Simulation of X-ray reflection topographs from misfit dislocations

Abstract

Abstract Images of misfit dislocations as obtained from X-ray reflection topography with a low incidence angle are simulated. New algorithms for integrating numerically the Takagi–Taupin equations are presented with decoupled, variable and adaptively chosen step sizes. This reduces drastically the computation time required. The adaptive integration is faster by a factor of ten or more over integration with fixed steps, is more accurate and requires a minimum of free parameters. Rocking topographs are introduced to show the contrast variation over the Bragg peak. It is shown that the contrast of dislocations parallel to the surfaces vanishes as the depth goes to zero, for any anisotropic medium and any Burgers vector.