To the Solution of the Inverse Problem of X-Ray Topo-Tomography. Computer Algorithms and 3D Reconstruction on the Example of a Crystal with a Point Defect of Coulomb Type

Abstract

A successive approach to the solution of the inverse problem of diffraction X-ray topo-tomography is proposed. It is based on the semikinematic solution to the Takagi–Taupin equations for the amplitude of diffracted σ-polarized wave. An example of a point defect of Coulomb type in a Si(111) single-crystal plate under conditions of symmetric Laue diffraction and a set of oblique two-dimensional topographic projections corresponding to the rotation of plane-parallel sample crystal around the diffraction vector [ $$\bar {2}20$$ ] is considered. Iterative algorithms for simulated annealing (SA) and quasi-Newton-type algorithms are used for computer reconstruction of the three-dimensional function of the displacement field around a point defect. The results of computer simulation of the displacement field function based on the data for one 2D projection, corresponding to the point defect image in an X-ray topogram in classical X-ray diffraction topography, are presented.