Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal.

Abstract

In the kinematical approximation, new analytical solutions are obtained that describe the diffraction of a restricted X-ray beam from a thin crystal. Calculation of the angular distribution of reflected X-ray beams within the framework of the developed approach significantly reduces the computational cost compared with numerical methods. For a thin silicon crystal, X-ray reciprocal-space mapping was simulated using analytical solutions, as well as calculated using numerical methods based on 2D recurrence relations and the Takagi-Taupin equations.