
%0 Journal Article
%A Davis, TJ 
%T Imperfect Crystals and Dynamical X-ray Diffraction in the Complex Reflectance Plane
%J Australian Journal of Physics
%D 1991/10/01
%V 44
%N 6
%P 693-704
%K 
%R https://doi.org/10.1071/PH910693
%U https://www.publish.csiro.au/paper/PH910693 
%X A theoretical framework is developed to describe the dynamical diffraction of X-rays in perfect and imperfect crystals. The propagation of the X-ray beam inside the crystal is described by the evolution of a set of trajectories in the complex reflectance plane. The trajectory path is determined from a form of the Takagi-Taupin equations and leads naturally to simple forms for the crystal reflectivity for perfect crystals. A stochastic model for the effects of crystal defects is developed in terms of the Langevin equation which leads to a description of diffraction from imperfect crystals as the evolution of densities in a parameter space, described by a Fokker-Planck equation. 
