Grimes, R.

Minervini, L.

Sickafus, K.

UNT Digital Library

\Approvedforpubkrdease;distributionIsrmlimitad.Title: The Stability of Pyrochlore OxidesAuthor(s): Lick Minervini, Imperial College, U.K.Robin W. Grimes, Imperkl College, U.K.Kurt E. Sickafus, MST-8Submitted to: proceedings of tie ~temation~ Conference: “Ivhss and ChargeTransport in Inorganic Materials”, Lido di Jesolo, Veneziaj ITALY,May 28- June 2,2000Los AlamosNATIONAL LABORATORYLosAlemosNationalLaboratory,an effirmatiie actiordequalopportunityemployer,isoperatedbythe Univers”~of Caliiomiaforthe U.S.Departmentof EnergyundercontractW-7405-ENG-36. 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Images areproduced from the best available originaldocument.-...—. ...-. .— .,—..= -- .-—.— ... -... .= --- ----—-THE STABILITY OF PYROCHLORE OXIDESLicia MINERVINI and Robin W. GRIMESDept. of Materials, Imperial College, London, SW7 2BP, UKKurt E. SICKAFUSLos Alamos National Laboratory, Los Alamos, NM 87454 USAA Contour plot of the disorder reaction energies across a wide variety of&B,O, pyrochlore oxides has been produced using atomistic simulationcalculations based on energy minimization techniques. Cations studied rangefrom LU3+ to La3+ on the A site and Ti4+ to Ce4+ on the B site. The resultsrelate the experimentally observed stability range of the pyrochlorestructure to A and B cation size and disorder. Disorder enthalpies decreasedramatically with increasing B cation size whilst the rate of increase withA cation size depends markedly on the particular B cation. The associationof anion Frenkel and cation antisite disorders is found to be of importance.1. INTRODUCTIONA large number of ternary oxides with the formula ~Bz07, where A is a 3+ ionand B is a 4+ ion, adopt the pyrochlore structure. Elemental versatilityensures thatA few of thefluorescencepyrochlore compounds exhibit a variety of interesting properties.applications for which pyrochlores have been candidates are:centersi, catalysts2’3, actinide host phase’in nuclear waste”s andas both cathode and electrolyte materials in solid oxide fuel cellsG-a.Previously there has been a trend in delimiting the ppochlore stabilityfield by a simple consideration of the cation radius ratio r(A3+)/r(B4+).Theradius ratio is generally chosen empirically to best fit the availableexperimental datag’io.However, this does not take into account the effects ofoxygen sublattice relaxation, which may be significant. We wish to proposealternative methods of determining pyrochlore stability based on energy“minimization calculations.1.1 CrystallographyThe general formula of oxide pyrochlores is written as AZBZOGO’. The spacegroup is Fd3m with the unit cell containing 8 molecules (2.8) and fourcrystallographically non-equivalent sites. When the origin is fixed on the Bsite the atoms occupy48f and O’ at 8b. 48fx.the following special positions: Aoxygen ions are characterized by aat 16d, B at 16c, O atpositional parameterJ,The most popular depictions of the pyrochlore structure are those based on afluorite type cell. In this description the structure is equivalent to anordered defective fluorite. The A and B cations form the face-centered cubicarray and are ordered into rows in c11O> directions. (In defective fluoritesthe seven oxygen atoms are tetrahedrally coordinated by four random cations andevenly distributed over eight equivalent oxygen sites.) In the pyrochlorestructure two different oxygen sites occur. Six oxygen atoms occupy the 48fsites surrounded by two A cations and two B cations while the seventh oxygenatom occupies the 8b site and is surrounded by four A cations. The remainingunoccupied 8a site is surrounded by B cations. Finally, the 48f anions areshifted towards the smaller B cations by an amount defined by the x(48f)positional parameter. In the ideal fluorite structure, the position parameterX= O.375. Figure 1 shows one eighth of a unit cell of the pyrochlore structure;this partial unit cell is analogous to a single fluorite unit cell.AuBatnoc8aatO’ at 8bO at 48fHso/2Figure 1 Partial unit cell of