A stochastic model of crystal defects was incorporated into a Fokker-Planck equation which described dynamic X-ray diffraction from imperfect extended-face crystals. The Fokker-Planck equation was solved by forming a set of complex moments which described reflectance fluctuations in the crystal. This led to an infinite set of coupled differential equations that was solved by neglecting high-order moments and by numerically integrating the equations. The numerical solutions of X-ray rocking curves, from a set of imperfect Si films, yielded excellent agreement with a Monte Carlo simulation and with a kinematic calculation, away from the Bragg peak. The dynamic equations were suitable for describing Bragg diffraction from extended-face crystals which contained defects, strain and compositional variations.

T.J.Davis: Acta Crystallographica, 1994, A50[2], 224-31