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Solid StateCommunications,Vol. 21,pp. 903—905,1977. PergamonPress. Printedin GreatBritain
ELECTRONIC POLARIZABILITIES OFIONS IN TRANSITIONMETAL OXIDES*
Jai Shanker,H.P. SharmaandB.R.K. Gupta
Departmentof Physics,AgraCollege,Agra282002,India
(Received21 September1976by M.F. Collins)
A methodfor evaluatingthe electronicpolarizabiitiesfrom ionic radii intransitionmetaloxideshasbeensuggested.Theionic radii usedin thepresentcalculationsare thosededucedfrom theelectrondensitymeasure-ments.Thecalculatedpolarizabiitiesagreecloselywith the experimentalvaluesobtainedfromthe electronicdielectricconstant.
THE ELECTRONIC polarizabiitiesof ionsin transition It wasfor the first timeemphasizedby Fajansandmetal oxidesplay animportantrole in describingthe Joos9that theelectronicpolarizability of thecationsdielectricandlattice dynamicalbehaviourof thesecrys- increasesand that of theanionsdecreaseswhenthesearetals.1’2 No attemptseemsto havebeenmadeto evaluate transportedinto thecrystal from thefree state.A similartheelectronicpolarizabiitiesof ionsin transitionmetal effect for the ionic radii hasalsobeendiscussedby Fumioxides.Recentstudies2’3on the lattice dynamical andTosi.10 Theselooseningandtighteningeffectsforbehaviourof thesecrystalshavebeenbasedonthe cationsand anionsrespectivelyin the crystallinestateassumptionthat thetotal polarizabiityarisesfrom the relativeto free statehavebeenwell establishedquantumoxygenion andthe contributionof transitionmetalions mechanicallyby PetrashenetaL’1 andRuffaY~In factto thepolarizabiity is zero.However,theanalysisof the changesin the electronicpolarizabiityandradiusofelectronicpolarizabilitiespresentedherewill suggestthat an ion whenit passesfrom free stateto a crystalaresuchan assumptionis oversimplifiedandoneshouldtake relatedthroughthe polarizahility radiuscuberelation13’14into accountthe polarizabilityof transitionmetalion as which canbe expressedaswell asthatof oxygenion to describethe dielectric and a r~+latticedynamicalbehaviourof transitionmetal oxides.
Weconsidersix transitionmetaloxidesviz., TiO, and = (~) (2)VO, MnO, FeO,CoO andNiO crystallizingwith NaCl a~_ / r~\ ~structure.Thesecrystalscanbe consideredto be corn- = ~ (3)posedof divalenttransitionmetalionsand02-ions.5First we calculatethepolarizabilitiesof transitionmetal wherethe suffixes+ and — standfor cationandanionions(Ti2~,V2~,Mn2~,Fe2~,Co2~and Ni21) in free state respectively.a~anda
1arethe electronicpolarizabiityoffollowing themethodoriginally proposedby Pauling.
