Atomic Structure Prediction of Nanostructures, Clusters and Surfaces PDF
Preview Atomic Structure Prediction of Nanostructures, Clusters and Surfaces
CristianV.Ciobanu, Cai-ZhuangWang, andKai-MingHo AtomicStructurePrediction ofNanostructures,Clusters andSurfaces RelatedTitles Werner,W.S.M.(ed.) CharacterizationofSurfaces andNanostructures AcademicandIndustrialApplications 2008 ISBN:978-3-527-31760-8 Eftekhari,A.(ed.) Nanostructured Materialsin Electrochemistry 2008 ISBN:978-3-527-31876-6 Vedmedenko,E. CompetingInteractionsand PatternsinNanoworld 2007 ISBN:978-3-527-40484-1 Wilkening,G.,Koenders,L. NanoscaleCalibration StandardsandMethods DimensionalandRelatedMeasurements intheMicro-andNanometerRange 2005 ISBN:978-3-527-40502-2 Reich,S.,Thomsen,C.,Maultzsch,J. CarbonNanotubes BasicConceptsandPhysicalProperties 2004 ISBN:978-3-527-40386-8 Cristian V. Ciobanu, Cai-Zhuang Wang, and Kai-Ming Ho Atomic Structure Prediction of Nanostructures, Clusters and Surfaces TheAuthors AllbookspublishedbyWiley-VCHarecarefully produced.Nevertheless,authors,editors,and publisherdonotwarranttheinformationcontained Dr.CristianV.Ciobanu inthesebooks,includingthisbook,tobefreeof ColoradoSchoolofMines errors.Readersareadvisedtokeepinmindthat DivisionofEngineering statements,data,illustrations,proceduraldetailsor 1610IllinoisStreet otheritemsmayinadvertentlybeinaccurate. GoldenColorado80401 LibraryofCongressCardNo.:appliedfor USA BritishLibraryCataloguing-in-PublicationData Dr.Cai-ZhuangWang Acataloguerecordforthisbookisavailablefromthe IowaStateUniversity BritishLibrary. AmesLab/DeptofPhysics BibliographicinformationpublishedbytheDeutsche 12PhysicsHall Nationalbibliothek Ames,Iowa50011 TheDeutscheNationalbibliothekliststhis USA publicationintheDeutscheNationalbibliografie; detailedbibliographicdataareavailableonthe Dr.Kai-MingHo Internet at < http:// dnb.d-nb.d e> . IowaStateUniversity AmesLab/DeptofPhysics #2013Wiley-VCHVerlagGmbH&Co.KGaA, 12PhysicsHall Boschstr.12,69469Weinheim,Germany Ames,Iowa50011 Allrightsreserved(includingthoseoftranslationinto USA otherlanguages).Nopartofthisbookmaybe reproducedinanyform–byphotoprinting, microfilm,oranyothermeans–nortransmittedor translatedintoamachinelanguagewithoutwritten permissionfromthepublishers.Registerednames, trademarks,etc.usedinthisbook,evenwhennot specificallymarkedassuch,arenottobeconsidered unprotectedbylaw. PrintISBN: 978-3-527-40902-0 ePDFISBN: 978-3-527-65505-2 ePubISBN: 978-3-527-65504-5 mobiISBN: 978-3-527-65503-8 oBookISBN: 978-3-527-65502-1 CoverDesign Adam-Design,Weinheim Typesetting ThomsonDigital,Noida,India PrintingandBinding MarkonoPrintMediaPteLtd, Singapore PrintedinSingapore Printedonacid-freepaper j V Contents Preface IX 1 TheChallengeofPredictingAtomicStructure 1 1.1 Evolution:RealityandAlgorithms 2 1.2 BriefHistoricalPerspective 4 1.3 ScopeandOrganizationofThisBook 6 References 7 2 TheGeneticAlgorithminReal-SpaceRepresentation 11 2.1 StructureDeterminationProblems 12 2.1.1 ClusterStructure 12 2.1.2 CrystalStructurePrediction 16 2.1.3 SurfaceReconstructions 19 2.1.4 RangeofApplications 21 2.2 GeneralProcedure 23 2.3 SelectionofParentStructures 24 2.4 CrossoverOperations 26 2.4.1 Cut-and-SpliceCrossoverinRealSpace 27 2.4.2 CrossoversandPeriodicBoundaryConditions 28 2.5 Mutations 30 2.5.1 Zero-PenaltyMutations 31 2.5.2 RegularMutations 31 2.6 UpdatingtheGeneticPool:SurvivaloftheFittest 33 2.7 StoppingCriteriaandSubsequentAnalysis 34 References 35 3 CrystalStructurePrediction 37 3.1 ComplexityoftheEnergyLandscape 38 3.2 ImprovingtheEfficiencyofGA 40 3.3 