Formulation of perfect-crystal diffraction from Takagi–Taupin equations: numerical implementation in the crystalpy library

Abstract

The Takagi–Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

Keywords

• x-ray diffraction
• perfect crystal
• dynamical theory of diffraction
• crystalpy software package
• crystal optics