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Thermodynamic

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ThermodynamicThermo

    Thermodynamic

DAKiyohitob

    ;‘SchoolofMetallwgicalandEcologicalEngineering,UniversRyofScienceandTechnologyBelting,Beijing100083,China

    ;DepartmentofMateria~Science,GraduateSchoolofEngineering,ToholoaUniversity,Sendai980-8578,Japan

    ;Received5January2008;receivedinrevisedform27March2008;accepted29March2008 ;1]heNi.SbbinaryalloysystemwasthermodynamicallyassessedusingCALPHADapproachinthisarticle.ExcessGibbsenergiesofsolution

    ;phases,liquidandfeephases,wereformulatedusingtheRedlich-Kisterexpression.111eintermediatephasesweremodeledbythesublattice

    ;modelwithfNi,Va)0.s(Ni,Sb)02s(Ni)025forNi3Sb_HTphaseand(Ni,Va)o.3333(SD)o.3333(Ni,Va)o3333forNisbphase.111eotherphasesincluding

    ;Ni3Sb,NiTSb3,andNiSb2weretreatedasstoichiometficcompoundowingtotheirnan’owcompositionranges.Basedonthereportedther-

    ;modynamicpml~rtiesandphasediagramdata,thethermodynamicparametersofthesephaseswereoptimized,andtheobtainedvaluescan

    ;reproducetheavailableexperimentaldatawel1.

    ;Keywords:Ni-Sbbinarysystem;thermodynamicassessment;CALPHAD;phasediagram

    ;1.Introduetion

    ;Inrecentyears.thedevelopmentoflead-freesoldersfor

    ;electronicinterconnectionmaterialsusedinelectronicde

    ;viceshasreceivedgreatattentionbecauseofthehealthand

    ;environmentalsafetyproblemsposedbyconventionalPbSn

    ;solders.Forthedevelopmentofalcad.freesolder,thermo

    ;dynamiccalculationisanimportanttoolinthedesignand

    ;evaluationofvarioussolderingalloyssinceitsignificantly

    ;decreasestheamountofrequiredexperimentalwork.Re

    ;cently,athermodynamicdatabaseforthecalculationof

    ;phasediagramsinmicrosolderingalloysystemsbythe

    ;(LPHAD(CALculationofPHAseDiagram)approach

    ;hasbeendevelopedbyOhnumaandLiueta1.[121.Itcon-

    ;sistsoftheelementsAg,Bi,Cu,In,Pb,Sb,Sn,andZninthe

    ;initialstage.Inmodemmicroelectronicpackage.Nicoats

    ;areoftenplatedasanunder-bumpmetallurgy(UBM)layer

    ;onthesubstratebeforetheelectroniccomponentsaresol

    ;dered.111einterfaeialreactionsbetweenNiandthesolder

    ;thusplayanessentialroleinthereliabilityofsolderioint

    ;andshouldthereforebeconsideredcarefullyinthedesignof

;lead-fleesolder.Tounderstandtheinterfacereactionsbe

    ;tweenNiandsolder,itisnecessarytocontainNielement ;witIlinthecurrentdatabaseandtherelatedbinarysystemsof ;NiX()(=Ag,Bi,Cu,In,Pb,Sb,Sn,orZn)shouldbewell ;Correspondingauthor:CAOZhanminE-mail:zmcao@metallustb.edu.ca ;optimized.Theaimofthisarticleistooptimizethephase ;diagramandthermodynamicpropertiesoftheNiSbbinary

    ;system.

    ;2.Experimentaldata

    ;2.1.Phasediagram

    ;ThephasediagramoftheNi.Sbbinarysystemhasbeen ;studiedbysevemlinvestigatorsf3l81andreviewedre-

    ;cenl[1ybyChaeta1.[191.Theevaluatedphasediagramis ;showninFig.1.Besidestheliquidand2terminalsolutions. ;thefccstructurefNi),andtherhombohedralstructure(sb), ;thereare6intermediatephasesreportedinthissystem,that ;isNi15Sb,Ni3Sb,Ni5Sb2,NiTSb3,NiSbandNiSb2,andthe ;structuresofthesephasesarelistedinIble1.Amongthese ;phases,Nil5Sb,whichwasfastreportedbyOsawaandShi- ;bat51andShibataf61,isnottakenintoaccountintheopti- ;mizationsinceitsexistencewasdeniedbyrecentstudiesf1l, ;15.17l81.

