X-ray diffraction in perfect t x l crystals. Rocking curves

A general formalism, based on the Takagi-Taupin equations, for calculating rocking curves in perfect tx I crystals is presented. It includes nonsymmet rical scattering, refraction, and ordinary and anomalous absorption. t and l may be varied independently. In the limit of a semi-infinite crystal, the standard results from the fundamental theory are retrieved. For crystal di mensions less than the extinction length, the theory converges to the kinem atical limit. Simulations for germanium and silicon show significant influe nce of crystal finiteness. When dynamical effects are prominent, the curves exhibit various degrees of asymmetry and the full width at half-maximum is generally larger than the corresponding Darwin width. This is attributed t o combined Laue and Bragg contributions which are shifted with respect to e ach other owing to refraction.