Basic Concepts of X-Ray Diffraction

311 Pages·2014·9.591 MB·English

by  Emil Zolotoyabko

EmilZolotoyabko
BasicConceptsofX-RayDiffraction
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VII
Contents
Preface XI
Introduction 1
1 DiffractionPhenomenainOptics 5
2 WavePropagationinPeriodicMedia 11
3 DynamicalDiffractionofParticlesandFields:General
Considerations 21
3.1 TheTwo-BeamApproximation 23
3.2 DiffractionProfile:TheLaueScatteringGeometry 33
3.3 DiffractionProfile:TheBraggScatteringGeometry 38
4 DynamicalX-RayDiffraction:TheEwald–LaueApproach 45
4.1 DynamicalX-RayDiffraction:Two-BeamApproximation 49
4.1.1 TheRoleofX-RayPolarization 50
4.1.2 TheTwo-BranchIsoenergeticDispersionSurfaceforX-Rays 52
4.1.3 IsoenergeticDispersionSurfaceforAsymmetricReflection 56
5 DynamicalDiffraction:TheDarwinApproach 61
5.1 ScatteringbyaSingleElectron 61
5.2 AtomicScatteringFactor 64
5.3 StructureFactor 66
5.4 ScatteringAmplitudefromanIndividualAtomicPlane 68
5.5 DiffractionIntensityintheBraggScatteringGeometry 71
6 DynamicalDiffractioninNonhomogeneousMedia:TheTakagi–Taupin
Approach 77
6.1 TakagiEquations 77
6.2 TaupinEquation 84
6.2.1 TaupinEquation:TheSymmetricLaueCase 84
VIII Contents
6.2.2 TaupinEquation:TheSymmetricBraggCase 86
6.2.3 SolutionoftheTaupinEquationforMultilayeredStructures 88
7 X-RayAbsorption 91
8 DynamicalDiffractioninSingle-ScatteringApproximation:Simulationof
High-ResolutionX-RayDiffractioninHeterostructuresand
Multilayers 97
8.1 DirectWaveSummationMethod 103
9 ReciprocalSpaceMappingandStrainMeasurementsin
Heterostructures 121
10 X-RayDiffractioninKinematicApproximation 131
10.1 X-RayPolarizationFactor 133
10.2 Debye–WallerFactor 135
11 X-RayDiffractionfromPolycrystallineMaterials 139
11.1 IdealMosaicCrystal 139
11.2 PowderDiffraction 141
12 ApplicationstoMaterialsScience:StructureAnalysis 145
13 ApplicationstoMaterialsScience:PhaseAnalysis 155
13.1 InternalStandardMethod 158
13.2 RietveldRefinement 159
14 ApplicationstoMaterialsScience:PreferredOrientation(Texture)
Analysis 161
14.1 TheMarch–DollaseApproach 165
15 ApplicationstoMaterialsScience:LineBroadeningAnalysis 171
15.1 LineBroadeningduetoFiniteCrystalliteSize 174
15.1.1 TheScherrerEquation 175
15.1.2 LineBroadeningintheLaueScatteringGeometry 178
15.2 LineBroadeningduetoMicrostrainFluctuations 180
15.3 Williamson–HallMethod 181
15.4 TheConvolutionApproach 183
15.5 InstrumentalBroadening 184
15.6 RelationbetweenGrainSize-InducedandMicrostrain-Induced
BroadeningsofX-RayDiffractionProfiles 186
16 ApplicationstoMaterialsScience:ResidualStrain/Stress
Measurements 189
16.1 StrainMeasurementsinSingle-CrystallineSystems 189
16.2 ResidualStressMeasurementsinPolycrystallineMaterials 190