Bragg–Laue X-ray dynamical diffraction on perfect and deformed lateral crystalline structures

Abstract

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

Simulation of X-ray diffraction in a cylindrical crystal

“…For a crystal in which the lateral width exceeds its thickness, the Bragg case is realized. If the width of the crystal is less than the thickness, the Laue case is observed (Punegov et al, 2016). In the case of a cylindrical crystal, its lateral and vertical sizes are the same.…”

“…Previously, using two-dimensional recurrence relations, dynamical Bragg-Laue diffraction on a lateral crystal of rectangular cross section was studied (Punegov et al, 2016). It was shown that in such a crystal Bragg diffraction and Laue diffraction occur simultaneously.…”

“…At present, triple-crystal diffractometry (Iida & Kohra, 1979;Punegov, 2015) and Bragg coherent diffraction imaging (Robinson et al, 2001;Pavlov et al, 2017Pavlov et al, , 2018Shabalin et al, 2017) are widely applied to the study of crystalline structures. Calculations of rocking curves and reciprocal space maps RSMs) for lateral crystals of rectangular cross section have been performed using the Takagi equations (Kolosov & Punegov, 2005) and two-dimensional recurrence relations (Punegov et al, 2014(Punegov et al, , 2016. For a lateral imperfect crystal, a deterministic version of Bragg coherent diffraction imaging in the kinematical approximation has been considered (Pavlov et al, , 2018.…”

New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution

“…One can read a review of the results in the book by Authier (2005). The inhomogeneous distribution of the radiation field in the case of X-ray diffraction inside the crystal of a special form (parallelepiped or cylinder) was investigated by Olekhnovich & Olekhnovich (1978, Saldin (1982), Uragami (1983), Shulakov et al (1996, Punegov et al (2016) and Shabalin et al (2017). Both analytical and numerical approaches were used.…”

Dynamical scattering in coherent hard x-ray nanobeam Bragg diffraction

“…The nanobeam diffraction simulation presented here employs the Darwin theory of dynamical diffraction, accounting for primary extinction, multiple scattering, absorption, and refraction. Other dynamical effects, such as many-beam diffraction, lateral transport of x-ray intensity parallel to the surface, and lateral inhomogeneity within the illuminated volume are not described in the Darwin approach, and thus, are not part of the present work [10,15,16]. A key validation of this modeling approach is provided by comparing it in detail with a nanobeam diffraction experiment.…”