# Dynamical theory of X-ray diffraction in crystals with defects

Dynamical theory of X-ray diffraction in crystals with defects Sets of integral equations are obtained that describe the X-ray diffraction in defective crystals. A simple description of defects is suggested both for weakly and strongly distorted regions. In the case of ideal crystals, the solution for the wave fields with arbitrary incident beam distribution is given for crystals of arbitrary thickness. For distorted crystals, the integral equations give the universal method of treatment of both weakly and strongly distorted regions. The problem of image determination from strongly distorted regions is reduced to the solution of a simple one-dimensional integral equation. The first iteration approximation of initial integral equations is shown to give results similar to those of a Fourier analysis method with the defect being treated as a small perturbation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography International Union of Crystallography

# Dynamical theory of X-ray diffraction in crystals with defects

, Volume 27 (5): 421 – Sep 1, 1971

## Dynamical theory of X-ray diffraction in crystals with defects

, Volume 27 (5): 421 – Sep 1, 1971

### Abstract

Sets of integral equations are obtained that describe the X-ray diffraction in defective crystals. A simple description of defects is suggested both for weakly and strongly distorted regions. In the case of ideal crystals, the solution for the wave fields with arbitrary incident beam distribution is given for crystals of arbitrary thickness. For distorted crystals, the integral equations give the universal method of treatment of both weakly and strongly distorted regions. The problem of image determination from strongly distorted regions is reduced to the solution of a simple one-dimensional integral equation. The first iteration approximation of initial integral equations is shown to give results similar to those of a Fourier analysis method with the defect being treated as a small perturbation.

/lp/international-union-of-crystallography/dynamical-theory-of-x-ray-diffraction-in-crystals-with-defects-Ih0X0laF0u
Publisher
International Union of Crystallography
Copyright (c) 1971 International Union of Crystallography
ISSN
0567-7394
DOI
10.1107/S0567739471000962
Publisher site
See Article on Publisher Site

### Abstract

Sets of integral equations are obtained that describe the X-ray diffraction in defective crystals. A simple description of defects is suggested both for weakly and strongly distorted regions. In the case of ideal crystals, the solution for the wave fields with arbitrary incident beam distribution is given for crystals of arbitrary thickness. For distorted crystals, the integral equations give the universal method of treatment of both weakly and strongly distorted regions. The problem of image determination from strongly distorted regions is reduced to the solution of a simple one-dimensional integral equation. The first iteration approximation of initial integral equations is shown to give results similar to those of a Fourier analysis method with the defect being treated as a small perturbation.

### Journal

Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General CrystallographyInternational Union of Crystallography

Published: Sep 1, 1971