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Abstract <p>A new difference scheme for the numerical solution of the Takagi–Taupin equations for a distorted crystal is proposed, applied to the method of &#xa0;X-ray diffraction tomography from a sample in the exact Bragg position. A criterion of accuracy of numerical solution of Takagi–Taupin equations is proposed. The results of numerical calculations of the contrast of 2D images of a Coulomb-type point defect in a non-absorbing Si(111) crystal, purely phase contrast, and Borrmann contrast of a 2D image in a strongly absorbing SiC-6H crystal are presented. It is shown that in the case of a strongly absorbing SiC-6H crystal a new difference scheme for the numerical solution of the Takagi–Taupin equations, in which the defect displacement field function is used in an exponential form, provides contrast calculation accuracy acceptable for the comparative parameter “calculation time–accuracy.”</p>

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New Calculations and Comparative Analysis of Phase and Borrmann Contrast of Coulomb-Type Defect in Nonabsorbing Si(111) and Strongly Absorbing SiC-6H Single Crystals

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • P. V. Konarev,
  • F. N. Chukhovskii,
  • V. A. Grigorev,
  • V. V. Volkov

摘要

Abstract

A new difference scheme for the numerical solution of the Takagi–Taupin equations for a distorted crystal is proposed, applied to the method of  X-ray diffraction tomography from a sample in the exact Bragg position. A criterion of accuracy of numerical solution of Takagi–Taupin equations is proposed. The results of numerical calculations of the contrast of 2D images of a Coulomb-type point defect in a non-absorbing Si(111) crystal, purely phase contrast, and Borrmann contrast of a 2D image in a strongly absorbing SiC-6H crystal are presented. It is shown that in the case of a strongly absorbing SiC-6H crystal a new difference scheme for the numerical solution of the Takagi–Taupin equations, in which the defect displacement field function is used in an exponential form, provides contrast calculation accuracy acceptable for the comparative parameter “calculation time–accuracy.”