    ;111ecompleteliquidusofthissystemhasbeenmeasured ;byseveralinvestigators[3-4,8,14,17].Theextentofsolu- ;bilityofSbinNiwasdeterminedbyIshidaetaL131,and

    ;FeschotteandLorin[17.ThehomogeneityrangeofNisSb2

    ;wasreportedbyEremenkoandKruchininaf81,Pantelei

    ;monovetaLf91,andFeschotteandLorin[17].Thephase ;塑一

    ;

    ;Caoz.M.eta1.ThermodynamicassessmentoftheNiSbbinarysystem

    ;boundaryrangeofNiSbwasstudiedbyseveralresearchers ;[45,7,l0,l6l7].Shibata[4],ElbakkouriandDirand[15], ;andFeschotteandLorinl7]reportedthatNi3Sbwas

    ;formedinaperitectoidreactionfrom(Ni)andNi5Sb2For ;theNi7Sbphase,itisstillnotfullyclearfromtheavailable ;literaturedatawhethertheNi7Sbformsinaperitectoidre

    ;action[4-5,8,12,21]orwhetheritformscongruentlyfrom ;NiSb,7,l7].NiSb2isformedinaperitecticreactionre

    ;portedinRefs.[34,17].111esolubilityofNiin(Sb)wasre

    ;portedbyShibata4]andFeschotteandLorinfl7].

    ;Inthisstudy,thephasediagramdatausedinoptimization ;calculationaretakenfromFeschotteandLorinf17]and ;LeuboltetaLl4].

;Antimon)content/wt.%

    ;385

    ;Antimonycontent/at.%

    ;Fig.1.NiSbphasediagramfromRef.f201.

    ;Table1.NiSbcrystalstructuredata

    ;2.2.Thermodynamicdata

    ;KorberandOelsonf23]measuredthemixingenthalpyof ;liquidinthecompositionrangefrom7.5at.%to90at.%Sb ;atl873Kbydirectreactioncalorimetry.PredelandVoge1. ;bein[24]determinedthemixingenthalpyofNiSballoysin

    ;therangeof2at.%to5lat.%Sbat800Kbytheliquidtin ;calorimetricmeasurements.Also.usingtheliquidtincalo

    ;rimetry,PredelandRuge[25]measuredtheenthalpyof ;formationofNiSbforasinglecompositionr50at.%Sb).

    ;PerringetaLf26]measuredtheheatcapacityofNiSbfrom ;3l0KtOl080KusingtheDSCmethod.Usingtheisopi

    ;esticmethod,LeuboltetaL[14]andHuangetaL[27] ;measuredtheantimonyvaDorpressureofalloyintheNiSb ;phasebetween975Kandl375K.Popoviceta1.28]meas

    ;uredtheactivityofantimonyinthephasesofNiSb ;(D03type)andNiSb(B8type)bymeansofaKnudsenEf- ;fusionMassSpectrometric(KEMS)method.Allthese ;thermodynamicexperimentaldataareusedinthecurrent ;optimization.

    ;3.Thermodynamicmodeling

    ;3.1.Referencestates

    ;Asreferencestatesforthesystem,thepuresolidelements ;ofNiandSbintheirstablestatesat298.15K(stableele. ;mentreference,SER)arechosen.Thetemperaturedepend

    ;enceoftheGibbsfreeenergiesoftheelementswastaken ;fromScientificGroupThermodataEuroperSGTE)database ;f29]inthefollowingforn1:

    ;.G()J,(298.15K)=A++CTlnT+

    ;DTz+ET+FT3+fT+JT,,

    ;3.2.Solutionphases

    ;Thesubregularsolutionmodelisusedtodescribethe ;Gibbsenergyoftheliquid,fccphases,allowingcomplete ;mixingofNiandSbonthesamesublattice.Themolar ;Gibbsenergyofasolutionphasecanbeexpressedasfol

