Formulation of perfect-crystal diffraction from Takagi-Taupin equations. Numerical implementation in the crystalpy library

TL;DR

This paper presents a numerical implementation of the Takagi-Taupin equations for perfect-crystal diffraction, using a matrix model for plane-parallel plates, integrated into the open-source crystalpy library for practical applications.

Contribution

The paper introduces an open-source Python library that efficiently solves the Takagi-Taupin equations for perfect crystals, enabling advanced diffraction simulations.

Findings

Successful implementation of Takagi-Taupin equations in crystalpy

Accurate modeling of crystal reflectivity and diffraction

Open-source tool for crystal diffraction simulations

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.