Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. I

Abstract

This paper reports computer simulations of the transmitted-beam intensity distribution for the case of six-beam (000, 220, 242, 044, −224, −202) diffraction of X-rays in a perfect silicon crystal of thickness 1 mm. Both the plane-wave angular dependence and the six-beam section topographs, which are usually obtained in experiments with a restricted beam (two-dimensional slit), are calculated. The angular dependence is calculated in accordance with Ewald's theory. The section topographs are calculated from the angular dependence by means of the fast Fourier transformation procedure. This approach allows one to consider, for the first time, the transformation of the topograph's structure due to the two-dimensional slit sizes and the distance between the slit and the detector. The results are in good agreement with the results of other works and with the experimental data. This method of calculation does not require a supercomputer and it was performed on a standard laptop. A detailed explanation of the main features of the diffraction patterns at different distances between the slit and the detector is presented.