pyrochlore s~ructure2. METHODOLOGYAtomistic computer simulation techniques, based on energy minimization witha Born like description of the latticell, are used to generate the variousstructures. The procedures are based upon a description of lattice forces interms of effective potentials.i The perfect lattice is generated by defining aunit cell that is repeated throughout space using periodic boundary conditionsas defined by the usual crystallographic lattice vectors. The total energy ofthe crystal is minimized by allowing the ions in the unit cell and the latticevectors to relax to zero strain.We consider interactions due to long range Coulombic forces, which aresummed using Ewald’s method12 and short range forces, that are modeled usingparameterized pair potentials, S~j. In order to reduce the computational timethe short range interactions are set to zero beyond 20~. In this study the. -. ..—_.._-.----- ~ ,. .. ....=.. ., ...,,-, .. . ... ......,. ..... ,, . ~,-:-.-...—..,-.,,, ... ....$.. .. . . . . .,., ..7 ...--ATw.m ,. . . -7 ,. .,., ---Buckingham potential form was used,sit = A exp(-r~j/p)- C/rijswhere A, p and C are three adjustable parameters (see Table 1) .Table 1 Short-range potential parametersSpecies A (eV) p (A) C (eV\A’)(y-+2- 9547.96 0.2192 32.0Lu3*-02- 1618.80*3+-02- 1649.80~r3+_02- 1739.91~3+_02- 1766.40Gds+_Oz- 1885.75~u3+-02- 1925.71sm3+-02- 1944.44~&+-Oz- 1995.20La3+-02- 2086.01La3+-02- 2088.79‘l’i4+-02- 2131.04~u4+-02- 1215.78Mo4’-02- 1223.97Sn4+-02- 1414.32Zr4+-02- 1502.11~bd+-Oz- 1640.34~e4+-02- 1809.680.338490.33860.33890.338490.33990.34030.34140.34300.34300.34600.30380.34410.34700.34790.34770.35070.354719.2716.5717.5519.4320.3420.5921.4922.5923.9423.250.00.00.013.665.119.5020.40(1)In addition to studying the perfect lattice, this approach can be used topredict how the lattice accommodates defects. To do this lattice is partitionedinto two regions: a spherical inner region, I, at the center of which the“defect is introduced, and an outer region, II, which extends to infinity. InRegion I, interactions are calculated explicitly so that the response of thelattice to the defect is modeled by relaxing the positions of all ions to zeroforce using a Newton-Raphson minimization procedure. The response of Region IIis treated using the Mott-Littleton approximation13.The polarizability of the ions may be accounted for via the shell mode114.This consists of a massless shell with charge Xlel that is allowed to move withrespect to a massive core of charge Ylel; the overall charge state of each ionis therefore equal to (X+Y)Iel. The core and shell charges are connected by anisotropic harmonic spring force of constant k. Displacement of the shellrelative to the core gives a good description of electronic polarization. In.4-1./all calculations, 02- and the larger 4+ cations (Zr, Pb, Ce) are treated aspolarizable using the shell model: for 02-, Y= -2.04, k=6.3eV~-2; Zr4’, Y=-0.05, k=189.7eV~-2; Pb4+, Y=-O.05, k=205.0eV~-2; Ce4+, Y=-O.20,lc=177.84eV~-2.For further details of the computational methods see references 15 and 16.In all cases, calculations were carried out using the CASCADE codel’.3. RESULTS AND DISCUSSION.Our initial aim was to generate a contour plot of the disorder defect energy asa function of A and B cation radii. Through this we should obtain insight intothe stability range of the pyrochlore structure with respect to defectenergies. In previous studiesg’loa cation radius ratio argument, r(A3+)/r(B4+),is invoked to explain this stability range; however, r(A3+)/r(B4+)plottedagainst r(A3+) and r(B4+) is necessarily a straight line which cannot account forsubtle relaxation effects. In addition there is not a good analytical rationalefor choosing the best r(A3+)/r(B4+)ratio.When considering pyrochlore compounds the data set is extensive but notuniform. The present study ranges in ion size from lanthanum to lutetium on theA site and titanium to cerium on the B site. Ion sizes (radii) are those givenby Shannon16 and are taken to be VIII-coordinate for the B cation and VI-.coordinate for