Structural, elastic and electronic properties of F

-1-Structural,elasticandelectronicpropertiesofFe3Cfromfirst-principlesC.Jiang1,*,S.G.Srinivasan1,A.Caro2,andS.A.Maloy11MaterialsScience&TechnologyDivision,LosAlamosNationalLaboratory,LosAlamos,NM875452MaterialsScience&TechnologyDivision,LawrenceLivermoreNationalLaboratory,Livermore,CA94550Usingfirst-principlescalculationswithinthegeneralizedgradientapproximation,wepredictedthelatticeparameters,elasticconstants,vibrationalproperties,andelectronicstructureofcementite(Fe3C).Itsninesingle-crystalelasticconstantswereobtainedbycomputingtotalenergiesorstressesasafunctionofappliedstrain.Furthermore,sixofthemweredeterminedfromtheinitialslopesofthecalculatedlongitudinalandtransverseacousticphononbranchesalongthe[100],[010]and[001]directions.Thethreemethodsagreewellwitheachother,thecalculatedpolycrystallineelasticmoduliarealsoingoodoverallagreementwithexperiments.OurcalculationsindicatethatFe3Cismechanicallystable.TheexperimentallyobservedhighelasticanisotropyofFe3Cisalsoconfirmedbyourstudy.Basedonelectronicdensityofstatesandchargedensitydistribution,thechemicalbondinginFe3Cwasanalyzedandwasfoundtoexhibitacomplexmixtureofmetallic,covalent,andioniccharacters.*Correspondingauthor:[e-mail]scontinuetobethemostimportantstructuralmaterialseveralmillenniaaftertheirdiscovery.Precipitationofexcesscarbonascementite(Fe3C)insteadofgraphiteintheformofpearlite,uponslowcoolingtobelow1000K,isubiquitousinsteelswithcarboncontentgreaterthan0.02%.Cementiteisimportantbecauseitsmorphologydirectlycontrolsthemechanicalpropertiesofsteels.Contrastingtoitstechnologicalsignificance,knowledgeoftheelasticpropertiesofcementite,criticaltounderstandingthemechanicalpropertiesofsteels,isquitelimited.Untilrecently,polycrystallinebulkcementitewassuccessfullysynthesizedthroughacombinationofmechanicalalloyingandsparkplasmasintering.1,2Todate,directexperimentalmeasurementsofthesingle-crystalelasticconstantsofcementitearestillnotfeasibleduetodifficultiesingrowinglargeenoughsingle-crystalsamples.Fromthetheoreticalpointofview,theelectronicstructureofcementitehasbeencalculatedbyvariousauthors.3-5ItsbulkmodulushasalsobeenrecentlycalculatedbyFaraounetal.,5Vocadloetal.,6andHuangetal.7Inthiswork,wepresentfirst-principlescalculatedresultsforvariousphysicalpropertiesofcementite,includingitslatticeparameters,thecompletesetofsingle-crystalelasticconstants,equationofstate,andphonondispersionrelations.Itisalsoourpurposetoprovidesomeinsightintothenatureofbondingincementitebyinvestigatingitselectronicstructure.Asidefromthepracticalimportanceofourresults,theycanbeusedbycoarserscaleapproaches8todevelopapredictivecomputationalmodelforsteels.-3-II.COMPUTATIONALDETAILSFirst-principlescalculationswereperformedusingprojectoraugmentedwave(PAW)9pseudopotentialsandaplane-wavebasisset,asimplementedinViennaabinitiosimulationpackage(VASP).10Theexchange-correlationfunctionalwasdescribedwithinthegeneralizedgradientapproximation(GGA)asparameterizedbyPerdew,Burke,andErnzerhof(PBE).11ItisworthnotingthatGGAcorrectlypredictstheferromagneticbccstructureofFeasitsgroundstate,whilethelocaldensityapproximationincorrectlypredictsitsgroundstatetobeanonmagneticclose-packedstructure.12,13Spin-polarizedcalculationswereperformedtomodeltheferromagneticallyorderedcementite.Thek-pointmeshesforBrillouinzonesamplingwereconstructedusingtheMonkhorst–Packscheme.14Aftercarefulconvergencetests,aplanewavecutoffenergyof500eVandan11×9×13k-pointmeshforthe16-atomunitcellofcementitewerefoundtobesufficienttoconvergetheelasticconstantsto~1GPaandthetotalenergytobetterthan1meV/atom.III.RESULTSANDDISCUSSIONA.StructuralpropertiesCementitehasacomplexorthorhombiccrystalstructure(spacegroupPnma,No.62)with12Featomsand4Catomsperunitcell.15,16The12Featomsaredistributedbetweentwodistinctlatticesites:thespecialFeIsites(Wyckoffposition4c)andthegeneralFeIIsites(Wyckoffposition8d).AsshowninFig.1,thefundamentalbuildingblockofcementiteis-4-thetrigonalprismformedbyaCatomanditssixnearest-neighborFeatoms(2FeI+4FeII).Thetrigonalprismsareinterconnectedthroughedge-andcorner-sharingtoformalayer.Astackingofthoselayersalongthebaxisthusformsthecementitestructure.Bycomputingthequantummechanicalforcesandstresstensor,wefullyrelaxedtheunitcellvolumeandshapeaswellasallinternalatomiccoordinatesofcementiteusingaconjugate-gradientscheme,andourresultsaresummarizedinTableI.ThelatticeconstantscalculatedwithintheGGAagreewiththeexperimentaldatafromWoodetal.16towithin1%.Thecomputedcell-internalparametersarealsoinexcellentagreementwithexperiments.Theseresultsgiveusconfidenceintheaccuraciesoffirst-principlescalculationsinpredictingthepropertiesofcementite.B.Single-crystalelasticconstantsAnorthorhombiccrystalhasnineindependentsingle-crystalelasticconstants.Theycanbedeterminedbyapplyingasmallstraintotheequilibriumlatticeandcomputingtheresultantchangeinitstotalenergy.17,18Thedistortedlatticevectorscanbeobtainedviaamatrixmultiplication′R=RD,where′RandRarethe3×3matricescontainingthecomponentsofthedistortedandundistortedlatticevectors,