    ;lOWS:

    ;G=?.G+RT?ln+i=Ni,Sbi=Ni,Sb

    ;G+AgG(2)

    ;whereff=Ni,Sb)isthemolarfractionofcomponent ;offinthe(pphase,0GisthemolarGibbsfreeenergyof

;thepuref,whichwastakenfromSGTEdatabase29]inthis

    ;study,Ristheuniversalgasconstant.Tisthetemperaturein ;Kelvin,GistheexcessGibbsenergyofmixing,and ;AgGisthemagneticcontributiontotheGibbsfreeen

    ;\0JnQuJ

    ;

    ;386

    ;TheexcessGibbsenergyofmixingisexpressedbya ;Redlich-Kisterpolynomial[30]:

    ;xsG=XNiXsb[‘.

    ;sb+’i

    ;,

    ;sb(NiXSb)+

    ;.’i

    ;.sb(Nj—XSb)+…](3)

    ;wheretheinteractionparameter’i.sbmaybetempera-

    ;turedependentandtakestheformasfollows:

    ;)-sb=A+BT(4)

    ;where,AandBaretobeoptimized.

    ;The?agGwasomittedinthisstudyowingtothe

    ;lackofsufficientexperimentaldata.

    ;3.3.Intermetallicphaseswithsolubilityranges ;3.3.1.Ni3SbI-IT

    ;TheNi?-richhigh?-temperaturephaseoftheNi??Sbphase ;diagramwasfirstidentifiedbyLossew[3]in1906,which ;wasdesignatedasNisSb2inFig.1.Althoughitsexistence ;wasneverdoubted,theactualstructureofthisphaseis ;highlycontroversial:thefirstX-raydiffractionstudiesby ;FurstandHalla[31]andOsawaandSh~ata[5]provideda ;tetragonalstructure,whichwasrefutedbySchube~eta1. ;[32]whoclaimedacubic(D03)phase.Panteleimonoveta1. ;[9]foundahexagonalcell,whereasNaudandvarijs[21

    ;reconfirmedFurstandHalla’sfindings.Recently,Ni3Sb

    ;phaseathightemperaturehasbeenconfirmedtobetheD03 ;structurebyneutrondiffraction[3235].Therefore,this

    ;high-temperaturephasewithD03structurewasdesignated ;asNi3Sb_

    ;HTinthisstudy.

    ;Thecoherentneutronscatteringexperiments[3235]and

    ;abinitiocalculation[36revealedthatfortheNi3Sb_HT

    ;phase,thestructuraldefectfortheSbrichsystemistheNi

    ;vacancyonthealphasublattice,andthatthedominantde

    ;fectsforthestoichiometriccompoundareNivacancieson ;thealphassublattieeandNiantistructureatomsontheSb

;substance.Forsimplicity,hereNi3Sb_

    ;HTismodeledbya

    ;3-sublatticemodel(Ni,?1)0.5(Ni,Sb)0.25(Ni)o.25,forwhichthe

    ;molarGibbsenergyisgivenas ;G’b.HT=

    ;i

    ;GNiNi

    ;:

    ;+(7.

    ;Va

    ;Ni+

    ;‘sb

    ;y11(2

    ;Nj

    ;Ni

    ;:+G+

    ;,

    ;RTl0.5?.+0_25?lnE”l+l’’’Ii=Ni.SbNi,Sb/ ;TN+

    ;墙地i+

    ;(NiN?iS?bL,’N

    ;N

    ;j

    ;i:N

    ;s

    ;iS

    ;H

    ;b

    ;T

    ;:Ni+』』』.

    ;1

    ;地墙’j(5)

    ;RAREMETALS,VoL27,No.Aug2008

    ;where,riand”arethesite~actionsofelementiin ;sublatticeIandII,respectively,Ristheuniversalgascon-

    ;stant,andTisthetemperatureinKelvin.Byconvention,a

    ;commaandasemicolonseparateelementsondifferent

    ;sublatticesandonthesan’lesublattice,respectively.The ;N

    ;.

