Dynamical Theory of X-Ray Diffraction

by Andrï Authier

Overview

This is the first comprehensive book on the dynamical diffraction of x-rays since the development of synchrotron radiation. There is an introduction to the subject presenting early developments and the basic results, followed by a detailed development of the diffraction and propagation properties of x-rays in perfect crystals and by an extension of the theory to the case of slightly and highly deformed crystals. The last section gives three applications of the theory: x-ray optics for synchrotron radiation, locations of atoms at surfaces, and x-ray diffraction topography. The book is well illustrated and contains a wide range of references to the literature.

Product Details

ISBN-13:	9780198559603
Publisher:	International Union of Crystallography
Publication date:	09/06/2001
Series:	International Union of Crystallography Monographs on Crystallography , #11
Pages:	680
Product dimensions:	9.21(w) x 6.14(h) x 1.44(d)

About the Author

André Authier is Professor Emeritus at Université Pierre et Marie Curie in Paris.

Table of Contents

PrefaceI. Background and basic results1. Historical developments1.1. Prologue1.2. The discovery of X-ray diffraction1.3. The geometrical theory of diffraction1.4. Darwin's dynamical theory of diffraction1.5. Extinction theories1.6. Ewald's dynamical theory1.7. Early confirmations of the dynamical theory1.8. Laue's dynamical theory1.9. Umweganregung and Aufhellung1.10. The properties of wavefields1.11. Diffraction by deformed crystals1.12. Modern times2. Properties of the electromagnetic field - Propagation and scattering2.1. Maxwell's equations2.2. The electrodynamic potentials in vacuum2.3. The electrodynamic potentials in polarized media2.4. Hertz vectors (polarization potentials)2.5. Propagation of an electromagnetic wave in vacuum2.6. Scattering of X-rays by an electron2.7. Polarizability of matter for X-rays2.8. Ewald's dispersion theory2.9. Propagation equation of an electromagnetic wave in materials in Laue's dynamical theory2.10. Specular reflection - Fresnel relations3. Geometrical theory of x-ray diffraction3.1. Classical scattering by an electron - polarization3.2. Amplitude diffracted by a periodic electron distribution3.3. Intensity diffracted by a small crystal3.4. Reflectivity3.5. Integrated intensity3.6. Mosaic crystals4. Elementary dynamical theory4.1. Limitations of the geometrical theory4.2. Introduction of the dispersion surface4.3. Analogy with the band theory of solids4.4. Propagation equation4.5. Fundamental equations of dynamical theory4.6. Amplitude ratio of the refracted and reflected waves4.7. Solutions of plane-wave dynamical theory4.8. The diffracted waves in the transmission geometry4.9. The diffracted waves in the reflection geometry4.10. Influence of the asymmetry on the position and width of the rocking curve and of the angular distribution of the reflected beam4.11. Comparison with geometrical theory4.12. Dynamical diffraction by quasicrystalsII. Advanced dynamical theory5. Properties of wavefields5.1. Relations between the field vectors5.2. Fundamental equations of the dynamical theory5.3. The dispersion equation in the two-beam case5.4. Poynting vector of the wavefields5.5. Determination of the tiepoints - geometrical interpretation of the deviation parameter5.6. The deviation parameter in absorbing crystals5.7. Amplitude ratio of the refracted and reflected waves5.8. Anomalous absorption5.9. Dispersion surface when the Bragg angle is close to Pie/26. Intensities of plane waves in the transmission geometry6.1. Boundary conditions for the amplitudes at the entrance surface6.2. Amplitudes of the refracted and reflected waves6.3. Boundary conditions for the wavevectors at the exit surface6.4. Rocking curves of the reflected and refracted beams6.5. Integrated intensity7. Intensities of plane waves in the reflection geometry7.1. Thick absorbing crystals7.2. Standing waves7.3. Thin crystals8. Dynamical diffraction in highly asymmetric coplanar and non-coplanar geometries8.1. Introduction8.2. Diffraction at grazing incidence or grazing emergence8.3. Deviation from Bragg's incidence of the middle of the reflection domain8.4. Variation of the Darwin width for a grazing incidence8.5. Variation of the width of the