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Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid
Author(s) -
Bornemann Folkmar,
Li Yun Yvonna,
Wuttke Joachim
Publication year - 2020
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273320002065
Subject(s) - reflection (computer programming) , discretization , bragg's law , grid , crystal (programming language) , distortion (music) , matrix (chemical analysis) , mathematical analysis , optics , physics , mathematics , geometry , materials science , diffraction , computer science , amplifier , optoelectronics , cmos , composite material , programming language
The generalized Darwin–Hamilton equations [Wuttke (2014). Acta Cryst . A 70 , 429–440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two‐ray Darwin–Hamilton equations are obtained as a first‐order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially if the detector only covers a finite solid angle.