Two-phase-solid–liquid-coexistence-by-molecular-dy

Two-phasesolid–liquidcoexistenceofNi,Cu,andAlbymoleculardynamicssimulationsusingthemodifiedembedded-atommethodEbrahimAsadi,a,⇑MohsenAsleZaeem,a,*SasanNouranianbandMichaelI.BaskescaDepartmentofMaterialsScienceandEngineering,MissouriUniversityofScienceandTechnology,Rolla,MO65409,USAbDepartmentofChemicalEngineering,TheUniversityofMississippi,University,MS38677,USAcDepartmentofAerospaceEngineering,MississippiStateUniversity,MississippiState,MS39762,USAReceived30September2014;revised24November2014;accepted7December2014Abstract—Thetwo-phasesolid–liquidcoexistingstructuresofNi,Cu,andAlarestudiedbymoleculardynamics(MD)simulationsusingthesecondnearest-neighbor(2NN)modified-embeddedatommethod(MEAM)potential.Forthispurpose,theexisting2NN-MEAMparametersforNiandCuweremodifiedtomakethemsuitablefortheMDsimulationsoftheproblemsrelatedtothetwo-phasesolid–liquidcoexistenceoftheseelements.Usingthesepotentials,wecomparecalculatedlow-temperaturepropertiesofNi,Cu,andAl,suchaselasticconstants,structuralenergydifferences,vacancyformationenergy,stackingfaultenergies,surfaceenergies,specificheatandthermalexpansioncoefficientwithexperimentaldata.Thesolid–liquidcoexistenceapproachisutilizedtoaccuratelycalculatethemeltingpointsofNi,Cu,andAl.TheMDcalculationsoftheexpansioninmelting,latentheatandtheliquidstructurefactorarealsocomparedwithexperimentaldata.Inaddition,thesolid–liquidinterfacefreeenergyandsurfaceanisotropyoftheelementsaredeterminedfromtheinterfacefluctuations,andthepredictionsarecomparedtotheexperimentalandcomputationaldataintheliterature.2014ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.Keywords:Moleculardynamics;MEAM;Solid–liquid;Melting;Solidification1.IntroductionMicrostructuralfeatures,suchasgrains,phases,disloca-tionsanddefects,determinethepropertiesofmetals.Inmetalsaswellasmanyothermaterials,thesolidificationorcrystallizationistheinitialstepofthemicrostructureformation,andathoroughunderstandingofthephysicsofsolid–liquidcoexistenceisakeyfactorindeterminingthemechanismscontrollingthemicrostructuralfeaturesofthematerial.Theexperimentalstudyofthephenomenarelatedtothecoexistenceofsolid–liquidstructuresisgener-allychallenging,becausethemeasurementshavetobedoneatthemeltingpointsofthematerials.Thankstorecentimprovementsincomputationalpowerandsupercomput-ingcapabilities,manyresearchandindustrialinstitutionshavestartedtoutilizecomputationalmaterialsmodelingasasuitablealternativetocostlyand/orimpracticalexper-iments.Moleculardynamics(MD)simulationandphase-fieldmodeling(PFM),includingphase-fieldcrystal(PFC),arethemaintechniquescommonlyusedtostudythesolid-ificationandsolid–liquidcoexistenceofdifferentmaterials[1].PFMisanefficientcomputationaltechniqueinthemesoscaleformodelingsolidificationandpolycrystallineproblems[2–4],andPFCisanewgenerationofPFMwithatomisticdetails,directlyderivedfromdensityfunctionaltheory[5–7].Ontheotherhand,MDisawell-developedcomputationalmethodwithgreataccuracythatcantrackindividualatomsandtheirenergiesatsmallerlengthandtimescales.Inaddition,theMDsimulationsofsolid–liquidcoexistenceofmaterialscanbeusedtodeterminemanymaterialproperties,suchasmeltingpoint,liquidstructurefactor,solidandliquiddensities,solid–liquidinterfacefreeenergyandsurfaceanisotropy.Thesepropertiesprovidevaluableinsightsinunderstandingthematerialsolidifica-tionprocesses.TheycanalsobeusedtodeterminethePFCandPFMmodelparameters,andtesttheaccuracyofthesemodelsinsimulatingthenano-andmicrostructuresresultingfromsolidification[7–10].Therefore,theMDmodelingofcoexistingsolid–liquidstructuresisaveryimportantaspectininvestigatingthesolidificationphenomenon.InMDsimulations,choosingapropertechniqueformodelingthetwo-phasesolid–liquidcoexistenceofmaterialtocalculatethetargetproperties,suchassolid–liquidinter-facefreeenergy,isofcriticalimportance[11].ThemajorMDsimulationtechniquestocalculatethesolid–liquidinterfacefreeenergyandsurfaceanisotropyarethecleav-ingtechnique,criticalnucleusmethod(CNM)andcapillary2014ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.⇑Correspondingauthors.Tel.:[phone];fax:[phone];e-mailaddresses:[e-mail];[e-mail](2015)169–181fluctuationmethod(CFM).Thecleavingtechnique,whichwasfirstusedbyBroughtonandGilmer[12]andfurtherdevelopedbyDavidchackandLaird[13,14],isbasedonperformingmultiplestepsofMDcalculationsatthetriplepointsofelementalsystemsandintroducingacleavingpotentialtoformthesolid–liquidinterface.CNMisatech-niquebasedondeterminingthecriticalsolidnucleusradiusfromtheGibbsfreeenergyandcomparingittotheMDcalculationstofindthemeltingpoint,andformacoexistingsolid–liquidstructure.Althoughcalculatingthesolid–liquidinterfacefreeenergybytheCNMisarelativelystraightfor-wardtask,thismethodhasnotbeenutilizedyettodeter-minethesolid–liquidinterfaceanisotropy[15–18].TheCFMisbasedonequilibratingacoexistingsolid–liquidstructureattheexactmeltingpointoftheelement,deter-miningthe