6 a given ion in the crystallineandfreestatesrespectively.Accordingto Paulingthe free statepolarizability(a
1) of Similarly r~andr1arethe radii of thesameion in theanatomor ion canbe expressedin anapproximate two states.mannerasfollows: Thecrystallineelectronicpolarizabiitiesof ions(a~+
a1 = KZ4 (1) anda~_)in transitionmetaloxides cannow beestimated
from equations(2) and(3) providedwe know thevalueswhereZ isthe nuclearchargeandK is a constantdepend-of thecrystallineradii r~÷andr~_.For determiningr~+
ing uponstructureof the ion. Thevalueof K canbeassumedto bethesamefor the seriesof divalent tran- andr~_we makeuseof the information availablefromsitionmetalionsim~erstudyassuggestedby Pauling.6’7 theelectrondensitymeasurementsin crystals.Slater15It is remarkableto observefrom Table 1 thata~.for hasreportedthevaluesof ionic radii for Ni2~and02
transitionmetalionsthusestimatedfrom equation(1) ionsestimatedfrom thelocation of minimumchargedecreasesregularlyfrom lighter to heavierion. The densitybetweenthe neighbouringionsin NiO. Basedon
thesevaluesof radii andfollowing theadditivity rule wesimilar trendof variationis alsoapparentfrom thevalueshavederivedr~÷andr~,_(listed in Table1) in thefamily
of free ion radii r1~for transitionmetal ionsreportedby
Pauling7’8(Table 1). of transitionmetaloxides.Thevaluesof r~+andr~_thus
obtainedare respectivelylargerandsmallerby about0.25A thanthecorrespondingvaluesof r
1~andr1_
(Table 1). This predictionis consistentwith theearlier* Work supportedby theU.G.C., India studieson ionic radii performedby Fumi and Tosi.’°
903
904 IONS IN TRANSITION METAL OXIDES Vol. 21, No.9
Table1. Ionic Radii (A) andelectronicpolarizabiities crystalcannow beestimatedfrom the relation(A3). (Free-ion radii r
5+ and Tf_, fromPauling,7Free-ion
polarizabiityaf~calculatedin thepresentstudyandaf_, a = a~÷+ a~_. (4)averageofthe valuescitedbyPauling6and Fa/ansandJ005. Crystalradii r~+and r~_basedon theelectron The valuesof acanalsobe determinedfrom the exper-
densitymeasurementscitedbySlater15) imental valuesof electronicdielectricconstante using
the Lorentz—LorenzrelationCrystal r
1÷ r1... ~ a1_ r~+ r~_3Ve—1
TiO 0.86 1.40 0.97 3.32 1.11 1.15 a = — (5)4ir � + 2VO 0.79 1.40 0.81 3.32 1.04 1.15MnO 0.82 1.40 0.58 3.32 1.07 1.15 where Vis thevolumeperion pair. TheexperimentalFeO 0.77 1.40 0.50 3.32 1.01 1.15 valuesof electronicdielectricconstanthavebeenCoO 0.74 1.40 0.43 3.32 0.98 1.15 measuredonly for MnO,CoOandNiO.
16 It is interestingNiO 0.70 1.40 0.37 3.32 0.94 1.15 to observefrom Table2 that thetheoreticalvaluesof a
obtainedfrom equation(4) agreewithin 5% with theexperimentalvaluesof aobtainedfrom equation(5).
Table2. Crystallineelectronicpolarizabilities(A3) This remarkablycloseagreementachievedforashould
be consideredasa strongpoint in favourof our analysisCrystal a~+ a~ a From aExper- of electronicpolarizabiitiesof ionsin transitionmetalequation(4) mental oxides.
TiO 2.08 1.84 3.92 — An importantaspectof thepresentanalysisis,VO 1.85 1.84 3.69 — however,the investigationof thefact that the contri-MnO 1.28 1.84 3.12 2.97 butiona~+of transitionmetal ionsto theelectronicFeO 1.13 1.84 2.97 — polarizabiitiesa is substantialandcannotbeneglectedCoO 0.99 1.84 2.83 2.72 ascomparedto thatof oxygenion (Table 2).This is whyNiO 0.89 1.84 2.73 2.66 UpadhyayaandSingh2andGoyal etal.3 havenotbeen
able to obtainan agreementfor the phononfrequencies
Thevaluesof a~÷for transitionmetalionscalculated in MnO, CoO andNiO usingalattice dynamicalmodelin which thepolarizabiityof transitionmetalion hasfrom equation(2) usingrf÷,a
1÷andr~+from Table 1havebeenlisted in Table2. In orderto calculatethe beenneglected.UpadhyayaandSingh
2haveattributedvalueof a~_for oxygenion we needto know the free this disagreementto thelack of polarizability dataof
individual ionsin transitionmetaloxides.It would,statepolarizabiitya~_.In literaturetherearetwo values therefore,be interestingto studythephonondispersion2.75A3 and 3.88 A3 of af_for oxygenion reportedbyFajansandJoos9andby Pauling6respectively.There- in thesecrystalsby developinga bothion polarizablefore,we havecalculatedar...from equation(3) usingan latticedynamicalmodel.Such a model canbeworked
outwith thehelp of electronicpolarizabiitiesof ionsaveragevalue3.32 A3 for af_of oxygenion.
reportedin the presentstudy.Theelectronicpolarizabiityperion pair in each
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