X-Ray Multiple-Wave Diffraction: Theory and Application

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Springer Science & Business Media, Jun 24, 2004 - Science - 431 pages
2 Reviews
X-ray multiple-wave diffraction, sometimes called multiple diffraction or N-beam diffraction, results from the scattering of X-rays from periodic two or higher-dimensional structures, like 2-d and 3-d crystals and even quasi crystals. The interaction of the X-rays with the periodic arrangement of atoms usually provides structural information about the scatterer. Unlike the usual Bragg reflection, the so-called two-wave diffraction, the multiply diffracted intensities are sensitive to the phases of the structure factors in volved. This gives X-ray multiple-wave diffraction the chance to solve the X-ray phase problem. On the other hand, the condition for generating an X ray multiple-wave diffraction is much more strict than in two-wave cases. This makes X-ray multiple-wave diffraction a useful technique for precise measure ments of crystal lattice constants and the wavelength of radiation sources. Recent progress in the application of this particular diffraction technique to surfaces, thin films, and less ordered systems has demonstrated the diver sity and practicability of the technique for structural research in condensed matter physics, materials sciences, crystallography, and X-ray optics. The first book on this subject, Multiple Diffraction of X-Rays in Crystals, was published in 1984, and intended to give a contemporary review on the fundamental and application aspects of this diffraction.
 

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Contents

Introduction
1
12 Development of Theories for XRay TwoWave Diffraction
3
13 Development of MultipleWave Diffraction
6
Elements of XRay Physics and Crystallography
13
212 Synchrotron Radiation Sources
15
22 Interaction of XRays with Matter
19
23 Reciprocal Lattice Structure Factor and Electron Density Distribution
25
24 Factors Affecting the Diffraction Intensity
27
714 Numerical Computing Procedures
152
72 Approximations
156
722 Born Approximation
180
723 QuantumMechanical Approach
184
724 Quantitative Approach for Phasing An Iterative Approximation
200
725 Approach Using TakagiTaupin Equation
204
726 Expanded DistortedWave Born Approximation
215
727 Resonance Perturbation Bethe Approximation
219

242 LorentzPolarization Factor
28
243 Temperature Factor
29
Diffraction Geometry
31
312 Systematic Coplanar and Coincidental MultipleWave Diffraction
33
32 Grazing Incidence Diffraction Versus WideAngle Incidence Diffraction
34
33 LorentzPolarization Factor in MultipleWave Cases
36
34 MultipleWave Diffraction in MultiCrystal Systems
39
Experimental Techniques
43
411 ReferenceVector Method for Indexing Renninger Scan
45
42 DivergentBeam Method Kossel Diagram
48
421 Indexing Kossel Diagrams
51
43 RotationCrystal Methods ReferenceBeamStereoscopic Imaging
53
431 Indexing Multiple Wave Diffraction Diagram by Crystal Orientation Matrix
62
44 Diffractometer and Detector
65
Kinematical Theory of XRay Diffraction
71
51 PowerTransfer Equation
72
511 TwoWave Laue Diffraction and Bragg Reflection
74
512 Multiple Wave Diffraction
76
52 Approximate Solutions to the PowerTransfer Equation
77
53 HigherOrder Approximation and Iterative Calculation
80
54 Integrated Intensity and XRay Path Length in Crystals
82
55 MultipleWave Diffraction Profile
85
Dynamical Theory of XRay Diffraction
89
61 Fundamental Equation of Wavefield
90
62 Formalism of Photonic Band Theory
94
63 Polarization of Wavefields
95
64 Equation of Dispersion and Excitation of Dispersion Surface
98
65 Energy Flow and Group Velocity
109
66 Mode of WavePropagation
112
661 Wavefields of Modes for Symmetric TwoWave Transmission Diffraction
113
662 Wavefields of Modes for Symmetric ThreeWave Transmission Diffraction
115
663 Wavefields of Modes for Symmetric iVWave Diffraction
119
67 Number of Modes and Number of Permitted Modes
122
68 Absorption
125
69 Boundary Conditions
127
691 Boundary Conditions at an Entrance Surface
128
692 Boundary Conditions at an Exit Surface
131
Scattering Matrix
135
611 Excitation of Mode and Intensity of Wavefield
137
612 SphericalWave Nature of XRays
139
613 Dynamical Diffraction in Distorted Crystals
141
Theoretical Approaches
143
71 Numerical Calculation Procedures
144
712 Linear Approximation
145
713 Cartesian Coordinates Representation of Eigenvalue and Eigenvector
146
Dynamical Diffraction Properties and Behaviors
223
812 Extremely Asymmetric TwoWave Diffraction
230
813 Grazing Incidence TwoWave Diffraction
238
814 TwoWave Back Diffraction
244
82 ThreeWave Diffraction
246
821 ThreeWave LaueLaue Diffraction
247
822 ThreeWave BraggLaue Diffraction
253
823 ThreeWave BraggBragg Diffraction
258
824 ThreeWave BraggSurface Diffraction
259
825 ThreeWave Grazing Incidence Diffraction
262
826 ThreeWave Coplanar Diffraction
271
83 Polarization Aspects of Three Wave Diffraction
280
831 Indirect Excitation of Three wave Diffraction with a PolarizationForbidden Reflection
282
832 Polarization Suppression of Multiple Wave Interaction
284
833 PolarizationResolved MultipleWave Diffraction
286
84 HighOrder MultipleWave Diffraction
289
842 Coincidental TwentySixWave Diffraction
291
843 MultipleWave Back Diffraction
294
9 Applications
299
911 Qualitative and Quantitative Determination of Phase
300
912 Determination of Absolute Configuration of Crystals
317
913 Phase Determination for ChargeDensityWave Reflections
318
914 Phase Determination for Diffraction in QuasiCrystals
321
915 Determination of Phase Shift due to Resonance
322
916 Phase Determination of Surface InPlane Reflection
326
917 Phase Determination for Diffraction in Thin Films and Substrates and Reconstructed Surfaces
329
92 Phasing Macromolecular Structures and Structure Determination with Triplet Phases
333
922 Structure Determination with Triplet Phases
334
93 Determination of Crystal Lattice Constants and Perfection
339
932 Strain Measurements of Epitaxy Layer on Crystal Substrate
341
933 Characterization of Crystal Perfection of Semiconductor Surfaces
348
94 MultipleWave Diffraction Excited Fluorescence
353
MDAFS
359
95 Studies of Phase TransitionTransformation
364
96 MultipleWave XRay Optics
368
961 MultipleWave XRay Monochromators
369
962 MultiWave Phase Plate and XRay Polarimeter
378
97 Other Applications
382
972 MultipleWave XRay Topography
383
98 Prospects of Future Development
384
References
387
Figure Acknowledgements
409
Index
413
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