Volume76A, number1 PHYSICSLETTERS 3 March 1980

CORRELATION OF SURFACE SEGREGATION WITHBULK DIFFUSION FOR BINARY METAL ALLOYS

DennisG. SWARTZFAGERCentralResearchandDevelopmentDepartment,E.I. duPontdeNemours& Co., Inc.,Wilmington,DE 19898,USA

and

MichaelJ.KELLEYEngineeringTechnologyLaboratory, ExperimentalStation,E.I. du PontdeNemours& Co., Inc.,Wilmington,DE 19898,USA

Received17 September1979Revisedmanuscriptreceived12 October1979

Previoustreatmentsof surfacesegregationin metalalloyshaveall failed in somesystems,dueeither to inadequaciesinthe theoriesor in thethermochemicaldata.A new model is proposedhereusingonly alloy diffusion data.Predictedsurfacecompositionsagreequantitativelywith ISS measurementsandqualitatively AES results.

Thesurfacecompositionof metalalloysandits andthe energyto createit canthenbe relatedto therelationshipto thatof the underlyingbulkhaveattract- surfaceenergyof thesolid [8]. More recently,bond-edmuchexperimentalandtheoreticalinterestsince breakingargumentsbasedon sucha concepthavebeensurfacecompositionswere first measuredsometen usedto estimatethis formationenergyandotheryearsago.Now,thoughsurfacecompositionsfor many energies[4,29], suchas thatbindinga soluteatombinary alloyscanbecalculatedfrom basicthermoche- to thevacancyor thesurface.Thus the freeenergymical data,that for manysystemsof practicalinterest changefor interchangingsolventandsolutesurfacecannot[1].Evenwheresurfacecompositionscanbe atomscanbe shownto beproporionalto that for inter-calculated,agreementwithexperimentis notentirely changingsolventandsoluteatomsadjacentto avacancy.satisfying [2,31.Moreover,the theoriesthat give better G — G 1agreementwith experiment[1,4] requireextensive GAS — BS — ~~GAV BV

computercalculationsand so arenot easilyaccessible wherethevalueof the proportionalityconstantk de-to mostinvestigators. pendson thedetailsof the particularmodelused.Now

A simplified theoryor empiricalcorrelationwhich the left-handsideof eq.(1) relatesto thesurfacecom-canbe appliedbroadlythushasconsiderableappeal. positionthroughAttempts[5,30] to at leastpredictwhichmemberof x5 Xb i G~5— GBS\abinary alloy will concentrateon the surfacehavemet — = exp ) . (2)with only limited success[6,7]. Wehereoffer another“correlation” to estimatebinary alloy surfacecompo- The differencein vacancybindingenergieson the right-sition explicitly, notmerelywhich elementwill segre- handside of eq.(1)is relatedto thetracerdiffusiongate. coefficientswhenB is animpurity in A by [9]

Twenty-fiveyearsago,it wassuggestedthata va- D f w G — Gcancymaybethoughtof asa smallcavity in the solid DA = fAwA exp (— AV BY) (3)

Volume 76A, number1 PHYSICSLETTERS 3 March1980

wherethef’s arethe correlationfactors,thew’s the 1.0 I

jumpfrequenciesanddiffusion is by a vacancymecha-nism.Combiningthesethreeequationsgives:

X~ / Xb - k’ DB(Xb) 0.8 0 -

1—XS/l—Xb DA(Xb)’ ~

wheretheD’s arethe tracerdiffusion coefficientsof 0.6 -

A and B in thebulk alloy containingatomfractionXb ~5

of elementB at thetemperaturewhereX~,thesurface Ag

concentrationof elementB, is measuredandall the 0.4 ~ -

previousconstantsare containedin k’.Forsimplicity, wehavetakenk’ = 1 in makingthe °

calculationsshownin figs. 1, 2 to testwhethereq.(4) 0.2 .

