O9_Mohsin - Surface Functionalization of Metal Chalcogenides and Their Bio-Organic Derivatives
Electronic polarizabilities of ions in the chalcogenides of Zn and Cd
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Solid State Communications, Vol. 26, pp. 675—677. 0038—1098/78/0615—0675 $02.00/0 © Pergamon Press Ltd. 1978. Printed in Great Britain ELECTRONIC POLARIZABILITIES OF IONS IN THE CHALCOGENIDES OF Zn AND Cd * Jai Shanker, S.C. Agrawal and A.K.G. Lashkari Department of Physics, Agra College, Agra-282002, India (Received 10 January 1978 byM.F. Collins) In the present communication we show that the energy level analysis yields consistent values of the electronic polarizabilities of individual ions in crystals of chalcogenides of Zn and Cd. It has been possible to explain the loosening of cations and the tightening of anions in the crystalline state relative to the free state. FOR MANY PURPOSES it is desirable to have reliable energy of the ion. When the ion is transported into the values of the electronic polarizabilities of individual ions crystal from the free state, the parameter E, and the in crystals. In highly ionic crystals like alkali halides, the corresponding polarizability is changed. For cations, one additivity rule works well and it is therefore possible to can write [4] derive a set of electronic polarizabilities of individual e 2h2n ions [1, 2]. However, in crystals composed of divalent ~ + = 4~2m1E — eV ~2 (2) ions like chalcogenides, the additivity rule does not hold ~ 1 ml so well and large deviations from this rule are observed where a~denotes the crystalline polarizability of [1]. It is therefore desirable to explore an alternative cation. Vm is the Madelung potential existing at the method for estimating the electronic polarizabilities of cation site in crystal. An equation similar to (2) can, ions in these crystals. The most striking feature of the however, not be used for anions due to a somewhat dif- electronic polarizabilities is the fact that these increase ferent case. In fact, the existence of the excitation levels for cations and decrease for anions in going from free provides a contribution to the anion polarizability in the state to a crystal. Such changes, although small for crystal which has no counterpart in the free state. In alkali and halogen ions, are significantly large for the addition, quantum states above the first ionization con- chalcogenide ions as is evident from the analysis per- tinuum contribute substantially to the free anion polar- formed by Tessman eta!. [1] (hereafter referred to as izability. Considering these points, Ruffa [4] has derived TKS). This suggests the loosening of cations and the 2h2 tightening of anions in crystals relative to the free state. = 2 (3) Following an energy level analysis used by Seitz ‘~ mE~_ [3], Ruffa [4] has suggested a method which determines where a~,. is the crystalline polarizability of anion. The the changes in electronic polarizabilities of ions upon energy parameter E~_ is entering the crystal from free state. In fact the Thomas—Kuhn sum rule allows the sum representing the E~_= ~ [(is — e2/ro) + 3(E 1 + ~ — E)] (4) electronic polarizability to be expressed by one effective with parameter. The polarizability a1. of an ion in isolated or free state is thus given as = 2e(V~ — VR) + E — I + Q. (5) e 2h2n r 0 is the nearest neighbour separation, eVm and eVR are = 4ir 2mE2 (1) the Madelung and repulsive energies respectively. E is the 1 electron affinity of the anion and I is the ionization where e and m are electronic charge and mass respec- potential of the alkali atom. Q is the energy of inter- tively. h is Planck’s constant, n is the number of elec- action between free ions and the crystal environment. trons in the ion and E~ is the effective parameter which In the present study we consider Il—VI semicon- can be loosely referred to as being the mean excitation ducting crystals viz. ZnO and CdSe with wurtzite struc- ture, ZnS, ZnSe, ZnTe, CdS and CdTe with zincblende * Permanent address: Department of Physics, C.L. Jam structure and CdO with rocksalt structure. Values of E 1 College, Firozabad, U.P., India. are estimated from equation (1) using free state polar- ~ Department of Physics Government P.G. College izabiities from Pauling [5]. Values of the repulsive Morena, M.P., India. energies have been estimated from the Hildebrand 675
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Transcript of Electronic polarizabilities of ions in the chalcogenides of Zn and Cd
Solid StateCommunications,Vol. 26,pp. 675—677. 0038—1098/78/0615—0675$02.00/0© PergamonPressLtd. 1978.Printedin GreatBritain
ELECTRONICPOLARIZABILITIES OF IONS IN THE CHALCOGENIDESOFZn AND Cd*
Jai Shanker,S.C. Agrawal andA.K.G. Lashkari
Departmentof Physics,AgraCollege,Agra-282002,India
(Received10January 1978byM.F.Collins)
In thepresentcommunicationwe showthat theenergylevel analysisyieldsconsistentvaluesof theelectronicpolarizabilitiesof individual ionsin crystalsof chalcogenidesof Zn andCd. It hasbeenpossibleto explainthe looseningof cationsandthetighteningof anionsin thecrystallinestaterelativeto thefree state.
