铝的晶格常数体弹模量及弹性常数分子模拟Word格式.docx
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铝的晶格常数体弹模量及弹性常数分子模拟Word格式.docx
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Aluminumisoneoftheworld'
smostusedmetals,thecalculatedaluminumlatticeconstantandbulkmoduluscanbeusedtoimprovetheperformanceofthealuminumconsequentlymakebetteruseofaluminum.Invirtueofmoleculardynamicssimulationsoftware,wecansolvethelatticeconstant.Bythederivativeofthelatticeconstant,thebulkmoduluscanbeobtained.Theelasticconstantsofamaterialdisplaytheelasticityandwecanusethesoftwarematerialstudiotosimulateandgetthem.Thesimulationresultsmatchtheexperimentalvalues.
Keywords:
Aluminum,latticeconstant,bulkmodulus,elasticconstant,simulation.
Introduction:
Inmaterialsscience,inordertofacilitateanalysisaboutthewayinwhichthecrystalparticlesarearranged,thebasicunitcanberemovedfromthecrystallatticeasarepresentative(usuallythesmallestparallelhexahedron)asacompositionunitofdotmatrix,calledacell(i.e.solidStatePhysics"
originalcell"
concept);
latticeconstant(orso-calledlatticeconstant)referstothesidelengthoftheunitcell,inotherwords,thesidelengthofeachparallelhexahedralcells.Latticeconstantisanimportantbasicparametersofcrystalstructure.FigureAisthebasicformofthelatticeconstant.
FigureA
Latticeconstantisabasicstructuralparameter,whichhasadirectrelationshipwiththebondingsbetweentheatoms,ofthecrystalsubstance.Itreflectsthechangesintheinternalcompositionofthecrystalofthelatticeconstant,forcestatechanges,etc.
Thebulkmodulus(KorB)ofasubstancemeasuresthesubstance'
sresistancetouniformcompression.Itisdefinedastheratiooftheinfinitesimalpressureincreasetotheresultingrelativedecreaseofthevolume.Itsbaseunitisthepascal.FigureBdescribestheeffectofbulkmodulus.
FigureB
Thebulkmoduluscanbeformallydefinedbytheequation:
whereispressure,isvolume,anddenotesthederivativeofpressurewithrespecttovolume.
Ourresearchobjectisaluminum,whoseatomicnumberis13andrelativemassis27.Thereservesofaluminumranksonlysecondtoferrumcomparedwithothermetallicelements.Aluminumandaluminumalloyareconsideredthemosteconomicandapplicableinmanyapplicationfieldsasaconsequenceoftheirexcellentproperties.What’smore,increasedusageofaluminumwillresultfromdesigners'
increasedfamiliaritywiththemetalandsolutiontomanufacturingproblemsthatlimitsomeapplications.
Thecrystalstructureofaluminumisface-centeredcubic.Theexperimentalvalueoflatticeconstantandbulkmodulusare0.0.40491nmand79.2Gpa.
Computingtheoryandmethods:
Oursimulationisonthebasisthataluminumisofface-centeredcubiccrystalstructure.Wecangettheexactvalueoflatticeconstantinvirtueofmoleculardynamicssimulationsoftware.ThenbythederivationoflatticeconstantforenergyE,weobtainbulkmodulus.
Tostartwith,compileascriptfortheuseofoperationandsimulationinlammps.Wesetperiodicboundaryconditionsinthescriptandcreateananalogbox,whosex,y,zcoordinatevaluesareallconfinedto[0,3].Runthescriptinlammps,calculatingthepotentialenergy,kineticenergyaswellasthenearestneighboratomsforeachatom.Finallyputoutthepotentialenergyfunctionofaluminum.
Extractthedatasunderthelinuxsystemproducedbylammpstocontinuethecomputationbymeansofmatlab,fromwhichwecangetthelatticeconstantthroughseveraltimesofmatching.
FigureC
FigureC——thecurveshowstherelationshipbetweencohesiveenergyandlatticeconstant,whichiswhatwegetintheprocessofcomputinginmatlab,pointsoutthelatticeconstantcorrespondingwiththeleastcohesiveenergy.Thehorizontalordinateoftherockbottomstandforthelatticeconstantofaluminumwhichcanbeclearlylocatedas0.40500nm.
Sincewehaveobtainedthelatticeconstant,wesimulatedthevisualizationofaluminu’scrystalstructure.FigureDiswhatwegetthroughthevisualization.
FigureD
Thebulkmodulusisdefinedas:
Asforcubiccell,theformulacanbetransformedintothe
followingpattern:
Thebulkmoduluscanbecalculatedwiththeformulaabovecombinedwiththelatticeconstant.Finally,thebulkmodulusis78.1Gpa.
Besides,toenrichourresearch,wehavecalculatedtheelasticconstantsofaluminum.Becauseofthesymmetryofface-centeredcubic,aluminumonlyhasthreeelasticconstants.Toreachthetarget,wehavetoestablishacellofaluminuminthesoftwarematerialstudiointhefirstplaceandthentransformitintoaprimitivecell.FigureEandfigureFarethecellandtheprimitivecellwehaveestablishedduringthesimulation.
FigureE
FigureF
ItcomestotheCASTEPstepafterthegeometryoptimization.WemanagedtomakeEcut=350eVand
Kpoints=16*1
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- 关 键 词:
- 晶格 常数 体弹模量 弹性 分子 模拟