Equations describing the coherent and diffuse scattering in a crystal modulated by a surface acoustic wave (SAW) are derived using the dynamical X‐ray diffraction theory. The effect of depth attenuation of the Rayleigh surface wave amplitude on the crystal rocking curve profiles is investigated. Results of the numerical simulation of the dynamical diffraction in a mosaic crystal modulated by a SAW, taking into account a block size distribution, are presented. It is shown that the diffuse scattering is distributed in the reciprocal space not only in the vicinity of the main diffraction peak but also about the satellite diffraction peaks, and this distribution depends on the size fluctuations of the crystal defects. Theoretical reciprocal space maps and rocking curves are compared with the corresponding experimental results.

The statistical dynamical theory of X‐ray diffraction is applied to the analysis of simulated rocking curves (RCs) from multilayer systems with randomly distributed microdefects. Recursion formulae for calculating RCs in the general case of multiple diffraction on multilayer crystals are obtained for the Bragg‐Bragg and Laue‐Laue cases. The behaviour of coherently and incoherently scattered intensities for epitaxial films, heterostructures, and superlattices is discussed. It is shown that the alternation of the perfect and imperfect layers of the superlattice leads to the increase of the coherently scattered intensity of satellite peaks.

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.research papers

The statistical dynamical theory of X-ray diffraction is developed for a crystal containing statistically distributed microdefects. Fourier-component equations for coherent and diffuse (incoherent) scattered waves have been obtained in the case of so-called triple-crystal diffractometry. New correlation lengths and areas are introduced for characterization of the scattered volume.

The mosaic structure of an (Al, Ga) N layer grown on (0001) sapphire showing natural ordering was studied by high-resolution X-ray diffraction (HRXRD) reciprocal-space mapping. The direction-dependent mosaicity of the layer has been elaborated using maps of symmetrical and asymmetrical reflections. The reciprocal-lattice points show significant broadening depending on the direction in reciprocal space, the diffraction order and the reflection type ( fundamental or superstructural). The evaluation followed two paths: (i) a procedure based on the Williamson - Hall plot and (ii) a new approach based on the statistical diffraction theory (SDT). Here, the transformed Takagi equations were implemented for the simulation of the reciprocal-space maps (RSM) for symmetrical and asymmetrical reflections. The reconstruction comprised the mosaic block size, their average rotation angle and the spatial distribution of some components of the microdistortion tensor. The results based on the SDT modelling agree well with those obtained by the Williamson - Hall method, while providing a higher degree of precision and detail

Darwin's dynamical theory of X-ray diffraction is extended to the case of lateral (i.e., having a finite length in the lateral direction) crystalline structures. This approach allows one to calculate rocking curves as well as reciprocal-space maps for lateral crystalline structures having a rectangular cross section. Numerical modelling is performed for these structures with different lateral sizes. It is shown that the kinematical approximation is valid for thick crystalline structures having a small length in the lateral direction.

The statistical kinematical X-ray diffraction theory is developed to describe reciprocal-space maps (RSMs) from deformed crystals with defects of the structure. The general solutions for coherent and diffuse components of the scattered intensity in reciprocal space are derived. As an example, the explicit expressions for intensity distributions in the case of spherical defects and of a mosaic crystal were obtained. The theory takes into account the instrumental function of the triple-crystal diffractometer and can therefore be used for experimental data analysis.

A deterministic variant of Bragg Coherent Diffraction Imaging is introduced in its kinematical approximation, for X-ray scattering from an imperfect crystal whose imperfections span no more than half of the volume of the crystal. This approach provides a unique analytical reconstruction of the object’s structure factor and displacement fields from the 3D diffracted intensity distribution centred around any particular reciprocal lattice vector. The simple closed-form reconstruction algorithm, which requires only one multiplication and one Fourier transformation, is not restricted by assumptions of smallness of the displacement field. The algorithm performs well in simulations incorporating a variety of conditions, including both realistic levels of noise and departures from ideality in the reference (i.e. imperfection-free) part of the crystal.