FORMANY PURPOSESit is desirableto havereliable energyof the ion. Whentheion is transportedinto thevaluesof the electronicpolarizabilitiesof individual ions crystal from thefree state,theparameterE, andthein crystals.In highly ionic crystalslike alkali halides,the correspondingpolarizability is changed.Forcations,oneadditivity rule workswell andit is thereforepossibleto canwrite [4]derivea setof electronicpolarizabilitiesof individual e2h2nions [1, 2]. However,in crystalscomposedof divalent ~ + = 4~2m1E— eV ~2 (2)ionslike chalcogenides,theadditivity rule doesnot hold ~ 1 ml
sowell andlargedeviationsfrom this rule are observed wherea~denotesthecrystallinepolarizability of[1]. It is thereforedesirableto explorean alternative cation.Vm is the Madelungpotentialexistingat themethodfor estimatingtheelectronicpolarizabilitiesof cationsite incrystal.An equationsimilar to (2) can,ionsin thesecrystals.The moststriking featureof the however,notbe usedfor anionsdue to a somewhatdif-electronicpolarizabilitiesis the fact that theseincrease ferentcase.In fact, the existenceof the excitationlevelsfor cationsanddecreasefor anionsin goingfrom free providesa contributionto theanionpolarizability in thestateto a crystal.Such changes,althoughsmall for crystalwhichhasno counterpartin the free state.Inalkali andhalogenions,are significantlylarge for the addition,quantumstatesabovethe first ionizationcon-chalcogenideionsasis evidentfrom theanalysisper- tinuumcontributesubstantiallyto the freeanion polar-formedby Tessmaneta!. [1] (hereafterreferredto as izability. Consideringthesepoints,Ruffa [4] hasderivedTKS). Thissuggeststhe looseningof cationsandthe 2h2tighteningof anionsin crystalsrelativeto thefree state. = 2 (3)
Following anenergylevelanalysisusedby Seitz ‘~ mE~_[3], Ruffa [4] hassuggesteda methodwhich determines wherea~,.isthe crystallinepolarizability of anion.Thethe changesin electronicpolarizabilitiesof ionsupon energyparameterE~_isenteringthe crystalfrom free state.In fact theThomas—Kuhnsumrule allows thesumrepresentingthe E~_= ~ [(is — e2/ro)+ 3(E
1 + ~ — E)] (4)electronicpolarizability to be expressedby one effective withparameter.Thepolarizabilitya1. of an ion in isolatedorfreestateis thusgiven as = 2e(V~— VR) + E — I + Q. (5)
e2h2n r
0 is the nearestneighbourseparation,eVm and eVRare
= 4ir2mE2 (1) theMadelungandrepulsiveenergiesrespectively.E is the
1 electronaffinity of the anionand I is the ionizationwheree and m areelectronicchargeandmassrespec- potentialof thealkali atom.Q is theenergy of inter-tively. h is Planck’sconstant,n is the numberof elec- actionbetweenfree ionsand thecrystalenvironment.tronsin the ion andE~is the effectiveparameterwhich In the presentstudywe considerIl—VI semicon-canbe loosely referredto asbeingthe meanexcitation ductingcrystalsviz. ZnO andCdSewith wurtzitestruc-
ture,ZnS,ZnSe,ZnTe,CdSandCdTe with zincblende* Permanentaddress:Departmentof Physics,C.L. Jam structureand CdO with rocksalt structure.Valuesof E
1College,Firozabad,U.P., India. are estimatedfrom equation(1) usingfree statepolar-
~ Departmentof PhysicsGovernmentP.G.College izabiitiesfrom Pauling[5]. Valuesof the repulsiveMorena,M.P., India. energieshavebeenestimatedfrom theHildebrand
675
676 ELECTRONICPOLARIZABILITIES OFZn AND Cd Vol. 26,No. 11
Table1. Valuesofinputdata usuallyacceptedvalue [6]. Electronaffinity E andion-izationpotentialI for different ionsandatomsare taken,
Ion a1.(A3) E
1 (eV) E (eV) I (eV) repectively,from HugginsandSakamoto[7] andAhrens
Zn2~ 0.29 103.2 — 18.0 [8]. Following von Hippel [9],the interactionparameter
