Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals
Abstract
The nonstandard theory of X-ray scattering in a deformed crystal has been generalized. The vector of atomic-plane displacement is introduced into the crystal polarizability model like in the generalized Takagi dynamic theory. The solution to the wave equation is sought for using the procedure of expanding the field amplitude and vector operators in the Fourier components of polarizability χ{sub H} in a series according to the multiscale method. It is shown that considering lattice strain generally calls for introducing various characteristic spatial regions for the diffraction equation, which is in complete agreement with the main concept of the multiscale method. A particular case of a strain field depending on one scale is considered. If a relative change in strain occurs at a length on the order of the extinction length, one can obtain equations generalizing the Takagi equations to the case of arbitrary diffraction geometries.
- Authors:
- Kabardino-Balkarian State University (Russian Federation)
- Publication Date:
- OSTI Identifier:
- 22311421
- Resource Type:
- Journal Article
- Journal Name:
- Crystallography Reports
- Additional Journal Information:
- Journal Volume: 58; Journal Issue: 7; Other Information: Copyright (c) 2013 Pleiades Publishing, Inc.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7745
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICAL METHODS AND COMPUTING; CRYSTALS; MATHEMATICAL SOLUTIONS; POLARIZABILITY; WAVE EQUATIONS; X-RAY DIFFRACTION
Citation Formats
Dyshekov, A. A., E-mail: dyshekov@yandex.ru. Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals. United States: N. p., 2013.
Web. doi:10.1134/S1063774513070067.
Dyshekov, A. A., E-mail: dyshekov@yandex.ru. Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals. United States. https://doi.org/10.1134/S1063774513070067
Dyshekov, A. A., E-mail: dyshekov@yandex.ru. 2013.
"Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals". United States. https://doi.org/10.1134/S1063774513070067.
@article{osti_22311421,
title = {Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals},
author = {Dyshekov, A. A., E-mail: dyshekov@yandex.ru},
abstractNote = {The nonstandard theory of X-ray scattering in a deformed crystal has been generalized. The vector of atomic-plane displacement is introduced into the crystal polarizability model like in the generalized Takagi dynamic theory. The solution to the wave equation is sought for using the procedure of expanding the field amplitude and vector operators in the Fourier components of polarizability χ{sub H} in a series according to the multiscale method. It is shown that considering lattice strain generally calls for introducing various characteristic spatial regions for the diffraction equation, which is in complete agreement with the main concept of the multiscale method. A particular case of a strain field depending on one scale is considered. If a relative change in strain occurs at a length on the order of the extinction length, one can obtain equations generalizing the Takagi equations to the case of arbitrary diffraction geometries.},
doi = {10.1134/S1063774513070067},
url = {https://www.osti.gov/biblio/22311421},
journal = {Crystallography Reports},
issn = {1063-7745},
number = 7,
volume = 58,
place = {United States},
year = {Sun Dec 15 00:00:00 EST 2013},
month = {Sun Dec 15 00:00:00 EST 2013}
}