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Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid
- Source :
- Acta Crystallographica. Section A, Foundations and Advances, Acta crystallographica / A Foundations and advances Section A 76(3), 376-389 (2020). doi:10.1107/S2053273320002065
- Publication Year :
- 2020
- Publisher :
- International Union of Crystallography, 2020.
-
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.<br />The generalized Darwin–Hamilton equations [Wuttke (2014 ▸). Acta Cryst. A70, 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.
- Subjects :
- Discretization
010103 numerical & computational mathematics
010403 inorganic & nuclear chemistry
01 natural sciences
Biochemistry
Inorganic Chemistry
Crystal
Structural Biology
Darwin–Hamilton equations
Distortion
General Materials Science
ddc:530
0101 mathematics
Physical and Theoretical Chemistry
Physics
spectral collocation
Mathematical analysis
Solid angle
Bragg's law
Condensed Matter Physics
Transfer matrix
Research Papers
0104 chemical sciences
multiple scattering
Distribution function
Convection–diffusion equation
mosaic crystals
Subjects
Details
- Language :
- English
- ISSN :
- 20532733
- Volume :
- 76
- Issue :
- Pt 3
- Database :
- OpenAIRE
- Journal :
- Acta Crystallographica. Section A, Foundations and Advances
- Accession number :
- edsair.doi.dedup.....4b8a81c410d6f2fe2be8ab0df4d8c19d