X-Ray Diffraction Tomography Recovery of the 3D Displacement-Field Function of the Coulomb-Type Point Defect in a Crystal

Abstract

Abstract A successive approach to the solution of the inverse problem of the X-ray diffraction tomography (XRDT) is proposed. It is based on the semi-kinematical solution of the dynamical Takagi–Taupin equations for the σ-polarized diffracted wave amplitude. Theoretically, the case of the Coulomb-type point defect in a single crystal Si(111) under the exact conditions of the symmetric Laue diffraction for a set of the tilted X-ray topography 2D-images (2D projections) is considered provided that the plane-parallel sample is rotated around the diffraction vector [$$\bar{{\bf{2}}}$$ 2 ¯ 20]. The iterative simulated annealing (SA) and quasi-Newton gradient descent (qNGD) algorithm codes are used for a recovery of the 3D displacement-field function of the Coulomb-type point defect. The computer recovery data of the 3D displacement-field function related to the one XRDT 2D projection are presented. It is proved that the semi-kinematical approach to the solution of the dynamical Takagi–Taupin equations is effective for recovering the 3D displacement-field function even for the one XRDT 2D projection.