InteractionModels 41 3.3.1 ClassicalPotentials 41 3.3.2 AbInitioMethods 42 3.3.3 AdaptiveClassicalPotentials 42 j VI Contents 3.4 CreatingtheGeneration-ZeroStructures 44 3.5 AssessingStructuralDiversityofthePool 45 3.5.1 FingerprintFunctions 45 3.5.2 GeneralFeaturesofthePES 47 3.6 VariableComposition 48 3.7 Examples 51 3.7.1 IdentificationofPost-PyritePhaseTransitions 51 3.7.1.1 ComputationalDetails 52 3.7.1.2 ResultsandDiscussion 52 3.7.2 Ultrahigh-PressurePhasesofIce 57 3.7.2.1 ComputationalDetails 58 3.7.2.2 ResultsandDiscussion 59 3.7.3 StructureandMagneticPropertiesofFe–CoAlloys 63 3.7.3.1 ComputationalDetails 63 3.7.3.2 ResultsandDiscussion 64 References 67 4 OptimizationofAtomicClusters 71 4.1 Alloys,Oxides,andOtherClusterMaterials 71 4.2 OptimizationofSubstrate-SupportedClustersviaGA 73 4.3 GASolutiontotheThomsonProblem 81 References 85 5 AtomicStructureofSurfaces,Interfaces,andNanowires 87 5.1 ReconstructionofSemiconductorSurfacesasaProblemofGlobal Optimization 88 5.1.1 TheGeneticAlgorithmforSurfaceReconstructions:theCaseof Si(105) 89 5.1.1.1 ComputationalDetailsforSi(105) 89 5.1.1.2 ResultsforSi(105) 91 5.1.2 NewReconstructionsforaRelatedSurface,Si(103) 95 5.1.3 ModelReconstructionsforSi(337),anUnstableSurface:GAFollowed byDFTRelaxations 99 5.1.3.1 ResultsforSi(337)Models 101 5.1.3.2 Discussion 106 5.1.4 AtomicStructureofStepsonHigh-IndexSurfaces 107 5.1.4.1 SupercellGeometryandAlgorithmDetails 107 5.1.4.2 ResultsforStepStructuresonSi(114) 110 5.2 GeneticAlgorithmforInterfaceStructures 114 5.2.1 GAforGrainBoundaryStructureOptimization 115 5.2.2 StructuresGeneratedbyGA 116 5.2.3 GrainBoundaryEnergyCalculations 121 5.3 NanowireandNanotubeStructuresviaGAOptimization 123 5.3.1 PassivatedSiliconNanowires 123 5.3.2 One-DimensionalNanostructuresunderRadialConfinement 130 j Contents VII 5.3.2.1 Introduction 131 5.3.2.2 DescriptionoftheAlgorithm 132 5.3.2.3 ResultsforPrototypeNanotubes 135 5.3.2.4 Discussion 139 5.3.2.5 ConcludingRemarks 144 References 144 6 OtherMethodologiesforInvestigatingAtomicStructure 149 6.1 ParallelTemperingMonteCarloAnnealing 151 6.1.1 GeneralConsiderations 151 6.1.2 AdvantagesoftheParallelTemperingAlgorithmasaGlobal Optimizer 153 6.1.3 DescriptionoftheAlgorithm 154 6.2 BasinHoppingMonteCarlo 158 6.3 OptimizationviaMinimaHopping 160 6.4 TheMetadynamicsApproach 163 6.5 ComparativeStudiesbetweenGAandOtherStructuralOptimization Techniques 165 6.5.1 ReconstructionsofSi(114):ComparisonbetweenGAandPTMC 165 6.5.1.1 PTMCResults 166 6.5.1.2 GAResults 167 6.5.1.3 DFTCalculations 167 6.5.1.4 StructuralModelsforSi(114) 169 6.5.1.5 Discussion 174 6.5.1.6 ConcludingRemarks 175 6.5.2 CrystalStructurePrediction:ComparisonbetweenGAandMH 175 6.5.2.1 GAAppliedtoAlxSc1(cid:2)xAlloys 176 6.5.2.2 Boron 180 6.5.2.3 MinimaHopping 182 References 185 7 PerspectivesandOutlook 187 7.1 ExpansionthroughtheCommunity 187 7.2 FutureAlgorithmDevelopments 187 7.3 ProblemstoTackle–DiscoveryversusDesign 188 Index 191 j IX Preface Knowledgeoftheatomicstructureofamaterialssystemisthekeytounderstanding most of its properties, as well as the physical phenomena that can occur in that system.Evenwhenthebulkcrystalstructureofamaterialisknownorunderstood, thatknowledgedoesnotreadilyimplythatweknowthestructureofatomicclusters ornanowiresmadeofthatparticularmaterial.Wemightventureagoodguessfor clusters with verylarge numbers of atoms, orin thecase of verythick nanowires (whiskers),butmostofthenewandinterestingphenomenawillnothappeninthe regimes of large dimensions but at the nanoscale. At the nanoscale, often the