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 new dynamical diffraction approach to X-ray diffraction on lateral crystalline structures has been developed to investigate the angular and spatial distribution of wavefields in the case of the Bragg-Laue geometry in non-perfect lateral structures. This approach allows one to calculate reciprocal space maps for deformed lateral crystals having rectangular cross sections for both the transmitted and reflected wavefields. Numerical modelling is performed for crystals with different lateral sizes, thicknesses and deformations. The approach can be used in coherent diffraction imaging to simulate Fraunhofer diffraction patterns produced by relatively large deformed crystals. research papers J. Appl. Cryst. (2016). 49, 1190-1202 Vasily I. Punegov et al. Bragg-Laue X-ray dynamical diffraction 1191

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Using the two-dimensional recurrence relations of X-ray dynamical diffraction, a numerical simulation of reflection and transmission intensity in a cylindrical crystal has been performed. It is shown that for crystals with a small radius Bragg diffraction is realized. For crystals of large radius, Bragg–Laue diffraction occurs, which is characterized by Bragg diffraction on the upper part of the crystal, as well as the presence of Pendellösung oscillations inside the cylindrical crystal. The reciprocal space maps of dynamical and kinematical diffraction have been calculated.