canaccuratelypredictsurfacecomposition.The diffu-siondataweremainly takenfrom Askill’s compilation 7[10] with the individual referencesindicated.Wehave /‘ I I I I

chosenion-scatteringspectroscopy(ISS) measurements 0 0. 2 0.4 0.8 0.8 1.0

of surfacecompositionsto comparewith thecalcula-tionsbecauseof its superiority [11] to othertechniques F.2ft Ag—Au alloys..Diffusioncal-for measurmgfirst monolayercompositions.Thiscom-parisonis frequentlycomplicatedby the unavailabilityof diffusion and ISSdatain thesametemperature range.Comparisonof the compositionestimatesforrange. Cu-richCu—Ni at 730 and1025°C(1003 and 1298K)

Theresultsshownin fig. 1 for severalcopper-based suggeststhatsomealloysmayshownearlyathermalalloysshow remarkableagreementwhenthe diffusion behaviorathighconcentrationof the surfaceactivedataare notextrapolatedoveran extremetemperature element.Theresultsfor Ag—Au (fig. 2) showequally

goodagreement.Finally, table 1 showsgoodagreementfor severalotheralloy systemswhenthe soluteis in very

1.0 --~ low concentration.The diffusion correlationpredictsandISS measure-

7 — — ~2,A —— mentsshowno segregationof Ni to the surfaceof Au-

y _~——v // rich Ni—Au alloys, in contrastwith earlierAESresults/

7~,~ Tablel

0.5 - / -‘ Surfacesegregationfor dilute alloys.

xs ~PvCu / Solvent DB/DA T(°C) Ref. Segregationa) Ref.

(solute)

Fe(Cr) 1.3 800 [101 yes [5]Fe(Ni) 1.4 700 [19,21] ?Fe(Sn) 27.7 700 [19,211 yes [5]

0 Ni(Pd) 259Ob) 800 [10,23]. yes [24]I Pt(Fe) 144 1250 [10,22] no [5]

0 xb 0.5 10 Zr(Fe) 3.88 750 [26] yes [5]Cu Ag(Pd) 0.042 750 [10,26] no [25]

Fig. 1. Surfacesegregationin Cu alloys. Diffusion calculations:• Cu—Pt 730°C, ~ Cu—Ni730°C, ~ Cu—Ni1025°C.ISS results: a)As determinedby AugerElectronSpectroscopy.o Cu—Pt 730°C[2], A Cu—Ni500°C[16], A Cu—Ni 500°C b) The value forD (Pd in Fe) reported in ref. [23] seems un-[16], vCu—Ni730°C[17]. reasonably high.

87

Volume76A, number1 PHYSICSLETFERS 3 March1980

[7]. Further,the diffusion correlationandothers[30] platinumgroupmetals,andto examinenonmetalsasdisagreewith the AESfinding [28] of the absence well. Nonetheless,thediffusion correlationoffers aof Fe enrichmentin Pt(Fe).However,AEShasproven usefultool for anticipatingboththe directionandex-insufficiently sensitiveto detectAg enrichmentin tent of surfacesegregationevenwith the limited experi-Ag—Au [2] or measurethe extentof Cuenrichment mentaldataavailable.in Cu—Ni [1], comparedto ISS.ThoughthePt(Fe)diffusion data [22] canbe questioned,webelievea Referencescareful ISSstudyis merited.

Now eq.(4) mayberewritten to expressthe temper- [1] M.J. Kelley, J. Catal.57 (1979) 113.

aturedependenceof the diffusion coefficientdirectly: [2] M.J. Kelley, D.G. SwartzfagerandV.S. Sundaram,J. Vac.Sci. Tech.16 (1979)664.

X5 / Xb , Dçj~ ( QA — QB “ [3] M.J. Keiley, D.G. SwartzfagerandP.W. Gilmour, J. Vac.exp

1—X~/1 — Xb = ‘~ Ri’ ) . (5) Sci. Tech.,to bepublished.[4] R.G. DonnellyandT.S.King, Surf. Sci. 74 (1978) 89.