structureandpropertiesofmaterialshavelittletodowiththestructureofthebulk crystallinematerial!Thisrealizationhasprovidedstrongmotivationforthedevel- opment of methodologies aimed at finding the atomic configuration of nano- structures. If we analyze deeper the field of atomic structure determination, we wouldrecognize,forexample,thatouroldcollegetextbooksprovidedonlylimited understandingofthecorrelationbetweenthecompositionofanalloyorcompound and itsequilibrium structure:this situation was described afewdecadesagoasa “continuingscandalinphysicalsciences”(JohnMaddox,1988).Thischallengealso sparkedsignificantandlong-standingeffortstopredictthecrystalstructurefromits composition.Thetwomainimpedimentstocrystalstructurepredictionandtothe determinationoftheatomicconfigurationofnanostructureshavebeenforalong timethelackofrealisticmodelsofatomicinteractionsandthelackofanefficient optimizationscheme.Bothoftheseimpedimentshavebynowbeenremediedfora respectable number of materials systems, and the time seems ripe to describe atomicstructurepredictioninabook.Wearedoingthathere,focusingmainlyon onemethod,thegeneticalgorithm.Geneticalgorithms“mimic”theprocessesofthe naturalevolutiontocreateprogressivelybetter-fitatomicstructures,andeventually find or predict their equilibrium configurations. While one may argue that the naturalevolutionisoverlysimplifiedinthiscase,practicehasshownthatitisthe simplification of dealing with real-space configuration (as opposed to their repre- sentation as genotype, akin to actual genes) that is responsible for obtaining solutions within a reasonable time and computational resources. The main purpose of this book is to offer a beginning practitioner (often a graduatestudent)adetailedbackgroundinthewaygeneticalgorithmsforatomic structure prediction work. As noted in the book, we use the terms “genetic” and j X Preface “evolutionary”interchangeably,althoughafewworkersinthefieldtendtoreserve the term “genetic” to describe the algorithm in the binary representation of the coordinatespace.Confusionsareunlikely,sincenowadaysthebinaryrepresentation is hardly used anymore. When this book was commissioned by Wiley-VCH, the focus was only on nanostructures, clusters, and surfaces, hence the cover title. However,whilethisprojectprogressed,sodidthestateofthefield–culminating withthegeneticalgorithmsolutionofoneofthemostimportantproblemsinsolid- statephysics,thatis,thepredictionofcrystalstructuresolelyfromtheknowledgeof itscomposition.Wehaveincludedthisimportantdevelopmentinthebook,sothe reader obtains a timely and up-to-date view of the field. Whileouraimistoprovideaclearunderstandingofhowthegeneticalgorithm worksandofitsstrengthsandsuccesses,thisbookisbynomeansareviewofall geneticalgorithmworkspublishedsofar.Giventherapiddevelopmentsinthefield, suchareviewwouldbebothtoolongandincomplete.Wehavestructuredthisbook asaprimerthatintertwinesbasicgeneraldescriptionsofthealgorithms(e.g.,the operations, the fitness functions, boundary conditions, where and how the algo- rithmcanbeapplied,etc.)withfull-detailapplicationstospecificsystemsincluding crystals(3D),surfaces(2D),nanowiresandnanotubes(1D),andcertainlyclusters (0D).Webelievethatthereaderwouldbenefitfromthisapproach,aswellasfrom thefactthatalltheexamplesorcasestudieshavebeenscrutinizedinthepeer-review process(astechnicaljournalpublications)andcontainvirtuallyallworkingdetailsof theapproachandoftheanalysis.Assuch,wehopethatthebookprovidessignificant understandingofthemethodsothatanyreaderinterestedinapplyingthealgorithm tohisorherproblemcandosowithrelativeeaseandconfidence–whetherornot his/her problem has already been covered in the book. Throughouttheyears,wehavebeenfortunatetoworkwithanumberoffaculty colleagues, postdoctoral associates, and graduate students from Ames Laboratory, IowaStateUniversity,andColoradoSchoolofMines,aswellasfrommanyother institutions. The work that is described in most detail (i.e., the full-detail applica- tions) in this book has been performed alongside with them, and we gratefully recognize them here: R.M. Briggs, T.