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.
Includes bibliographical references (p. [583]-636) and indexes.
Preface
I. Background and basic results
1. Historical developments
1.1. Prologue
1.2. The discovery of X-ray diffraction
1.3. The geometrical theory of diffraction
1.4. Darwin's dynamical theory of diffraction
1.5. Extinction theories
1.6. Ewald's dynamical theory
1.7. Early confirmations of the dynamical theory
1.8. Laue's dynamical theory
1.9. Umweganregung and Aufhellung
1.10. The properties of wavefields
1.11. Diffraction by deformed crystals
1.12. Modern times
2. Properties of the electromagnetic field - Propagation and scattering
2.1. Maxwell's equations
2.2. The electrodynamic potentials in vacuum
2.3. The electrodynamic potentials in polarized media
2.4. Hertz vectors (polarization potentials)
2.5. Propagation of an electromagnetic wave in vacuum
2.6. Scattering of X-rays by an electron
2.7. Polarizability of matter for X-rays
2.8. Ewald's dispersion theory
2.9. Propagation equation of an electromagnetic wave in materials in Laue's dynamical theory
2.10. Specular reflection - Fresnel relations
3. Geometrical theory of x-ray diffraction
3.1. Classical scattering by an electron - polarization
3.2. Amplitude diffracted by a periodic electron distribution
3.3. Intensity diffracted by a small crystal
3.4. Reflectivity
3.5. Integrated intensity
3.6. Mosaic crystals
4. Elementary dynamical theory
4.1. Limitations of the geometrical theory
4.2. Introduction of the dispersion surface
4.3. Analogy with the band theory of solids
4.4. Propagation equation
4.5. Fundamental equations of dynamical theory
4.6. Amplitude ratio of the refracted and reflected waves
4.7. Solutions of plane-wave dynamical theory
4.8. The diffracted waves in the transmission geometry
4.9. The diffracted waves in the reflection geometry
4.10. Influence of the asymmetry on the position and width of the rocking curve and of the angular distribution of the reflected beam
4.11. Comparison with geometrical theory
4.12. Dynamical diffraction by quasicrystals
II. Advanced dynamical theory
5. Properties of wavefields
5.1. Relations between the field vectors
5.2. Fundamental equations of the dynamical theory
5.3. The dispersion equation in the two-beam case
5.4. Poynting vector of the wavefields
5.5. Determination of the tiepoints - geometrical interpretation of the deviation parameter
5.6. The deviation parameter in absorbing crystals
5.7. Amplitude ratio of the refracted and reflected waves
5.8. Anomalous absorption
5.9. Dispersion surface when the Bragg angle is close to Pie/2
6. Intensities of plane waves in the transmission geometry
6.1. Boundary conditions for the amplitudes at the entrance surface
6.2. Amplitudes of the refracted and reflected waves
6.3. Boundary conditions for the wavevectors at the exit surface
6.4. Rocking curves of the reflected and refracted beams
6.5. Integrated intensity
7. Intensities of plane waves in the reflection geometry
7.1. Thick absorbing crystals
7.2. Standing waves
7.3. Thin crystals
8. Dynamical diffraction in highly asymmetric coplanar and non-coplanar geometries
8.1. Introduction
8.2. Diffraction at grazing incidence or grazing emergence
8.3. Deviation from Bragg's incidence of the middle of the reflection domain
8.4. Variation of the Darwin width for a grazing incidence
8.5. Variation of the width of the diffracted beam for a grazing emergence
8.6. Equation of the dispersion surface
8.7. Relation with the traditional dynamical theory
8.8. Specularly and Bragg-reflected intensities
8.9. Grazing incidence diffraction (non-coplanar geometry)
9. n-beam dynamical diffraction
9.1. Introduction
9.2. The general three-beam case
9.3. The three-beam coplanar case
9.4. Determination of phases using n-beam diffraction
9.5. The super-Borrmann effect
10. Spherical-wave dynamical theory: Kato's theory
10.1. Extension of the dynamic theory to any kind of incident wave
10.2. Fourier expansion of a spherical wave in plane waves
10.3. Direct integration in the transmission geometry
10.4. Intensity distribution on the exit surface
10.5. Equal-intensity (Pendelld"osung) fringes
10.6. Integration by the stationary phase method
10.7. Integrated intensity
10.8. Influence of polarization
10.9. Bragg geometry
11. Spherical-wave dynamical theory: Takagi's theory
11.1. Introduction
11.2. Generalized fundamental equations
11.3. Reduction of Takagi's equations in the plane-wave case
11.4. Absorbing crystals
11.5. Analytical resolution of Takagi's equations for perfect crystals
11.6. Analytical solution for a point source using the method of integral equations
11.7. Analytical resolution of Takagi's equations using the Riemann function
11.8. Analytical solution for an incident spherical wave using the method of Riemann functions
12. Ray tracing in perfect crystals
12.1. Ray tracing
12.2. The structure of real waves
12.3. Wave packets made of the superposition of separate plane waves
12.4. Wavepackets made of a continuous distribution of wavevectors
12.5. Group velocity and Poynting vector
12.6. Angular amplification
12.7. Intensity distribution along the base of the Borrmann triangle (transmission geometry)
12.8. Geometrical properties of wavefield trajectories within the Borrmann triangle
12.9. Experimental proof of double refraction
12.10. Experimental observation of the separation of the wavefield paths
12.11. Fresnel diffraction near the Bragg incidence
12.12. Ray tracing in finite crystals
12.13. Coherence of extended, non-strictly monochromatic sources
III. Extension of the dynamical theory to deformed crystals
13. Ray tracing in slightly deformed crystals
13.1. X-ray propagation in deformed materials
13.2. Effective misorientation
13.3. Polarizability of a deformed crystal
13.4. The Eikonal approximation
13.5. Ray trajectories
13.6. The case of a constant strain gradient
13.7. Diffracted intensities - plane-wave case
13.8. Diffracted intensities - spherical-wave case
14. Propagation of X-rays in highly deformed crystals
14.1. Introduction
14.2. Takagi's equations in a deformed crystal
14.3. Resolution of Takagi's equations in the deformed crystal case
14.4. Ray concept applied to highly distorted crystals
14.5. Statistical dynamical theories
IV. Applications
15. X-ray optics
15.1. X-ray sources
15.2. Flat monochromators
15.3. Applications of multiple-crystal arrangements to beam conditioning
15.4. Focusing optics
15.5. X-ray interferometers
15.6. Imaging with X-rays
16. Location of atoms at surfaces and interfaces using X-ray standing waves
16.1. Principle
16.2. Theory
16.3. Bulk crystals
16.4. Solution to the surface registration problem
16.5. Thin films and buried interfaces
16.6. Standing waves in deformed crystals
16.7. Standing waves due to specular reflection
17. X-ray diffraction topography
17.1. Introduction
17.2. Single-crystal reflection topography (Berg-Barrett technique)
17.3. Single-crystal transmission topography
17.4. Double- or multiple-crystal topography
Appendices
Appendix 1: Useful formulae
Appendix 2: The early days of dynamical theory, by P.P. Ewald
References
List of symbols
Index