RELATIONSHIPOFLENNARD-JONESPOTENTIALANDMORSE POTENTIALWITHW_x(r)POTENTIALXie,Youqing(Dep artementofMaterialsScienceandEngineeing,Cen tralSouthUniversityofTechnology,Changsha410 083)RELATIONSHIPOFLENNARD-JONESPOTENTIALAND MORSEPOTENTIALWITHW_X(r)POTENTIAL¥Xie,Youqi ng(DepartementofMaterialsScienceandEngineei ng,CentralSouthUniversityofTechnology,Chang sha410083)ABSTRACTItwasprovedthatLennard-Jo nespotentialcanbetransferedtoW_x(r)potentia laccordingtorelationshipoftheirparameterses tublishedinthispaper.TheempiricalW_1(r)pote ntialhasbeendevelopedintosemi-empiricalW_x( r)potentialrelatedtoelectronicstructureofcr ystuls.Relation-shipsofparametersbetweenMor sepotentialandW_x(r)potentialhavebeenalsoob tained,butifMorsepotentialequalsW_x(r)poten tial,theparametera_minMorsepotentialcannotb econstant.Comparingitwithothertwopotentials ,theW_x(r)potentialisthemostperfect.Keyword s:potentialfunctioncohesiveenergythermalexp ansionelasticmodulus1INTRODUCTIONThestudyof H2moleculeusheredinanewwayofestablishingmic rotheoryofcorrelatingpo-tentialenergywithel ectronicstructureofatomsinsolids.Butthemicr otheoryofmetalsandalloyshasmadeslowprogress ,becausetherearealotofdifficultiesindescrip tionofelectronicstructureofatomsinsolids,de signofpotentialfunctionwiththemany-atominte ractionandsolutionofSchredinger’sequationdu etocomplexityofmany-bodyproblem.Forthisreas onanotherwayhasbeendevelopedforstudyingrela tionsbetweeninter-actionpotentialenergyandp ropertiesofatomsinsolidsusingpotentialfunct ion.Thewell-knownpo-tentialsare,respectivel y,bennard-Jonespotential(referedasW_1(r))[1 ]:W_1(r)=A_1/rn1-B1/rm1,(1)andMorsepotentia l(referedasW_m(r)wherer0andrare,respectivel y,distancesofin-teratomsincrystalsatequilib riumandunequilibri-um;Eciscohesiveenergyofc rystals;andallofpa-rameters,A1,B1,n1,m1,nma ndamareconstants.Recently,anewpotentialfunc tionwithmany-atominteractionsinsolidshasbee nproposedbytheauthorforstudyingrelationsofc rystallinestructure,electronicstructureandp ropertiesofmet-alsandalloys(referedasWx(r)) [2]:Itpossessesthefollowingcharacters:(1)It isestablishedonthebasisofmany-atominteracti onmodel.(2)IntheWx(r)potential,thevariablei sthereduceddistanceorbondlengthofinteratoms ,sotheformoftheWx(r)potentialdoesnotbecomec omplexduetoconsideringmany-atominterac-tion s.(3)TheWx(r)potentialisasemi-empiricalequa tion,becausethepotentialenergyandbondlength ofthecrystalinequilibriumstutemaybecal-cula tedfromtheelectronicstructureofcrystals.(4) Therelationsofparametersnxandmxwithmi-croqu antitieshavebeenestablished,andonlynxisinde pendent.(5)Aseriesofequationsforcalculat-in gvariouselasticmodulihavebeenderivedfromthe Wx(r)potential.(6)ItisunnecessarytoknowProj ectsupportedbytheNationalNaturalScienceFoun dationofChina;ManuscriptreceivedJune25,1993 thebulkmedulusforcalculatingthethermalexpan -sioncoefficientasafunctionoftemperature.Th epurpoesofthispaperareestablishingrelations ofW.1(r)andWm(r)potentialswithWx(r)potentia l,obtainingtransferequationsoftheirparamete rsandmakingthebestselectionfromthesepotenti alsinpracticalapplicatons.2RELATIONBETWEENW 1(r)ANDWx(r)POTENTIALSItisnecessarytoestabl ishtransferequationsfromA1,B1,n1andm1parame tersinW1potentialtomxandnxparametersinWx(r) potentialinordertostudyrelationbetweenW1(r) andWx(r)potentials.Forthispurposeitissuppos edthatW1(r)andWx(r)potentialshaveidenticalc haracters,name-ly,thesameW(r)~rcurveforanid enticalcrys-tal.Ithasbeenprovedthatonlyonep arameternxinWx(r)potentialisaconstantawaiti ngdeterminedandcanbeobtuinedaccordingtoonee xperimentalvalueofthermalexpansioncoefficie nt.Therela-tionbetweenmxandnxparametershasb eenderivedaccordingtotheprincipleofmechanic sandDebye’stheory[3]:andwhereθisDebyetemper ature;KB,boltzmann’sconstant;h,Planck’scons tunt;m,atomicmass;λ,averagewavelengthofelas ticwave;λD,Debyewavelength;andjisthemultipl eofthehalfDe-byewavelength.Inordertoestabli shtherelationshipbetweenW1(r)andWx(r),theWx canberewrittenasComparingEq.(1)withEq.(6),thefollowinge-quationscanbeobtuined:someknowledgescanbedrawnfromEqs.(7)~(11):(1)TheparametersA1,B1,n1andm1inW1(r)potentialarefunct
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