Research Article: Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid

Date Published: May 01, 2020

Publisher: International Union of Crystallography

Author(s): Folkmar Bornemann, Yun Yvonna Li, Joachim Wuttke.

http://doi.org/10.1107/S2053273320002065

Abstract

To describe multiple Bragg reflection from a thick, ideally imperfect crystal, the transport equations are reformulated in three-dimensional phase space and solved by spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially for finite detectors.

Partial Text

In a preceding paper, designated as Part I (Wuttke, 2014a ▸), multiple Bragg reflection from a thick, ideally imperfect crystal was studied mainly by analytical means. The planar two-ray transport equations of Darwin (1922 ▸) and Hamilton (1957 ▸) were generalized to account for out-of-plane trajectories. Expanding these equations into a recursive scheme led to some asymptotic results, but did not provide a practicable solution algorithm for the generic case with crystals of finite thickness. Reflection probabilities depend strongly on propagation directions, and with each reflection the next reflection probability can vary by orders of magnitude. This makes the transport equations ill conditioned, and straightforward Monte Carlo simulations inefficient and unreliable.

To summarize, we have simplified the transport equation of Part I (Wuttke, 2014a ▸) by making consequential use of energy conservation and projecting everything to the sphere .

 

Source:

http://doi.org/10.1107/S2053273320002065

 

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