the A cation. Gaps arise in this data set because: (1) someAZB207 compounds do not form cubic pyrochlores and (2) Zr, Pb, and Ce do notform pyrochlores with the larger 3+ cations. Unfortunately, it was found that areliable contour plot could not be achieved if these hypothetical compounds areexcluded. Essentially the number and distribution of data points is such thatextrapolation cannot proceed. far enough beyond the data set for the contourplot to be useful. The nature of the present calculations has enabled us togenerate the missing data points by using potentials derived fromexperimentally observed pyrochlore compounds to investigate hypotheticalpyrochlore compounds.Cation disorder increases the similarity between non-equivalent oxygensites. Thus it has been proposed by Wilde and Catlo#g that the presence ofcation disorder will decrease the anion Frenkel energy.ALX + B~x + OOX + ~’ + B~” + VO{A~~)””+ O~(Ba)” (2)Our calculations support this view, with the presence of a cation antisite pairadjacent to an anion Frenkel pair greatly reducing the anion Frenkel energy.Figure 2 shows the contour map for the formation energy of a clusteredcation antisite pair adjacent to an anion Frenkel pair as a function of A and B,~ —.rA .,, ,, . . . ..=. ,.-..-+,: ..< ., .,,..- , , . . . . . . , ....,.-;~~, - , ,I,.,Ication radii. The thick light contour on the right side of Figure 2 defines aboundary for the calculated stability of the ternary compound with respect tothe binary oxides,~03 + 2B0, + AJ3,0, (3)A negative reaction enthalpy indicates stability so that stable compounds lieto the left of the contour while unstable compounds lie to the right of thiscontour. This immediately eliminates the possibility of forming the ceratepyrochlores, except for La2CezOz, and %PbzOz where A = Lu, ~, Er.‘11.150:u-l-j 1.102% 1.()()Ru Mo Sn Zr Pb Ce Disorder EnergyLaPrNciSmEuGdYErYbLu—4.80 – 5.204.40 - 4.80:~;& 4.00 - 4.40~% 3,60 - 4.oo= 3.20 - 3.60= 2.80- 3.20m 2.40-2.80_ 2.00 - 2.40~ 1.60-2.00~ 1.20 - 1.60m 0.80 - 1.20, 0.40 - 0.80-0.00 - 0.400.65 0.70 0.75 0.80 0.85B4+ Cation Radius (~)Figure 2 Contour map of the defect formation energy for an anion Frenkel pair—adjacent to a cation antisite pairPyrochlore co~ounds observed experimentally are shown as black circles.Pyrochlore compounds for which experimental data is not available but for whichcalculations have been carried out are shown as white crosses. White circlesindicate compounds that have been synthesized by high pressure techniques(300MPa, 700”C)2”. Non-cubic &B20T compounds are shown as black crosses: inthese cases, calculations predict the cubic phase to be stable with respect tothe binary oxides, but experimentally a non-cubic phase is observed. Non-cubicphases have not been thoroughly characterized crystallographically and hencecalculations have not been attempted on these phases. Thus it appears thatequation 3 predicts the stability of a number of materials incorrectly.However, equation 3 does not consider that such materials may be stablesolutions as disordered fluorites or may undergo non-cubic distortions that are,more stable than the simple cubic structure. “,.,The most strikingcompounds the defectfeature that arises from Figure 2 is that for someenergy is actually negative. Furthermore, there is now aclear plateau of stability so that beyond acation radii a further increase in B radiusdestabilizes the pyrochlore structure. Thuscritical combination of A and Bor decrease in A radius quicklycertain combinations of A and Bcations which are to the left of the black line (the reaction enthalpy isnegative) will nevertheless form disordered fluorites; i.e. there is no drivingforce for cation ordering in these compounds because the introduction of“defects via disorder processes is energetically favorable. Of course, adisordered fluorite region will also include materials where the disorderreaction enthalpy is small, yet positive, since the driving force for orderingmay not be great enough to overcome kinetic barriers. Although an appropriatecutoff in disorder enthalpy