Cd2~ 0.47 103.9 — 16.9 Q necessaryfor the calculationof z~isset equalto02- 3.92 16.77 7.03 — — I eV for all cases.S2~ 10.3 13.87 4.29 Valuesof the crystallinestatepolarizabilitiesa~÷Se2 10.6 19.32 5.07 anda~_estimatedfrom equations(2) and (3) areTe2 14.2 20.49 421 — includedin Table 2. It is interestingto notefrom there
that thepolarizabiityof a given anionis almostsameinZn and Cd compounds.The polarizability of cation (Zn
Table2. Calculatedvaluesof thecrystallinestatepolar- or Cd) decreasesregularly from anoxide to the corres-izabilities________________________________________________________ pondingtelluride crystal.In Table3 we presenta corn-Crystal r
0 ~ eVm eVR a~+ a~_ parisonof the averagevaluesof the calculatedpolariz-(A) (in eV) (in eV) (A
3) (A3) abilities with thoseobtainedby TKS from a detailedanalysisof the experimentalrefractiondatausingthe
ZnO 1.95 1 .64132 24.25 8.21 0.50 1 .69 additivity rule. Our calculatedpolarizabiitiesof chalco-ZnS 2.36 1 .63805 20.04 5.60 0.45 5.05 genideionsare in fair agreementwith thoseof TKS.ZnSe 2.45 1 .63805 19.30 5.20 0.44 7.19 However,TKS werenotable to assigna singlevalueforZnTe 2.63 1 .63805 17.98 4.51 0.43 11.27 theelectronicpolarizabiityof a chalcogenideion
becauseof thefailure of theadditivity rule. The elec-CdO 2.35 1.74756 21.47 6.03 0.75 1.66CdS 2.52 1.63805 18.77 4.92 0.70 5.04 tronic polarizabiitiesof 02, S2,Se2,and Te2 ions
obtainedby TKS showthe variationsin broadrangeandCdSe 2.62 1.64132 18.05 4.55 0.69 7.19CdTe 2.78 1.63805 17.01 4.04 0.67 11.09 are representedby spreadin Table3. Thepresentstudy
on polarizabilitiesof chalcogenideionshas thusremovedtheuncertaintiesrevealedby theanalysisof TKS and it
Table3. Comparisonofthecalculatedpolarizabilities(in hasbeenpossibleto assigna uniquepolarizability toA3) with thosederivedfromadditivity rule eachchalcogenideion. Our polarizabilitiesof Zn andCd
Ion (a) (b) ions aresmaller than thoseof TKS. It shouldbe empha-sisedthat the polarizabilitiesof theseions were obtained
Zn2~ 0.46 0.8 by TKS from therefractiondataon ZnF2 andCcIF2.
Cd2~ 0.70 1 .8 Thesecrystalsare quitedifferent from chalcogenides
understudyas far asthecrystalstructure,natureof the02 1.68 0.5— 3.2s2 ~.05 4.8 5.9 chemicalbond andinteratomicforces,and theeffectiveSe2 7.19 6.0— 7.5 field polarizinganion are concerned.In fact, theTe2 11.18 8.3—10.2 Madelungpotentialexistingat thecationsite in ZnF
2and CdF2 is muchlargerthanthat in chalcogenides[10]andis thusresponsible[equation(2)] for largermagni-(a) Averagevaluesof the polarizabilitiescalculatedin
thepresentstudy. tudesof polarizabiitiesof Zn and Cd ionsin thesecrystals.A calculationof theeffect of the Madelung
(b) Derived by Tessmaneta!. [1].potentialin ZnF2 crystal [11] yields0.70A
3 for thepolarizabilityof Zn ion, which is quitecloseto thevalue
equationof state [6] by adoptingthe Born—Mayer of TKS. Thusit becomesevidentthat thetheoryofexponentialform andusing thecrystal equilibrium con- crystallinepotentialusedin thepresentstudy is capabledition.Onecanthusfind
of explainingthevariationof polarizabiityfrom onebz2e2p structureto the other. Finally it shouldalso be remarked
eVR = B exp (— r0/p) = 2 (6) that thepresentanalysisof electronicpolarizabilitiesis
Toconsistentwith earlierpredictionsaboutthe loosening
whereB andp arethe Born repulsiveparameters.~ of cationsandthetighteningof anionsin crystalsrelativeMadelung’sconstant.Wehavetakenp = 0.33A, a to free state[12-—is].
Vol. 26,No. 11 ELECTRONIC POLARIZABILITIES OF Zn AND Cd 677
REFERENCES
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10. PAULING L., Natureofthe ChemicalBond, Cornell University Press, Ithaca (1960).
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