Crystallography and surface structure: an introduction for surface scientists and nanoscientists

447 Pages·2017·169.473 MB·English

by  Hermann, Klaus

KlausHermann
CrystallographyandSurfaceStructure

KlausHermann
Crystallography and Surface Structure
AnIntroductionforSurfaceScientistsandNanoscientists
Second,RevisedandExpandedEdition
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V
Contents
PrefacetotheSecondEdition IX
PrefacetotheFirstEdition XI
1 Introduction 1
2 BulkCrystals:Three-DimensionalLattices 7
2.1 BasicDefinition 7
2.2 RepresentationofBulkCrystals 11
2.2.1 AlternativeDescriptionsConservingtheLatticeRepresentation 12
2.2.2 AlternativeDescriptionsAffectingtheLatticeRepresentation 14
2.2.2.1 Cubic,Hexagonal,andTrigonalLattices 16
2.2.2.2 SuperlatticesandRepeatedSlabs 25
2.2.2.3 LinearTransformationsofLatticeVectors 29
2.2.3 CenteredLattices 31
2.3 PeriodicityCellsofLattices 35
2.4 LatticeSymmetry 38
2.5 ReciprocalLattice 49
2.6 NeighborShells 52
2.7 NanoparticlesandCrystallites 63
2.8 IncommensurateCrystalsandQuasicrystals 71
2.8.1 ModulatedStructures 71
2.8.2 IncommensurateCompositeCrystals 73
2.8.3 Quasicrystals 76
2.9 Exercises 82
3 CrystalLayers:Two-DimensionalLattices 91
3.1 BasicDefinition,MillerIndices 91
3.2 Netplane-AdaptedLatticeVectors 96
3.3 SymmetricallyAppropriateLatticeVectors:Minkowski
Reduction 98
3.4 MillerIndicesforCubicandTrigonalLattices 100
3.5 AlternativeDefinitionofMillerIndicesandMiller–Bravais
Indices 106
VI Contents
3.6 SymmetryPropertiesofNetplanes 109
3.6.1 CenteredNetplanes 110
3.6.2 Inversion 111
3.6.3 Rotation 114
3.6.4 MirrorOperation 119
3.6.5 GlideReflection 131
3.6.6 SymmetryGroups 139
3.7 CrystalSystemsandBravaisLatticesin
TwoDimensions 144
3.8 CrystallographicClassificationofNetplanes
andMonolayers 149
3.8.1 ObliqueNetplanes 151
3.8.2 PrimitiveRectangularNetplanes 151
3.8.3 CenteredRectangularNetplanes 155
3.8.4 SquareNetplanes 157
3.8.5 HexagonalNetplanes 158
3.8.6 ClassificationOverview 163
3.9 Exercises 164
4 IdealSingleCrystalSurfaces 169
4.1 BasicDefinition,Termination 169
4.2 MorphologyofSurfaces,SteppedandKinkedSurfaces 175
4.3 MillerIndexDecomposition 178
4.4 ChiralandAchiralSurfaces 192
4.5 Exercises 204
5 RealCrystalSurfaces 209
5.1 SurfaceRelaxation 209
5.2 SurfaceReconstruction 210
5.3 GrowthProcesses 222
5.4 Faceting 226
5.5 Exercises 231
6 AdsorbateLayers 235
6.1 DefinitionandClassification 235
6.2 AdsorbateSites 241
6.3 WoodNotationofSurfaceStructure 251
6.4 High-OrderCommensurate(HOC)Overlayers 258
6.5 InterferenceLattices 263
6.5.1 BasicFormalism 264
6.5.2 InterferenceandWoodNotation 272
6.5.3 AnisotropicScaling,Stretching,andShifting 279
Contents VII
6.6 SymmetryandDomainFormation 283
6.7 AdsorptionatSurfacesandChirality 293
6.8 Exercises 299
7 ExperimentalAnalysisofRealCrystalSurfaces 305
7.1 ExperimentalMethods 305
7.2 SurfaceStructureCompilations 306
7.3 DatabaseFormatsforSurfaceandNanostructures 311
7.4 Exercises 313
8 Nanotubes 315
8.1 BasicDefinition 315
8.2 NanotubesandSymmetry 319
8.3 ComplexNanotubes 323
8.4 Exercises 326
AppendixA:SketchesofHigh-SymmetryAdsorbateSites 329
A.1 Face-CenteredCubic(fcc)SurfaceSites 330
A.2 Body-CenteredCubic(bcc)SurfaceSites 338
A.3 HexagonalClose-Packed(hcp)SurfaceSites 342
A.4 DiamondSurfaceSites 346
A.5 ZincblendeSurfaceSites 349
AppendixB:ParameterTablesofCrystals 351
AppendixC:MathematicsoftheWoodNotation 355
C.1 BasicFormalismandExamples 355
C.2 Wood-Representability 361
AppendixD:MathematicsoftheMinkowskiReduction 367
AppendixE:DetailsofNumberTheory 371
E.1 BasicDefinitionsandFunctions 371
E.2 Euclid’sAlgorithm 376
E.3 LinearDiophantineEquations 377
E.4 QuadraticDiophantineEquations 380
E.5 NumberTheoryand2×2Matrices 386
AppendixF:DetailsofVectorCalculusandLinearAlgebra 391
AppendixG:DetailsofFourierTheory 395
AppendixH:ListofSurfaceWebSites 399
VIII Contents
AppendixI:ListofSurfaceStructures 401
GlossaryandAbbreviations 403
References 417
Index 425