diffracted beam for a grazing emergence8.6. Equation of the dispersion surface8.7. Relation with the traditional dynamical theory8.8. Specularly and Bragg-reflected intensities8.9. Grazing incidence diffraction (non-coplanar geometry)9. n-beam dynamical diffraction9.1. Introduction9.2. The general three-beam case9.3. The three-beam coplanar case9.4. Determination of phases using n-beam diffraction9.5. The super-Borrmann effect10. Spherical-wave dynamical theory: Kato's theory10.1. Extension of the dynamic theory to any kind of incident wave10.2. Fourier expansion of a spherical wave in plane waves10.3. Direct integration in the transmission geometry10.4. Intensity distribution on the exit surface10.5. Equal-intensity (Pendellösung) fringes10.6. Integration by the stationary phase method10.7. Integrated intensity10.8. Influence of polarization10.9. Bragg geometry11. Spherical-wave dynamical theory: Takagi's theory11.1. Introduction11.2. Generalized fundamental equations11.3. Reduction of Takagi's equations in the plane-wave case11.4. Absorbing crystals11.5. Analytical resolution of Takagi's equations for perfect crystals11.6. Analytical solution for a point source using the method of integral equations11.7. Analytical resolution of Takagi's equations using the Riemann function11.8. Analytical solution for an incident spherical wave using the method of Riemann functions12. Ray tracing in perfect crystals12.1. Ray tracing12.2. The structure of real waves12.3. Wave packets made of the superposition of separate plane waves12.4. Wavepackets made of a continuous distribution of wavevectors12.5. Group velocity and Poynting vector12.6. Angular amplification12.7. Intensity distribution along the base of the Borrmann triangle (transmission geometry)12.8. Geometrical properties of wavefield trajectories within the Borrmann triangle12.9. Experimental proof of double refraction12.10. Experimental observation of the separation of the wavefield paths12.11. Fresnel diffraction near the Bragg incidence12.12. Ray tracing in finite crystals12.13. Coherence of extended, non-strictly monochromatic sourcesIII. Extension of the dynamical theory to deformed crystals13. Ray tracing in slightly deformed crystals13.1. X-ray propagation in deformed materials13.2. Effective misorientation13.3. Polarizability of a deformed crystal13.4. The Eikonal approximation13.5. Ray trajectories13.6. The case of a constant strain gradient13.7. Diffracted intensities - plane-wave case13.8. Diffracted intensities - spherical-wave case14. Propagation of X-rays in highly deformed crystals14.1. Introduction14.2. Takagi's equations in a deformed crystal14.3. Resolution of Takagi's equations in the deformed crystal case14.4. Ray concept applied to highly distorted crystals14.5. Statistical dynamical theoriesIV. Applications15. X-ray optics15.1. X-ray sources15.2. Flat monochromators15.3. Applications of multiple-crystal arrangements to beam conditioning15.4. Focusing optics15.5. X-ray interferometers15.6. Imaging with X-rays16. Location of atoms at surfaces and interfaces using X-ray standing waves16.1. Principle16.2. Theory16.3. Bulk crystals16.4. Solution to the surface registration problem16.5. Thin films and buried interfaces16.6. Standing waves in deformed crystals16.7. Standing waves due to specular reflection17. X-ray diffraction topography17.1. Introduction17.2. Single-crystal reflection topography (Berg-Barrett technique)17.3. Single-crystal transmission topography17.4. Double- or multiple-crystal topographyAppendicesAppendix 1: Useful formulaeAppendix 2: The early days of dynamical theory, by P.P. EwaldReferencesList of symbolsIndex

Editorial Reviews

"Provides an current account of the theory of diffraction and its applications. Authier (Université P. et M. Curie) begins with an introduction to dynamical theory, some historical considerations, a review of geometrical theory, and the interaction of X-rays and matter. He then discusses the dynamical diffraction of plane and spherical waves by perfect crystals, and extends the theory to both slightly and highly deformed crystals. The last section applies the concepts to X-ray optics, standing wave studies of surfaces and interfaces, and diffraction topography."—SciTech Book News

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