The three-dimensional arrangement of atoms and molecules in crystals and the comparable magnitude of x-ray wavelengths and interatomic distances make it possible for crystals to have more than one set of atomic planes that satisfy Bragg's law and simultaneously diffract an incident x-ray beam - this is the so-called multiple diffraction. This type of diffraction should, in prin ciple, reflect three-dimensional information about the structure of the dif fracting material. Recent progress in understanding this diffraction phenome non and in utilizing this diffraction technique in solid-state and materials sciences reveals the diversity as well as the importance of multiple diffraction of x-rays in application. Unfortunately, there has been no single book written that gives a sys tematic review of this type of diffraction, encompasses its diverse applica tions, and foresees future trends gf development. It is for this purpose that this book is designed. It is hoped that its appearance may possibly turn more attention of condensed-matter physicists, chemists and material scientists toward this particular phenomenon, and that new methods of non-destructive analysis of matter using this diffraction technique may be developed in the future.

Inhalt

1. Introduction.- 2. Geometry, Peak Indexing, and Experimental Techniques.- 2.1 Geometry of Multiple Diffraction.- 2.2 Experimental Techniques for Obtaining Multiple Diffraction.- 2.3 Indexing Multiple Diffraction Patterns.- 2.4 Indexing Kossel Patterns.- 3. Kinematical Theory of Diffraction.- 3.1 Equation of Power Transfer for Multi-Beam Cases.- 3.2 Approximate Solutions to the Equation of Power Transfer.- 3.3 Integrated Intensity and the Lorentz-Polarization Factors.- 3.4 Path Lengths of X-Ray Beams in Crystals.- 3.5 Exact Solution to the Power-Transfer Equation.- 3.6 Iterative Calculation for Reflection Power.- 3.7 Dynamical Treatment for Kinematical Reflections.- 3.8 Diffraction in Multi-Layered Crystals.- 3.9 Peak Width, Beam Divergence, and Mosaic Spread.- 4. Dynamical Theory of X-Ray Diffraction.- 4.1 Fundamental Equation of Wavefields.- 4.2 Polarization of Wavefields.- 4.3 Dispersion Surface.- 4.4 Energy Flow.- 4.5 Modes of Wave Propagation.- 4.6 Absorption.- 4.7 Boundary Conditions.- 4.8 Excitation of Mode and Excitation of Beam.- 4.9 Intensity of Wavefield (Standing-Wave) in Crystal.- 4.10 Consideration of the Spherical-Wave Nature of the Incident X-Rays.- 5. Approximations, Numerical Computing, and Other Approaches.- 5.1 Two-Beam Approximation for Three-Beam Diffraction.- 5.2 Procedures for Numerical Computing.- 5.3 Quantum Mechanical Approach.- 5.4 N-Beam Diffraction in Other Types of Interaction.- 6. Case Studies.- 6.1 Bragg-Type Multiple Diffraction from Gallium Arsenide, Indium Arsenide and Indium PhosphideKinematical Interpretation.- 6.2 Three-Beam Borrmann DiffractionDynamical Calculation.- 6.3 Simultaneous Four-Beam Borrmann Diffraction.- 6.4 Three-Beam Bragg-Laue and Bragg-Bragg Diffraction.- 6.5 Four-Beam Bragg-Laue Diffraction.- 7.Applications.- 7.1 Experimental Determination of X-Ray Reflection Phases; Application to Crystal Structure Determination.- 7.2 Determination of Lattice Constants of Single Crystals.- 7.3 Determination of Lattice Mismatch in Thin Layered Materials.- 7.4 Multi-Beam X-Ray Topography.- 7.5 Multi-Beam X-Ray Interferometer.- 7.6 Monochromatization of X-Ray Beams.- 7.7 Plasma Diagnosis.- 7.8 Determination of Mosaic Spread of Crystals.- 7.9 Multi-Beam X-Ray Standing-Wave Excited Fluorescence Technique for Surface StudiesA Proposed Method.- 7.10 Possible Future Trend of Development.- References.