-L. Chan, F.-C. Chuang, T. Davies, D.M. Deaven, G.H. Gilmer, B. Harmon, M. Ji, B. Liu, N. Lu, D.E. Lytle, D.P. Mehta, J.R. Morris, M.C. Nguyen, C. Predescu, J.-L. Rodriguez-Lopez, V.B. Shenoy, K. Umemoto, R.M. Wentzcovitch, S. Wu, J. Zhang, and X. Zhao. Wethankthemfortheirworkandinsights,andwelookforwardtoourcontinued collaborations.Lastbutnotleast,wethankverymuchtheeditorofPhysicalSciences BooksatWiley-VCH,NinaStadthaus,whohasguidedthisprojectwithunmatched professionalism, patience, and dedication. Golden, CO Cristian V. Ciobanu Ames, IA Cai-Zhuang Wang Ames, IA Kai-Ming Ho September 2012 j 1 1 TheChallengeofPredictingAtomicStructure Theatomicstructureisthemostimportantpieceofinformationthatisnecessary whenstudyingthepropertiesofcrystals,surfaces,interfaces,ornanostructures.If the bulk crystal structure of a material or compound is known, this may, under certain conditions, help in determining the structures of surfaces, clusters, or nanowires; however, such knowledge does not at all imply that we automatically knowthestructureofasurfaceorofananoparticlemadeoutofthatmaterial.Often the surfaces and nanostructures adopt very intriguing atomic configurations, especially when their size is small (e.g., small number of atoms for clusters, thindiameterfornanowires,etc.).Bynow,thestructureofmanycrystalsisalready known and usually taken for granted, sometimes to the point of considering a surface or a nanostructure as a simple truncation of the bulk material. As we seeinotherchapters,thisisrarelythecaseatthenanoscale:thestructureofatomic small clusters has little (usually nothing) to do with that of the bulk crystalline material! Comingbacktotheissueofbulkcrystalstructure,onfundamentalgrounds,we have to recognize that retrieving the crystal structure from a given material or compoundsolelyfromknowingitscompositionisnotaneasyorastraightforward task: what determines, say, molybdenum to “choose” a body-centered cubic structure at normal conditions of temperature and pressure, when palladium hasaface-centeredcubic(fcc)structureandrutheniumadoptsahexagonalclose- packedone?WhydoesNaCl,thecommonsalt,adoptastructureinwhichboththe fcc sublattices of Na and those of Cl are displaced along the side of the conventional cube, but CsCl adopts a different structure even though Cs is in thesamegroupasNaintheperiodictable?Granted,onecaneasilygiveapartial answertothisquestionongroundsthattheCsatom,althoughofsamevalenceas Na, has a larger ionic radius and therefore would tend to have more Cl atoms around it than Na has. Still, what made NaCl adopt its specific structure (Figure1.1)inthefirstplace?WhyarethesodiumatomsinNaClcrystalarranged in an fcc structure, could they not have chosen a different arrangement? Some decades ago, John Maddox [1] phrased the problem of determining the crystal AtomicStructurePredictionofNanostructures,ClustersandSurfaces, FirstEdition.CristianV.Ciobanu,Cai-ZhuangWang,andKai-MingHo. #2013Wiley-VCHVerlagGmbH&Co.KGaA.Published2013byWiley-VCHVerlagGmbH&Co.KGaA.
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