Dynamical Theory of X-Ray Diffraction

Abstract

X-ray diffraction is a major tool for the study of crystal structures and the characterization of crystal perfection. Since the discovery of X-ray diffraction by von Laue, Friedrich, and Knipping in 1912 two basic theories have been used to describe this diffraction. One is the approximate geometrical, or kinematical theory, applicable to small or highly imperfect crystals; it is used for the determination of crystal structures and the study of powders and polycrystalline materials. The other one is the rigorous dynamical theory, applicable to perfect or nearly perfect crystals and, for that reason, is the one used for the assessment of the structural properties of high technology materials. It has witnessed exciting developments since the advent of synchrotron radiation. This book provides an account of the dynamical theory of diffraction and of its applications. The first part serves as an introduction to the subject, presenting early developments, Ewald's theory of dispersion and the basic results of Laue's dynamical theory. This is followed in the second part by a detailed development of the diffraction and propagation properties of X-rays in perfect crystals, including the study of anomalous absorption, Pendellösung, grazing incidence diffraction (GID) and n-beam or multiple-beam diffraction. The third part constitutes an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchrotron radiation, location of atoms at surfaces and interfaces and X-ray diffraction topography.

Laue lens for astrophysics: Extensive comparison between mosaic, curved, and quasi-mosaic crystals

“…where Λ 0 is the extinction length as defined in Authier (2001) for the Laue symmetric case. The integrated reflectivity H M depends on the energy of the beam that is considered.…”

Proposal for a Laue lens relying on hybrid quasi-mosaic curved crystals

“…where the first factor is the diffraction efficiency and the latter is the attenuation factor due to absorption throughout the sample, μ is the linear absorption coefficient, d hkl the d-spacing of planes (hkl), θ B the Bragg angle, and Λ 0 the extinction length as defined by (Authier 2001) for the Laue symmetric case. Ω QM represents the bending angle of the CDPs, namely of the QM planes.…”

Structural Characterization of Doped GaSb Single Crystals by X-ray Topography

“…Variations within Δd/d ~ 10 -5 are very apparent. The extinction depth (that is the depth to which x-rays penetrate during diffraction) [19][20][21] has values varying from 1 μm to 50 μm. So, the detected Δd/d, caused by dislocations, precipitates or even structures due to the insufficient etching, lies very close to the surface.…”