Electronic polarizabilities of ions in transition metal oxides
3
Solid State Communications, Vol. 21, pp. 903—905, 1977. Pergamon Press. Printed in Great Britain ELECTRONIC POLARIZABILITIES OF IONS IN TRANSITION METAL OXIDES* Jai Shanker, H.P. Sharma and B.R.K. Gupta Department of Physics, Agra College, Agra 282002, India (Received 21 September 1976 by M.F. Collins) A method for evaluating the electronic polarizabiities from ionic radii in transition metal oxides has been suggested. The ionic radii used in the present calculations are those deduced from the electron density measure- ments. The calculated polarizabiities agree closely with the experimental values obtained from the electronic dielectric constant. THE ELECTRONIC polarizabiities of ions in transition It was for the first time emphasized by Fajans and metal oxides play an important role in describing the Joos 9 that the electronic polarizability of the cations dielectric and lattice dynamical behaviour of these crys- increases and that of the anions decreases when these are tals.1’2 No attempt seems to have been made to evaluate transported into the crystal from the free state. A similar the electronic polarizabiities of ions in transition metal effect for the ionic radii has also been discussed by Fumi oxides. Recent studies2’3 on the lattice dynamical and Tosi.10 These loosening and tightening effects for behaviour of these crystals have been based on the cations and anions respectively in the crystalline state assumption that the total polarizabiity arises from the relative to free state have been well established quantum oxygen ion and the contribution of transition metal ions mechanically by Petrashen et aL’1 and RuffaY~ In fact to the polarizabiity is zero. However, the analysis of the changes in the electronic polarizabiity and radius of electronic polarizabilities presented here will suggest that an ion when it passes from free state to a crystal are such an assumption is oversimplified and one should take related through the polarizahility radius cube relation13’14 into account the polarizability of transition metal ion as which can be expressed as well as that of oxygen ion to describe the dielectric and a r~+ lattice dynamical behaviour of transition metal oxides. We consider six transition metal oxides viz., TiO, and = (~) (2) VO, MnO, FeO, CoO and NiO crystallizing with NaCl a~_ / r~ \~ structure. These crystals can be considered to be corn- = ~ (3) posed of divalent transition metal ions and 02-ions.5 First we calculate the polarizabilities of transition metal where the suffixes + and — stand for cation and anion ions (Ti2~, V2~, Mn2~, Fe2~, Co2~ and Ni21) in free state respectively. a~ and a 1 are the electronic polarizabiity of following the method originally proposed by Pauling. 6 a given ion in the crystalline and free states respectively. According to Pauling the free state polarizability (a 1) of Similarly r~ and r1 are the radii of the same ion in the an atom or ion can be expressed in an approximate two states. manner as follows: The crystalline electronic polarizabiities of ions (a~+ a1 = KZ 4 (1) and a~_) in transition metal oxides can now be estimated from equations (2) and (3) provided we know the values where Z is the nuclear charge and K is a constant depend- of the crystalline radii r~÷ and r~_. For determining r~+ ing upon structure of the ion. The value of K can be assumed to be the same for the series of divalent tran- and r~_ we make use of the information available from sition metal ions im~er study as suggested by Pauling.6’7 the electron density measurements in crystals. Slater15 It is remarkable to observe from Table 1 that a~. for has reported the values of ionic radii for Ni2~ and 02 transition metal ions thus estimated from equation (1) ions estimated from the location of minimum charge decreases regularly from lighter to heavier ion. The density between the neighbouring ions in NiO. Based on these values of radii and following the additivity rule we similar trend of variation is also apparent from the values have derived r~÷ and r~,_ (listed in Table 1) in the family of free ion radii r 1~ for transition metal ions reported by Pauling 7’8 (Table 1). of transition metal oxides. The values of r~+ and r~_ thus obtained are respectively larger and smaller by about 0.25 A than the corresponding values of r 1~ and r1_ (Table 1). This prediction is consistent with the earlier * Work supported by the U.G.C., India studies on ionic radii performed by Fumi and Tosi.’° 903
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Transcript of Electronic polarizabilities of ions in transition metal oxides
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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