Its formalsimilarity to eq.(1) leadsusto comparethe [5] J.J.Burton andE.S.Machim,Phys.Rev. Lett. 37 (1976)

differencein activationenergies(strictly,enthalpies) 1433.to theenthalpyfor surfacesegregationandthepre- [6] N.S. Tsai,G.M.PoundandF.F.Abraham,J. Catal. 50

(1977) 200.exponentialfactorsto theentropy. [7] P.Wynblatt andR.C.Ku, in: Interfacial segregation(1977)

Table 2 showsthecomparisonfor the few systems (AmericanSocietyfor Metals,MetalsPark,OH).wheredataareavailable.Agreementis bestwhere [8] H. Brooks, in: Impurities andimperfections(1955)

critically evaluateddiffusion data [10,26] areavailable. (AmericanSocietyfor Metals,MetalsPark,OH, 1).

In Pt(Fe)andNi(Pd) wherethey arenot,agreement [9] A.D. LeClaire, J. Nucl.Mat. 69—70 (1978) 70.[10] J. Askill, Tracerdiffusiondatafor metals, alloys and simple

is vague.Forthe segregationentropy,theratio of dif. oxides(IFI/Plenum, New York, 1970).

fusion pre-exponentialfactorspredicts4.9eu (SsegIR), [11] D.P. Smith, Surf.Sci. 25 (1971)171.

while 2.6 euismeasuredby AES for Ni(Au) [15]. In [12] A.D. Kurtz, B.L. AverbachandM. Cohen,Acta Metal!.view of theproblemswith AESnotedabove,we find 3 (1955)442.

this agreementencouraging. [13] J.E. Reynolds,B.L. AverbachandM. Cohen,Acta Metall.

Finally, theprincipaldifficulty limiting moreexten- 5 (1957) 29.[14] J.J. Burton,C.R.HelmsandR.S.Polizzotti,J. Vac.Sd.sivetestinganduseof this correlationis, asalways,the Tech. 13(1976)204.

sparsityof good experimentaldata.Thougha recent [15] P. WynblattandR.C.Ku, Surf. Sci. 65 (1977)511.

critical compilation [26] providesdiffusion datafor [16] H.H. BrongersmaandT.M. Buck,Surf. Sci. 53 (1975)649.298 solvent(solute)systems,surfacecompositions [17] H.H. Brongersma,M.J. SparnaayandT.M. Buck,Surf.

Sci. 71(1978)657.havebeendeterminedonly for thosenotedabove.It [181 G.C. Nelson,Surf. Sci. 59 (1976)310.

thereforeoffers a challengeto physicistsandothers [19] D. Treheux,D. Marchire,J. DelagrangeandP. Giraldenq,

concernedwith diffusion measurementsandsurface C.R. Acad.Sci. ParisC274(1972) 1260.

scientiststo makemeasurementsin a commontempera. [20] F.S.Buffington, K. Hirano andM. Cohen,Acta Metall.

ture rangeon importantalloys,suchasthoseof the 9 (1961)434.[21] K. Hirano, B.L. Averbach and M. Cohen, Acta Metall.

9 (1961) 440.[22] M.I. Dekhtyar,V.N. Kolesnik,V.1. Patoka,V.1.Silantev

Table2 andI.Y. Dekhtyar,Phys.Stat.Sol. (a) 24 (1974)699.Segregationenthalpyfor dilute alloys. [23] G.A. Vorontsova,I.Y. Dekhtyar,A.M. Shalayeand

V.S. Karacye,Metallogizika(Kiev)48 (1973) 102.System QB—QA Hsega) Ref. [24] D.A. Mervyn, R.J.Baird andP. Wynblatt,Surf.Sd.82

(1979) 79.Ni(Au) 15 15 [7] [25] F.J. Kuijers andV. Ponce,I. Catal.60 (1979)100.Au(Ni) 0 1 [7] [26] C.J. Smithells,Metalsreferencebook, 5th edn.(Butter-Fe(Sn) 5 11 [7] worths,London,1976).Zr(Fe) 21 17 [27] [27] R.S.Polizotti andJ.J.Burton, J. Yac.Sci. Technol. 14Pt(Fe) —26 0 [28] (1977) 347.Ni(Pd) 21 7 [7] [281 J.J.Burton andR.S.Polizotti, Surf.Sci. 66 (1977)1.

[29] R.L. Schwoebel,J. Appl. Phys.38 (1968) 3154.a) In kcal/gmatom.A positivevalue favorssegregation. [30] D.F. Ollis, J. Catal.59 (1979)430.

88