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

J Synchrotron Radiat

European Synchrotron Radiation Facility, 71 Avenue des Martyrs, F-38000 Grenoble, France.

Published: November 2024

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.

Download full-text PDF

Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11542662PMC
http://dx.doi.org/10.1107/S160057752400924XDOI Listing

Publication Analysis

Top Keywords

takagi-taupin equations
8
formulation perfect-crystal
4
perfect-crystal diffraction
4
diffraction takagi-taupin
4
equations numerical
4
numerical implementation
4
implementation crystalpy
4
crystalpy library
4
library takagi-taupin
4
equations solved
4

Similar Publications

Simulation of reciprocal-space mapping using a new analytical solution of kinematical X-ray diffraction in a crystal.

Acta Crystallogr A Found Adv

January 2025

Institute of Physics and Mathematics, Federal Research Center `Komi Scientific Center, the Ural Branch of the Russian Academy of Sciences', Kommunisticheskaya st. 24, Syktyvkar, 167982, Russian Federation.

Article Synopsis
  • New analytical solutions have been developed to describe how a limited X-ray beam interacts with a thin crystal, specifically aimed at addressing diffraction.
  • This new method streamlines the calculation of reflected X-ray beam angles, making it far less computationally expensive than traditional numerical approaches.
  • The study involved simulating X-ray reciprocal-space mapping for a thin silicon crystal using both the new analytical solutions and established numerical methods, like 2D recurrence relations and Takagi-Taupin equations.
View Article and Find Full Text PDF

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

J Synchrotron Radiat

November 2024

European Synchrotron Radiation Facility, 71 Avenue des Martyrs, F-38000 Grenoble, France.

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.

View Article and Find Full Text PDF

An alternative method to the Takagi-Taupin equations for studying dark-field X-ray microscopy of deformed crystals.

Acta Crystallogr A Found Adv

November 2024

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, People's Republic of China.

Article Synopsis
  • - The study presents a new approach to analyze dark-field X-ray microscopy (DFXM) of deformed crystals, offering a solution when traditional methods (Takagi-Taupin equations) might lead to inaccuracies in data interpretation due to dynamical diffraction.
  • - This new method uses an exact dispersion relation and incorporates a modified finite difference scheme for numerical calculations, validated by investigating a diamond crystal with varying diffraction components.
  • - Results from the new method have produced DFXM images of diamond crystals (one with a stacking fault and another twisted) that differ significantly from those generated by the Takagi-Taupin equations, demonstrating its effectiveness and reliability.
View Article and Find Full Text PDF

Development of an innovative diffraction scattering theory of X-rays and electrons in imperfect crystals.

Acta Crystallogr A Found Adv

July 2024

A.V. Shubnikov Institute of Crystallography, Federal Scientific Research Centre Crystallography and Photonics RAS, Leninskii prospekt, 59, Moscow, 119333, Russian Federation.

Fundamental equations describing the X-ray and electron diffraction scattering in imperfect crystals have been derived in the form of the matrix Fredholm-Volterra integral equation of the second kind. A theoretical approach has been developed using the perfect-crystal Green function formalism. In contrast, another approach utilizes the wavefield eigenfunctions related to the diagonalized matrix propagators of the conventional Takagi-Taupin and Howie-Whelan equations.

View Article and Find Full Text PDF

A coupled mode theory based on Takagi-Taupin equations describing electromagnetic scattering from distorted periodic arrays is applied to the problem of light scattering from beetles. We extend the method to include perturbations in the permittivity tensor to helicoidal arrays seen in many species of scarab beetle and optically anisotropic layered materials more generally. This extension permits analysis of typical dislocations arising from the biological assembly process and the presence of other structures in the elytra.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!