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Dynamical X-ray diffraction from imperfect crystals: a solution based on the Fokker-Planck equation

Dynamical X-ray diffraction from imperfect crystals: a solution based on the Fokker-Planck equation A stochastic model of crystal defects is incorporated into a Fokker-Planck equation describing dynamical X-ray diffraction from imperfect extended-face crystals. The Fokker-Planck equation is solved by forming a set of complex moments describing the reflectance fluctuations in the crystal. This leads to an infinite set of coupled differential equations that are solved by neglecting high-order moments and numerically integrating the equations. The numerical solutions of X-ray rocking curves from a set of imperfect silicon films show excellent agreement with a Monte Carlo simulation and with a kinematical calculation away from the Bragg peak. The dynamical equations are suitable for describing Bragg diffraction from extended-face crystals containing defects, strain and composition variations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

Dynamical X-ray diffraction from imperfect crystals: a solution based on the Fokker-Planck equation

Dynamical X-ray diffraction from imperfect crystals: a solution based on the Fokker-Planck equation


Abstract

A stochastic model of crystal defects is incorporated into a Fokker-Planck equation describing dynamical X-ray diffraction from imperfect extended-face crystals. The Fokker-Planck equation is solved by forming a set of complex moments describing the reflectance fluctuations in the crystal. This leads to an infinite set of coupled differential equations that are solved by neglecting high-order moments and numerically integrating the equations. The numerical solutions of X-ray rocking curves from a set of imperfect silicon films show excellent agreement with a Monte Carlo simulation and with a kinematical calculation away from the Bragg peak. The dynamical equations are suitable for describing Bragg diffraction from extended-face crystals containing defects, strain and composition variations.

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Publisher
International Union of Crystallography
Copyright
Copyright (c) 1994 International Union of Crystallography
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767393009419
Publisher site
See Article on Publisher Site

Abstract

A stochastic model of crystal defects is incorporated into a Fokker-Planck equation describing dynamical X-ray diffraction from imperfect extended-face crystals. The Fokker-Planck equation is solved by forming a set of complex moments describing the reflectance fluctuations in the crystal. This leads to an infinite set of coupled differential equations that are solved by neglecting high-order moments and numerically integrating the equations. The numerical solutions of X-ray rocking curves from a set of imperfect silicon films show excellent agreement with a Monte Carlo simulation and with a kinematical calculation away from the Bragg peak. The dynamical equations are suitable for describing Bragg diffraction from extended-face crystals containing defects, strain and composition variations.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: Mar 1, 1994

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