Computer Simulation of the Effect of Coherent Dynamical Diffraction of Synchrotron Radiation in Crystals of Arbitrary Shape and Structure

A new scheme for the numerical solution of Takagi–Taupin equations, which makes it possible to simulate the effect of synchrotron radiation diffraction in crystals of arbitrary structure, is described in detail. The new scheme is convenient to perform calculations for crystals of arbitrary shape. The rectangular coordinate system and the algorithm for calculating derivatives at half of step have proven their efficiency and are used, but the recurrence equations of this algorithm have been modified towards simplification. The boundary conditions are in no way related to the crystal boundaries. A computer program is developed, and two examples are considered for the cases of diffraction in the Laue and Bragg geometries, for which the analytical solutions are known. The calculation results are in complete agreement with these solutions.