Extending the Takagi-Taupin equations for x-ray nanobeam Bragg coherent diffraction

TL;DR

This paper introduces a novel simulation method for x-ray nanobeam Bragg diffraction based on extended Takagi-Taupin equations, applicable to weakly strained systems and capable of handling complex wavefront effects.

Contribution

It extends the Takagi-Taupin equations to universally simulate weakly strained systems, including semi-infinite crystals, addressing wavefront curvature and beam re-divergence issues.

Findings

Excellent agreement with experimental data on strained thin films

Applicable to a wide range of weakly strained systems

Enables physical parameter extraction via automatic differentiation

Abstract

We present a new approach for simulating x-ray nanobeam Bragg coherent diffraction patterns based on the Takagi-Taupin equations. Compared to conventional methods, the current approach can be universally applied to any weakly strained system including semi-infinite crystals that diffract dynamically. It addresses issues such as the curved wavefront and re-divergence of the focused incident beam. We show excellent agreement against experimental data on a strained La0.7Sr0.3MnO3 thin film on SrTiO3 substrate, and a path to extracting physical information using automatic differentiation.