has not. yet been determined theoretically,comparison with-2.6eV (-O.7eVtechnique we doexperimental data in Figure’ 2 suggests a contour value ofper defect). Given the approximate nature of our theoreticalnot intend for this energy value to be regarded asrather as relative.Figure 2 also shows that the lead compounds synthesized by hightechniques exhibit lower disorder energies than existing compoundsabsolute butpressuresynthesizedat atmospheric pressure. These high pressure compounds clearly have comparable“energies to the hypothetical Zr pyrochlores which makes further high pressuresyntheses an intriguing prospect.4. CONCLUSIONSIt is now possible, based on disorder formation energies, to subdivide thestability range of compounds as a function of A and B cation radii into fourregions. Compounds in the region where the reaction enthalpy is positive willnever form ordered pyrochlore oxides of the form AZBZOZ. They may, of course,still form extensive %02:B02 solid solutions. Compounds whose disorderenthalpies lie above an energy contour (relative to the full ionic model) of-2.6eV (-.O.7eV per defect) will form ordered pyrochlore structures at“atmospheric pressure. There is then an intermediate transition region wherecompounds will remain defective fluorites. Finally, compounds with larger(A3+)/r(B4+)values, i.e. composed of large A cations and small B cations, seemto form non-cubic unit cells. The exact boundary of this fourth region is notyet clear.The disordered transition region provides us with some exciting experimentalchallenges. It includes compounds that have been synthesized by high pressure.-.-—-- ., n- . . . . . . . . . . . W---- , # _. . . ..-=– -? >> -.s7, . . . . . . . . ,, ... ‘., ~ ...: ‘.!mmw-r, ..v .,-m ;. ~ .—. - I,,’techniques, compounds in which micro-ordering has been observed and compoundsin which pyrochlore ordering has never been observed. Thus, if the presentanalysis is correct in that these compounds remain disordered due. to aninsufficient driving force for ordering, given appropriate conditions, such ashigh pressure, itordered or partlyshould be possibleordered pyrochloreto overcome kinetic barriers and formstructures.ACKNOWLEDGMENTSThe authors wish to acknowledge the support of the Department of Energy, Officeof Basic Energy Sciences, Division of Materials Science. Some computingfacilities were provided by EPSRC grant number GR/L86821.REFERENCES1) R.A. MCCAULEY and F.A. HUMMEL, J. Luminesc. 6(1972)105.2) J.B. GOODENOUGH and R.N. CASTELLANO, Solid State Chem 44(1982)108.3) S.J. KORF, H.J.A. KOOPMANS, B.C. LIPPENS, A.J. BURGGRASST, and P.J.GELLINGS, J. Chem. Sot. Faraday. Trans. 83(1987)1485.4) R.G. DOSCH, T.J. HEADLEY, and P. HLAVA, J. Am. Ceram. Sot. 67(1984)354.5) K.L. SMITH, N.IJ. ZALUZEC, and G.R. LUMPKIN, J. Nucl. Mater. 250(1997)36.6) A.J. BURGGRAAF, T. VAN DIJK, and M.J. VERKERK, Solid State Ionics5(1981)519.7) o.8) S.9) o.10) F.11) M.PORAT, C. HEREMANS, and H.L. TULLER, J. Am. Ceram. Sot. 80(1997)2278.KRAMER, M. SPEARS, and H.L. TULLER, Solid State Ionics 72(1994)59.KNOP, F. BRISSE, and L. CASTELLIZ, Can. J. Chem. 47(1969)971.BRISSE and O. KNOP, Can. J. Chem. 46(1968)859.BORN. Atomtheorie des Festen Zustandes. Teubner, Leipzig, 1923.12)P.P EWALD, Ann Physik 64(1921)253.13)N.F. MOTT and M.J. LITTLETON, Trans. Farad. Sot. 34(1932)485.14)B.G. DICK and A.W. OVERHAUSER, Phys. Rev. 112(1958)90.15) C.R.A. CATLOW and W.C. MACKRODT, editors. ComputerSpringer-Verlag, Berlin, 1982.16)The Practical Calculation of Interionic Potentialsissues of Ifo2. Sire.4[5] and 5[2] (1990), A.H. HARKERSimulation of Solids.in Solids. In specialand R.W. GRIMES, editors.17)M. LESLIE. {DL/scI/TM31T}. Tech. rep., SERC Daresbury Laboratory, 1982.18)R.D. SHANNON, Acts Cryst. A32(1976)751.19)P.J. WILDE and C.R.A. CATLOW, Solid State Ionics 112(1998)173.20)A.W. SLEIGHT, Inorg. 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THE STABILITY OF PYROCHLORE OXIDES

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THE STABILITY OF PYROCHLORE OXIDES

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