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1、CombinedclusterandatomicdisplacementexpansionforsolidsolutionsandmagnetismKevinF.GarrityMaterialMeasurementLaboratory,NationalInstituteofStandardsandTechnology,GaithersburgMD,20899(Dated:August2,2018)Finitetemperaturedisorderedsolidsolutionsandmagneticmaterialsaredicultto
2、studydi-rectlyusingrstprinciplescalculations,duetothelargeunitcellsandmanyindependentsamplesthatarerequired.Inthiswork,wedevelopacombinedclusterexpansionandatomicdisplacementexpansion,whichwettorstprinciplesenergies,forces,andstresses.Wethenusetheexpansiontocalculatether
3、modynamicquantitiesatnearlyrstprincipleslevelsofaccuracy.Wedemonstratethatbytreatingalltherelevantdegreesoffreedomexplicitly,wecanachieveimprovedconvergencepropertiesascomparedtoasimpleclusterexpansion,andourmodelnaturallyincludesbothcon-gurationalandvibrationalentropy.In
4、addition,wecantreatcouplingbetweenstructuralandchemicalormagneticdegreesoffreedom.Asexamples,weuseourexpansiontocalculatepropertiesofSi1 xGex,magneticMnO,Alwithvacancies,andBaxSr1 xTiO3.I.INTRODUCTIONsimpleclusterexpansionscanonlycalculateaverylim-itednumberofproperties.Inp
5、articular,interactionsbe-tweenstructuralandchemicaldegreesoffreedomcannotSolidsolutions,whicharematerialsthathavewell-betreatedeasily,whichexcludestechnologicallyrelevantdenedcrystalstructuresbutdisorderedoccupancyofmaterialslikepiezoelectrics,ferroelectrics,ferroelastics,
6、atomicpositions,areimportantforavarietyoftech-magnetocalorics,etc.thatinvolvecoupleddegreesofnologicalapplicationsasbothstructuralandfunctionalfreedom.materials1.AbouthalfoftheInorganicCrystalStructureInthiswork,wecombinetheframeworkofaclusterDatabaseconsistsofcompoundswith
7、partialoccupancy2.expansionforchemicalorspindegreesoffreedomwithSimilarly,compoundswithspindegreesoffreedomareof-anatomicdisplacementexpansion,whichhaslongbeentendisorderedatexperimentallyrelevanttemperatures.usedtocalculatenitetemperaturepropertiesofcrys-Unfortunately,bot
8、hofthesetypesofmaterialsaredi-tallinematerials.Atomicdisplacementexpansionsuptocu