Simulation of X-ray diffraction in a cylindrical crystal

Abstract

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.

Two-dimensional recurrence relations and Takagi–Taupin equations. I. Dynamical X-ray diffraction by a perfect crystal

“…If the beam deviates from the exact Bragg angle, additional changes in the phase of the X-ray wave occur. So, for example, for two points 0 and (x, z), there is an additional difference in optical paths (Punegov et al, 2014;Punegov & Kolosov, 2020). Consequently, for X-ray waves incident on the surface of the crystal, the difference in optical paths increases in the direction of the x axis with an increase in the site number m according to the law mÁx cos 1 .…”

“…3). Therefore, to calculate the diffraction of a restricted X-ray beam, one can apply the method that we used in the numerical simulation of X-ray scattering in a cylindrical crystal (Punegov & Kolosov, 2020).…”

“…To calculate the transmitted T and diffracted S waves using two-dimensional recurrence relations, a two-dimensional periodic network is considered (Fig. 3), in which the x axis is located along the input surface of the crystal, the z axis is directed deep into the periodic medium (Punegov et al, 2014(Punegov et al, , 2016Punegov & Kolosov, 2020).…”

“…One should note the advantage of recurrence relations over the T-T equations in setting the boundary conditions when calculating RSMs. Using a cylindrical crystal as an example, it was shown that two-dimensional recurrence relations can be used to simulate X-ray diffraction in crystals of arbitrary shape (Punegov & Kolosov, 2020). Unfortunately, this is difficult to do using the T-T equations.…”