    ;i3Sb

    ;.

    ;_

    ;H

;.

    ;T

    ;,

    ;Ni

    ;.

    ;3Sb_

    ;H

    ;.

    ;T

    ;,

    ;N

    ;I

    ;i

    ;.

    ;sS

    ;.

    ;b

    ;.

    ;H

    ;l

    ;T

    ;,

    ;andNi

    ;.du

    ;3Sb

    ;.

    ;_

    ;.

    ;H

    ;.

    ;TtheandV ;a

    ;aretlae1?.

    ;l,va.

    ;ll,1I. ;dD.l,.du.-1l

    ;Gibbsfreeenergiesofhypothesizedcompounds

    ;Ni03333Ni03333Ni03333,Va0.

    ;3333Ni0. ;3333Ni03333,Ni03333Sbo3333Ni03333,

    ;andVa03333Sbo.

    ;3333Ni0. ;3333,respectively,whicharetobeop

    ;timizedinthisstudy.”~rhenonlythezeroth-orderinteraction

;coefficients(0)LNi3

    ;

    ;SbHT

    ;iand(.)aretakeninto

    leyareexpressedas ;account,?

    ;(.)b_HTNj=(.)b_H=AI+BTVa:NiVa:Sb:Ni/1_/.JI(6)Ni,:NiNj.10,

    ;(0)LNiHTj=(.)NiHT=A2+.T

    ;Ni:NiSb:NVa:NiSb:Ni/.J2(7).i,20,

    ;where,A1,BI,A2,andB2aretobeoptimizedinthisstudy. ;3.3.2.NiSb

    ;ThestructureofNiSbishexagonal[4-5,7,10,37]andit ;isisotypicwithNiAs(spacegroup:P6dmmc).Intheideal ;structuralNiSbphase,theSbatomsformahexagonal ;close-packed(hcp)[Wyckoffposition2(c)]arrangement ;whiletheoctahedralinterstices[2(a)]areoccupiedbytheNi ;atoms.Nonstoichiometryisachievedbythevacancieson ;position[2(a)]ontheSbrichside,andbypartialfillingof ;thetrigonalbipyramidalinterstices[2(d)]byadditionalNi ;atomsontheNirichside[38].Thisdefectmechanismhas ;beenconfu’medbythecompositiondependenceofthelat-

    ;ticeparameters[7,10,16,3739]ofthepycnometricdensity

    ;[7,10,16]andoftheeleclricalconductivity[7,3839].Based

    ;ontheNiAstypestructureandthedefectmechanisminNiSb ;phase,a3-sublatticemodel,3333(sb)03333(Ni,Va)03333,is ;usedinthisstudy,whichisalsoconsistentwiththemodel ;usedinotherNiAstypephases[4044].

    ;ThemolarGibbsenergyofNiSbisexpressedas ;G.=iG:Ni+i111GNNii:

    ;S

    ;sb

    ;b:va+】』vNilHu/’2_vNiSsbb:Ni+

    ;.,,

    ;-?-

    ;v

    ;va

    ;lll

    ;u

    ;/’2NiSb

    ;:va+RTf?lnY,.+

    ;ki=Ni,Va

    ;}

    ;??1l1l+i(.)NiSbsb:w+

    ;i=Ni,Va/I

    ;.(.):sb:va+i.(.’:Ni.va+

;rv’a

    ;H

    ;i

    ;I

    ;va

    ;I11(0)TN

    ;v

    ;i

    ;a

    ;S

    ;:s

    ;b

    ;b:Ni_va(8)

    ;3.4.Linecompounds

    ;TheintermetallicphasesofNi3Sb,Ni7Sb3,andNi2Sb ;weredescribedasthestoichiometriccompoundowingto ;theirnarrowcompositionranges.Owingtothelackofthe ;experimentaldataofheatcapacityforNi3Sb,Ni7Sb3,and ;

    ;Caoz.M.eta1.ThermodynamicassessmentoftheNi-Sbbinarysystem

    ;NiSb2,byapplyingtotheNeumann-Kopprule,themolar ;GibbsenergyofNi,SbHisgivenasfollows:

    ;Gi=,”.

