A finite‐element approach to dynamical diffraction problems in reflection geometry

A finite‐element approach to the numerical solution of the Takagi–Taupin equations expressed in a weak form is presented and applied to simulate the X‐ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect crystals in symmetric reflection geometry. The propo...

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Bibliographic Details
Published in:Journal of applied crystallography 2018-04, Vol.51 (2), p.514-525
Main Authors: Honkanen, Ari-Pekka, Ferrero, Claudio, Guigay, Jean-Pierre, Mocella, Vito
Format: Article
Language:English
Subjects:
Computer simulation
Crystals
Deformation
dynamical diffraction
finite‐element approach
Mathematical analysis
Mathematical models
Neutron diffraction
Neutrons
Reflection
reflection geometry
Robustness (mathematics)
Takagi–Taupin equations
Wave diffraction
Wave propagation
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Summary:A finite‐element approach to the numerical solution of the Takagi–Taupin equations expressed in a weak form is presented and applied to simulate the X‐ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect crystals in symmetric reflection geometry. The proposed framework encompasses a new formulation of the Takagi–Taupin equations, which appears to be promising in terms of robustness and stability and supports the Fresnel propagation of the diffracted waves. The presented method is very flexible and has the potential of dealing with dynamical X‐ray or neutron diffraction problems related to crystals of arbitrary shape and deformation. The reference implementation based on the commercial COMSOL Multiphysics software package is available to the relevant user community. A finite‐element approach to the numerical solution of the Takagi–Taupin equations expressed in a weak form is presented and applied to simulate the X‐ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect crystals in symmetric reflection geometry.
ISSN:1600-5767
0021-8898
1600-5767
DOI:10.1107/S1600576718001930