Impurity configurations in metals

Volume 41A, numberI PHYSICSLETTERS 28 August 1972

IMPURITY CONFIGURATIONS IN METALS*

C.P. FLYNNDepartmentof PhysicsandMaterials ResearchLaboratory, University ofIllinois, Urbana,Illinois 61801, USA

Received24 June1972

Theexistenceof fully ionic andpartly ionic impurity configurationsin metalsis discussed.Thecontinuousrangeof impurity configurationsis indicatedandthe structuralvariationwith solventelectrongasdensityclarified forcertainimpurities.

Most investigationsof impurity structureinmetals be stablein metalsthe chargestateof lowest totalhavefocussedon casesin which thesolventvalence energywill, of course,occur in nature.We believethatorbitals penetratetheimpurity core regionto neutra- various ionicitiescanoccurin metals,asin salts [4].lize thedefect.However,chemistshavefor sometime Confusionover thispoint relatesto an oversimplifica-recognizedthathalidesmay enteralkali metalsas ions tion of one-electrontheory.Forexample,Pimpuri-neutralizedby repelledelectrons[1] andstrongevi- tiesin Geclearly introduceholes into all theGe coredeneefor similar ionic effectsassociatedwith chalco- bandsdespitethefact that the corebandslie belowagenshasrecentlybeenreported[2, 3]. In this letter full valenceband.Similarly, Tm metalmay haveonlywe outlinethemoregeneralnatureof ionic effectsin twelfe 4f orbitals occupiedbelow the conductionimpurity structure,andidentify the probableextent band.In the sameway 0 could,in principle,enterNato which suchconfigurationsoccurin practicalcases, with only five 2p orbitalsboundbelowthe band

We first studythelimit in which the electrongas bottom,andwith two valenceelectronsrepelledtoplays a minorrole. Consideran impurity in a dilute ensureelectricalneutrality (althoughthis paramagneticmonovalentlatticehaving a largeinteratomicspacing configurationprobablyis not the groundstateina.Whetheror nota falls beyondthe Mott transition practice).The importantpoint is that the atomic0thehostbandstateslie approximatelyat thefree andthe ionic 0= configurationsin themetalcouldatomlevels.The energyrequiredto transferone elec- conceivablyhavelargertotalenergiesthan that of thetron from a neighbouringatom to theimpurity is 0~-metalcomplex.Thus, to assessthe degreetoE = I—A — e2~a which impurity ionization takesplaceone mustin

1 / generalcomparea varietyof alternativeionic configu-

with I thehostionization potentialandA the impu- rations.rity affinity. ForI 4.5eV andA 3.5eV the transi- With increasinghostelectrondensity thevalencetion from an atomic to an ionic impurity configura- levelsof all impuritiesmusteventuallyrise into thetion lies at e2/a 1 eV, ora 25 a.u. This applied, conductionbandfirst asvirtual levelsand finally asfor example,to the elementsI(A = 3.3eV) and very broadbandstates.ThishappensbecausetheTe(A = 3.6eV) in K(I = 4.3eV) butnot to Xe for kinetic energyof bandstatesnearEF finally over-whichA —1 eV. The degreeto which furtherioniza- whelmstheimpurity potential.The spectrumof im-tion stepstakeplace presentsmoresubtleproblems. purity configurationsbegunaboveandcompletedbyFree doublychargedionsare universallyunstablein thesecasesis shownin fig. 1. With increasingelectronvacuoandmultiple affinities derivedfrom studiesof densityan impurity can,for favorableI-A, undergoacohesionin saltspertainonly to tightly boundorbit- transitionfrom the atomic to the first ionic configura-als. tion (aandb),andmay eventuallyevencompletea

Providedthata varietyof ionicitiescan,in principle, full valenceshell to attainits fully ionizedconfigura-tion (c). Whetheror not step(c) occurs,the occupied

* This work wassupportedin part by the AdvancedResearch corelevelsrise into the bandwith increasingelectronProjectsAgencyunderContractHC 15-67-C-0221. densityandthe virtual levels(d) finally broaden(e) in-

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Volume41.4, numberI PHYSICSLETTERS 28 August 1972

