polarizability of the ions as the Lhird di.mension. Although it is recog nized thal the polarizability of both the A and B ions plays an important part in determining the symmelly, only values for the divalent ions have been used. A two-dimensional chart, using only the ionic radii, shows that the perovskite compound s can be divided into orthorhombic and cubic symmetries with a belt of pseudocubic compounds separating the 87

14 --_.._- {25] G. Shirane and S. Hoshino, Acta Cryst. 7, 23 (954). {26]. Naray-Szabo, Miiegyetemi Gizlemenyek, 3 (947). [27] K. B. Alberman, R. C. Blakely, and J. S. Anderson,.. Chern. Soc. (London) 26, 352 (95). [28] L. P auling, Proc. Roy. Soc. (London) [A] 4, 8 (927). {29] J. A. A. Ketelaar, Chemical Constitution (Elsevier Publishing Co., Amsterdam, 953). [3] L. H. Ahrens, Geochim. Cosmochim. Acta 2, 55 (952). [3] J. Green, Bul. Geol. Soc. Am. 64, (953). [32] G. Shirane and S. Hoshino, Phys. R ev. 86, 248 (952). [33] M. M cquarrie and F. W. Behnke, J. Am. Cer. Soc. 37, 539 (954). [34] M. McQuarrie, J. Am. Cer. Soc. 38, 44 (955). [35] B. T. Matthias, U. S. Patent Office No. 2,69,738 (955). [36] J. T. Looby and L. K atz, J. Am. Chern. Soc. 76, 629 (954). [37] F. Askhan,. Fankuchen, and R. Ward, J. Am. Chern. Soc. 72, 3799 (95). [38] A. Wold and R. Ward, J. Am. Chem. Soc. 76, 29 (954). [39] C. P al ache, H. Berman, and C. Frondel, Dana's System of Mineralogy, vol. (John v'" iley and Sons, New York, N. Y., 95). [4] A. N. Winchell, E lements of Optical Mineralogy, Pt. (John Wiley a nd Sons, New York, N. Y., 948. [4] A. Silverman, G. Morey, and F. D. Rossini, Data on chemicals fol' cer amic lise (National Research Council, Washington, D. C., 949). [42] R. 'Nard, B. Gushee, \,y. McCarrol, and D. H. Ridgely. Univ. Conn. 2d T ech. R ep., NR , Contract ONR- 367 () (953). [43] H. L. Yakel, Acta Cryst. 8, 394 (955). [44] B. W. King and L. L. Suber, J. Am. Cer. Soc. 38, 35 (955). [45] J. Brolls,. Fankuchen, and E. Banks, Acta Cryst (953). [46] W. W. Coffeen, J. Am. Cer. Soc. 36, 27 (953). [47] G. Shirane and R. P epinsky, Phys. Rev. 9, 82 (953). [48] C. E. Curt is, L. M. Doney, a nd J. R. Johnson, Oak Ridge Nat!. Lab. ORNL- 68 (954). [49] E. Sawaguchi, H. Ma niwa, and S. Hoshino, Phys. Rev. 83, 78 (95). [5] E. Sawaguchi, G. Shirane, and Y. T akagi, J. Phys. Soc. J apan 6, 333 (95). [5] A. Dietzel and H. Tober, Bel'. deut. K era m. Ges. 3, 7 (953). [52] A. Hoffma n, Z. physik. Chem. [B] 28, 65 (935). [53] W. H. Zachariasen, Acta Cryst. 2,388 (949). [54] S. Geller, Bul. Am. Phys. Soc. 3, 5 (955). [55] N. N. P adul'ow and C. SchusterillS, Bel'. deu t. R eram. Ges. 32,292 (955). V{ ASHNG'l'O!'\, May 22,

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