towards a standardized setup for surface energy calculations 2017 jakub w. kaminski资料.pdf

该【towards a standardized setup for surface energy calculations 2017 jakub w. kaminski资料 】是由【小舍儿】上传分享，文档一共【11】页，该文档可以免费在线阅读，需要了解更多关于【towards a standardized setup for surface energy calculations 2017 jakub w. kaminski资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..PHYSICALREVIEWB95,085408(2017),1PeterKratzer,2andChristianRatsch31DepartmentofMathematics,UniversityofCalifornia,LosAngeles,LosAngeles,California90095,USA2FacultyofPhysics,UniversityofDuisburg-Essen,Lotharstrasse1,47057Duisburg,Germany3DepartmentofMathematicsandInstituteforPureandAppliedMathematics,UniversityofCalifornia,LosAngeles,LosAngeles,California90095,USA(Received25May2016;revisedmanuscriptreceived4October2016;published7February2017)High-throughputdesignofnewmaterialswithdesiredelectronicproperties,basedonscreeningoflargeanizedinthefromoflibrariesordatabasesrequirefast,widelyapplicable,-,,,%,andthatareaslowas2%:.,thematerialswherethetopandthebottomsurfacesareidenticalaredubbedsymmetric[(a)]-andEq.(1),materialsputerresourcesandestablishedmoderntechniquesfordatawithdifferenttopandthebottomsurfacesarelabeledasstorageanddataanalysis[1]enableshigh-throughputap-nonsymmetric[(b)].Wenotethatintheliteratureproacheswherelargelibrariesofchemicalstructuresaresymmetricandnonsymmetricaresometimesreferredtoasbined,roupsnonpolarandpolarsystems,respectively,butwebelievethatpoundswithspeci?,[2],ForsuchcasesEq.(1),γcanells,orthediscoveryofnewbeformallycalculatedfromthefollowingequation:batterychemistries[3].Irrespectiveoftheapplication,high-putationalmethodsNspecandalgorithmsthatarefastand“black-box”approaches(.,γ=E?Niμi?γe,(2)donotrequirehumaninput)-,,howcanwecalculatethissurfaceenergyγef?ciently?eputationalmaterialsscience,surfaceenergycal--dimensional(2D)thewedgemethod,aspecialatomicstructurewithatriangularperiodicity[(a),forexample]thesurfaceenergyγcrosssectionisusedthatisin?,??thesurfaceenergyofthethird,unknownsurfacecanbeNspec1??paredtotheslabmethod,theadvantageliesγ=E?Niμi,(1),.,foraverylargenumberofatoms[4,5].(～2%)2isterminatedbytwoidenticalsurfacesonthetopandthe[5],(whichallrequiredifferent2469-9950/2017/95(8)/085408(11)085408-1?2017AmericanPhysicalSociety:..,PETERKRATZER,ANDCHRISTIANRATSCHPHYSICALREVIEWB95,085408(2017)(a)sym-(a)showsa(111)surfacewithonedanglingbondstructureand(b)(b),anddiscusshowthispyramidconstructions),-throughputscreeningstudies,,,[6,7],butthistheapproachinthefastandunsupervisedhigh-throughputapproachisnontrivialandnotwellsuitedforhigh-.[10],?,,%(orbetter)andthatcanbeApplicationofEq.(2)tocalculatethesurfaceenergyγappliedtoanymaterialandanysurfacemorphology,putationsto?ndthepreparation,premodeling,,=γandEq.(2)isequivalenttoEq.(1).proposeaprocedureforthecalculationofsurfaceenergiesFornonsymmetricmaterialswheretheexactvalueofγeisessible,,asdemonstratedbySakongetal.[8].ASakongetal.[8],wedirectlyapproximatetheenergyofthefundamentalassumptionisthatallslabatomsuptothelastunknownsurfaceγeinEq.(2)(a),wherethetopsurfaceofSi(111),andwherewewanttouseEq.(2)[9,10].,(includingtheinternalenergyofthecappingWeshowthathydrogen,monlyusedatomsthemselves)canthenbeapproximatedwiththehelpofputationalmaterialsscience,isnotalwaysanauxiliarymoleculeSiH4[(b)]?μSaεSa?Ca=,(3)universallyapplicableforallthematerialsandleadstoa4plexityofthewhereSadenotesasurfaceatom,Caisthecappingatom,,weprovidesimpleguidelinesforisthechemicalpotentialofthesurfaceatomsasobtainedfromputations,andESaCa4isthetotal085408-2:..TOWARDSASTANDARDIZEDSETUPFORSURFACE...PHYSICALREVIEWB95,085408(2017),thissigni?cantlyfacilitatestheconstructionoftheauxiliarymoleculesusedtocalculatethebondenergiesεSa?(upiedwithasingleelectron),thematchingatomforsiliconwithN=,forsiliconwithN=1bonds,,whichdoesnotrequireanyadditionalcalculations,,.,instructurewiththe(100),[10].factthattheSiatomcreatesfourbonds,buttheenergyofonlyThenewcappingschemeisalsore?(111).,themolecule()Ca=SiandSa=,Eq.(2)canbestructuresofthesemoleculescorrespondtothestructuresofrewrittenintermsofεSa?CaasthecappingatomonthesurfaceandenableeasyextractionNspecofthebondenergiesusedinEq.(4).Notethattheauxiliarymoleculesinourapproachare?ctitiousobjectsandneednotγ=E?Niμi?NbεSa?Ca,(4)?[Nb=(a)].ForSi(111)%.[8]itwasshown,however,thatthismethodwouldForsurfacesterminatedwithonedanglingbond,.[8],(100),(b),?ectedinre?(b).isputinthecrystallatticepositions,thesamebondlengthsThereforeitwillnotbeincludedinthebondenergyεSi?,ifthatisobtainedfromEq.(3).Thisinturnwillleadtoapoorthepositionofthecappingatomisoptimized,thenthenewestimationofthesurfaceenergyγinEq.(4).(optimized).(3)and(4).:(i)choosinganappropriatecappingmoredanglingbondsatom,and(ii)=,wereplacethemutuallyinteractingcappingatoms(asthatcase,itismostintuitivetousegroup-)wi