77

r / ~2 ~ ‘I ~1~

~‘:_____________________ ____ ______

Te~jSn

~In Sn5Sb ~Te/ \n \ \ “ XeC__________________________ Cs

1 Na AgEF E 021 022 023Fig. 1. The p wavephaseshift for variousconfigurationsof

~e (cm3)

Te in metals: (a)atomic; (b) ionic; (c) fully ionic; (d) virtual; Fig. 2. The schemeof ionlclty I asa functionof hostelectron(e) broadenedbandconfiguration. In (a) and(b) thereare density for In, Sn,Sb, Te, I and Xe in monovalentmetals.Therespectivelytwo andonep orbitals with i~= 0. Thequantity ionicities of virtuallevels(seecaption to fig. 1)are indicated1 showsthe“ionicity” employedfor virtual orbitals in fig. 2. by brokenlines.

metals [7]. The observedaffinities, togetherwith ato weakly perturbedbandstates.The degreeof ioni- typical ionization energy,permit rough estimatesofcity establishedin steps(b) to (d) dependson details ~ for the first ionization.Furthermore,the observedof thehostmetaland impurity atom structures. susceptibilitiesin alkali metalshost [2, 3, 71 allow us

Becausethe precedingargumentsare expressedin to makereasonableestimatesof the ionicity for ~eintermsof specific configurationsthereare two qualify- the range of metallic densities.Theboundto virtualing pointsto bearin mind. First, the true wavefunc- transition(solid to brokenlinesin fig. 2) is estimatedtion of the impurity-metal complexmust be derived from the apparentlyrapidloweringof the energyoffrom an interactionamongconfigurations,andis re- Sn orbitalswith decreasing12e in NaK [71,and fromsolved into the simple pictureonly when thealterna- theoreticalstudies[3], but hasno sharpsignificance.tive configurationsare well spacedin total energy.The Available information makesthe broad schemeof theresultsof the interactioncannotbe depictedin the structuralpropertiesindicatedat leastqualitativelyone-electronschemeof fig. 1. Second,thedistinction reliable.betweenboundandvirtual levels losesclarity when It is not at presentclearwhetheralternativeionici-electroninteractionsaresuperposedon theone-elec- ties representlong-livesexcitedstatesanalogousto coretron scheme[5]. No abruptchangesof physicalpro- holesin metals. If theyexist asdiscreteexcitationspertiesare expectedin the transitionevenin one- theselevelsshouldcausetubstantialeffectsin theim-electrontheory [6], and for interactingelectronsthe purity excitationspectrum.A searchfor effectsofconceptof a transitionis itself blurred. this naturehasbeenundertakenin our laboratories.

Fig. 2 providesan assessmentof the probablecon-figurationsof In, Sn,Sb, Te, I andXe in monovalent Referencesmetalsas a function of hostelectrondensity“e~Xe Ill See the reviewby M.A. Bredigin Molten Salt Chemistry,almostcertainlyremainsatomic while I most probably ed. M. Rlander(lnterscience,New York, 1964)

remainsionic throughmostof the rangeshown.It [2] J.A. Rigert andC.P. Flynn, Phys.Rev. Letters26 (1971)

hasbeenobservedin detailedsusceptibilitystudies 1177, andto bepublished.13] C.P. Flynn andNO. Lipari, Phys. Rev.Letters 27 (1971)

[7] that Snundergoesa transitionfrom bandstatesto 1365, andto be publisheda virtual level at ~e 1.5 X 1022A~3,and the same [4] For a discussionof impurity structurein saltsseeC.P.transitionsfor Te andSb apparentlyoccur in the Flynn, Point Defectsand Diffusion (Oxford 1972) p. 579.

range2.3 x 1022<fle<5.l X l0~2A~3thatis, be- [5] N.F. Mott, J. Phys.Rad.23(1962)594.

tweenliquid Naandliquid Ag. Incipientsignsof a [6] W. Kohn andC. Majumdar,Phys.Rev. A128 (1965)1617.

similar transitionare seenfor In in heavieralkali Ill M.D. Mikolosko, J.A.Rigert andC.P. Flynn, PhysicsLetters 38.4 (1972)69.

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