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Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory

Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory A finite‐element method based on a weak formulation of the Takagi–Taupin equations was adopted to study the X‐ray diffraction of crystals with surface undulations. A general diffraction geometry was simulated to investigate the diffraction features caused by the surface undulations. The numerical results reveal that the effects of surface undulations on Bragg diffraction are local for those limited in the low‐frequency range and physically result from the refractive effect, brought on by the variation of the local asymmetry angle. Thus, a formula based on the local perfect flat crystal approximation was introduced to efficiently evaluate the change in the direction of the diffracted wave caused by surface undulations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Crystallography Wiley

Finite‐element simulation for crystals with surface undulations based on Takagi–Taupin theory

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Publisher
Wiley
Copyright
Copyright © 2023 Wiley Subscription Services, Inc., A Wiley Company
eISSN
1600-5767
DOI
10.1107/s1600576723000808
Publisher site
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Abstract

A finite‐element method based on a weak formulation of the Takagi–Taupin equations was adopted to study the X‐ray diffraction of crystals with surface undulations. A general diffraction geometry was simulated to investigate the diffraction features caused by the surface undulations. The numerical results reveal that the effects of surface undulations on Bragg diffraction are local for those limited in the low‐frequency range and physically result from the refractive effect, brought on by the variation of the local asymmetry angle. Thus, a formula based on the local perfect flat crystal approximation was introduced to efficiently evaluate the change in the direction of the diffracted wave caused by surface undulations.

Journal

Journal of Applied Crystallography – Wiley

Published: Apr 1, 2023

Keywords: Takagi–Taupin equations; finite‐element method; dynamical diffraction; surface morphologies

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