X-ray diffraction peak profiles were calculated, using the Monte Carlo method, for arbitrarily correlated dislocations without making any approximations or simplifications. The arrangement of dislocations in pairs with opposite Burgers vectors provided screening of the long-range strains. Moreover, any screening could be modelled by an appropriate distribution of the dislocation pairs. An analytical description of the peak profiles was compared with the Monte Carlo results. Symmetrical peaks due to screw dislocations and asymmetrical peaks due to edge dislocations were simulated and analyzed. The kinematic X-ray diffraction theory permitted the calculation of the scattered intensity for a crystal with any distribution of defects and their displacement fields. However, practical calculation required averaging over statistics of the defect distribution and spatial integration. Both integrations could be performed simultaneously by using the Monte Carlo method. The powder average over crystal orientations, as well as the intensity integration over a wide-open detector in double-crystal diffraction from a single crystal, reduced the spatial integration to a one-dimensional integral. In this case, the spatial integration could be performed via standard quadratures, while the statistical averaging was performed using Monte Carlo integration. This was done in the present work. Monte Carlo calculations included essential features of the experiment. The dislocations were distributed at random over a volume large enough to exclude finite-size effects. In these calculations, the number of dislocations in the simulated sample ranged from hundreds to tens of thousands; depending upon the correlation length of the dislocation distribution. The correlation function was calculated for separations much smaller than the sample size but large enough to reveal the whole diffuse scattering pattern.

X-Ray Diffraction Peaks From Correlated Dislocations: Monte Carlo Study of Dislocation Screening. V.M.Kaganer, K.K.Sabelfeld: Acta Crystallographica A, 2010, 66[6], 703-16