    ;N

    ;fc

    ;.

    ;c+”.srh

    ;bo..+AGp’.(9)

    ;where,?GfNisthemolarGibbsenergyofformation ;ofNimSb.andcanbeexpressedasfollows:

    ;AOVi=a+bTf10,

    ;ThemeasuredheatcapacitiesofNiSbinthetemperature ;rangeof310Kto1180KbvPeIngPr,.26]showthat

    ;theNeumann.Koppruledoesnotapplytotheheatcapacity ;descriptionofNiSbcompound,andtheGibbsenergyof ;formationofthehypothesizedcompounds

    ;Ni03333Sbo3333Vao3333inNiSbphaseisgivenbythefollow- ;387

    ;lngexpresslon:

    ;AGNi?00m3V0?3=a+671+c71ln71+dT2+

    ;eTfr+gT

    ;where,theparametersatogaretobeoptimizedinthis ;study.

    ;4.Resultsanddiscussion

;UsingthestabilitiesoftheelementsNiandSbcompiled

    ;byDinsdale[29],thephasediagramoftheNi-Sbbinary

    ;systemwasoptimizedbytheThermo-Calcsoftware[45].

    ;Theoptimizedthermodynamicparametersforallcondensed

    ;phasesinthissystemarelistedinTable2.

    ;Table2?ThermodynamicparametersfortheNi-Sbsystemobtainedinthisstudy(theenergi

    esaregiveninJ/molandthetem. ;peraturesinK.)

    ;PhaseandformulaThermodynamicparameters

    ;Liquid,(Ni,Sb)

    ;sb=116000+260217T

    ;sb=1500013.9962T

    ;sb=3160019.9934T

    ;fcc(Ni),(Ni,Sb)

    ;.b=34300.684+8.6829T ;sb=95724.008

    ;GNN

    ;.

    ;i

    ;lN

    ;,Sb

    ;iH=GHSERNI+13662.53613556T

    ;G.=0.5GHSERNI+685727571.778T

    ;V

    ;Ni3SbHT,罢曼;.

    ;71

    ;(.)Ni~Sb

    ;a

    ;INH

    ;l

    ;T

    ;.

    ;Nl=(LNi3S

    ;

    ;b

    ;

    ;HT

    ;Nl=0

    ;(mLN

    ;

    ;i,S

    ;,

    ;b

    ;l,…

;lIT

    ;NI=

    ;)

    ;[

    ;v

    ;N

    ;a

    ;i~Sbb

    ;b

    ;iT

    ;Nl=0

    ;Ni3Sb,(Ni)075(sb)o25GNi=o.75GHSERNI+0.25GHSERSB24062.406 ;Ni7Sb3,CNi)0.717(Sb)o283GNi,sbSb0.717GHSERNI+0.283GHSERSB26450+0.65T

    ;G=0.6666GHSERNI+0.3333GHSERSB26000+3T ;GN=0.3333GHSERNI+06666GHSERSB+12493.1764.5044T ;Gv=0.3333GHSERNI+0.3333GHSERSB256000.84T+0.51606284T1nT ;NiSb,2.

    ;6185856x1071+72446233×107T3+2.

    ;4361342×104T+2.

    ;283×1021T7

    ;(Ni,Va)o.3333(Sb)o.333j(Ni,Va)NiS

    ;s

    ;b

    ;bv:0.3333GHSERSB+2957.7891+181899T ;?

    ;.

    ;=N

    ;Nl_

    ;iS

    ;v

    ;b

    ;ava=2711.783625.4525T

    ;?v=‘N

    ;v

    ;iS

    ;:

    ;b

    ;v=3403.6838+0.16T

    ;NiSb2,CNi)03333(Sb)06667GNNimSb:=0.3333GHSERNI06667GHSERSB25602.56+204T

    ;Rhombohedral(Sb),(Sb).(7.srhbo.=GHSERSB

    ;Note:ThefollowinglatticestabilitiesofpureNiandSbweretakenfrom29] ;GHsERNI=』一579?59+7-8547’22?096/’InT0.0048407T

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