Molecular dynamic simulation of a homogeneous bcc - hcp tran

We have performed molecular dynamic simulations of a Martensitic bcc->hcp transformation in a homogeneous system. The system evolves into three Martensitic variants, sharing a common nearest neighbor vector along a bcc <111> direction, plus an fcc region.

Moleculardynamicsimulationofahomogeneousbcc→hcp

transition

arXiv:cond-mat/0103278v1 [cond-mat.mtrl-sci] 13 Mar 2001J.R.Morris andK.M.HoAmesLaboratory–U.S.DepartmentofEnergy,DepartmentofPhysicsandAstronomy,IowaStateUniversity,Ames,IA50011WehaveperformedmoleculardynamicsimulationsofaMartensiticbcc→hcptransformationinahomogeneoussystem.ThesystemevolvesintothreeMartensiticvariants,sharingacommonnearestneighborvectoralongabcc 111 direction,plusanfccregion.Nucleationoccurslocally,followedbysubsequentgrowth.Wemonitorthetime-dependentscatteringS(q,t)duringthetransformation,and ndanomalous,Brillouinzone-dependentscatteringsimilartothatobservedexperimentallyinanumberofsystemsabovethetransformationtemperature.Thisscatteringisshowntoberelatedtotheelasticstrainassociatedwiththetransformation,andisnotdirectlyrelatedtothephononresponse.64.70.Kb,61.72.-y,63.70.+h,61.43.BnI.INTRODUCTION.Thetopicofprecursorphenomenainmartensitictransformationshasbeenthesubjectofnumerousstudiesoverthepasttwodecades.Martensiticsystemsundergo rst-ordertran-sitionswhicharecharacterizedbyalatticestrainaccompaniedbya“shu ing”oftheatomsassociatedwithaparticularphononmode).12Experimentally,ithasbeenobservedfromvariousdi ractionmeasurementsthatstreakingoftheBraggspotsoccurintheparentphaseclosetotheindicatinganincipientinstabilitytowardstheformationofthemartensiticphase.Thereisalsoevidencethatinterestinganomalousdy-namicalbehavioroccursconcurrently:theexperimentallyobservedphononpeaksbecomeverybroadwithenhancedscatteringoccurringatlowfrequencies.4–Morepuzzling,thein-tensitiesandshapesofthesepeaksexhibitunexpectedvariationsbetweendi erentBrillouinzones.Whilemostoftheexperimentaldatawereobtainedfromalloysystemswherethee ectsofstoichiometryvariationsmaybeofimportance,similarbehaviorhavealsobeenobservedinpuremetals.812Inthispaper,weexploretherelationshipbetweenanomalousphononbehaviorandthe

phasetransformationprocessthroughmoleculardynamicssimulationsofZrasaprototypicalsystem,exhibitingabcctohcptransformation.Bymonitoringthebehaviorofthedynamicstructurefactorofthesystem,weexaminethemicroscopicoriginoftheanomalousphononbehaviorinthesesystems.Wealsostudythedynamicsofmicrostructureformationduringthetransformation.Toclarifytheproblem,wewillconcentrateonhomogeneoussystemswithoutdefects.Thee ectsofinhomogeneityonthedynamicalbehaviorofthetransitionwillbelefttoalaterstudy.

We have performed molecular dynamic simulations of a Martensitic bcc->hcp transformation in a homogeneous system. The system evolves into three Martensitic variants, sharing a common nearest neighbor vector along a bcc <111> direction, plus an fcc region.

Scatteringlineshapesin rst-orderstructuralphasetransformationshavebeenpreviouslystudiedusingvariousanalytictreatments13,14andsimulations15–17.Suchstudies,forboth rst-orderandsecond-ordertransformations,havefocusedontheone-phononcontributiontothescattering,whichdoesnotexhibitaBrillouinzonedependence,eveninafullanharmonictreatment.Furthermore,mostofthesestudies15–17havefocussedonmodelsthatdonotexhibitatrueelastictransformation:inthehightemperaturephase,thelinearizedphonon

2frequenciesbehaveasω2→ω0+c2k2ask→0,ratherthanω→ck.Suchmodelsaremore

appropriatefortransformationssuchasbcc→ω,characterizedbya“freezingin”ofaphononmodewitha nitefrequency(andwavevector),ratherthanthedevelopmentofastaticamplitudeofanelasticdegreeoffreedomthatoccursinmanyMartensitictransformations(includingthebcc→hcptransformation).

Anotherissuewithpreviousworkexaminingthedynamicresponseofthesesystemsisthatmostworkexaminesregionsoftheproduct(lowtemperature)phaseembeddedinthehightemperaturematrix13,18,19.Thisproductphaseishypothesizedtobeduetoeitherdefects18,19,orduetolong-lived“heterophase” uctuationsfromtheparentphase.Suchstudiesarenotsurprising,aslong-livedexcitationsarenecessarytoproduce“centralpeaks”inthescattering18.However,in rst-ordertransformations,theevidenceappearstoindicatethatthereisnoclearcentralpeakseparatefromthephononpeaks(andnolong-lived uctuationsintotheproductphase),especiallyinsystemswithlittledisorder.8–12,17

Inapreviouspaper,20whichweshallrefertoaspaperI,wedemonstratedthatinahomo-geneoussystem, uctuationsinthehigh-temperaturebccphasecanproduce“anomalous”scattering,withsigni cantlydi erentscatteringinequivalentBrillouinzones.Neutronscatteringrevealsdi erentlineshapesbetweendi erentBrillouinzones.5,7,8Thermaldif-fusescattering(energyintegratedscattering),observedinbothX-raystudies3andneutrondi ractionexperiments4–6,isnotfeatureless,asmightbeexpectedfromusualargumentsconcerningmultiplephononscattering,21butinsteadshowscharacteristicsthatimplyacon-nectionwiththeincipientMartensitictransition.Thatsuchcharacteristicscatteringcanoccurintheabsenceofstaticorlong-lived uctuationsintotheproductphaseissomewhatsurprising,yetisborneoutbyexperimentalwork.8–12InpaperI,wearguedthatthesearedueto uctuationstoward,butnotinto,thelowtemperaturephase.

Morerecentmoleculardynamicssimulations22–24haveexaminedtheformationofmi-crostructureduringahomogeneousbcc→hcptransformation,utilizingasimpleEAMmodelforzirconium,aswellasthee ectofstressonthemicrostructure.Thesesimulationsdemon-strateanumberofkeypointsconcerningtheformationofmicrostructure.Ofparticularimportancerelevanttotheworkpresentedhere,theyhavedemonstratedthatfccregionsformatthejunctionofthreehcpvariantssharingacommon 11¯20 direction,ratherthanformingatriplepointbetweentwinboundaries,andthatthetwinregionscontainbasalplanestackingfaultsthatmaintainthe60 orientationbetweenhcpvariants.Thetransfor-mationisinterpretedtooccurviatheNishiyama-Wassermannmechanism25(describedinSectionIIIbelow),ratherthantheBurgersmechanism.26

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