Dynamical theory of x-ray diffraction in flat, focusing, and distorted crystals by Abelés's matrix method

Results of the standard dynamical theory of x-ray diffraction by Bragg planes parallel to a crystal surface are reproduced using Abel\'es's 2 ×{} 2 matrix method for finding reflection and transmission by layered isotropic structures. In addition to giving a somewhat different insight into the problem this technique can be used to compute reflection and transmission in crystals with varying lattice spacing such as might be formed by thermal or impurity gradients between the surfaces. The method is also used to obtain reflection in point-to-point focusing x-ray monochromators made with ideal elastically curved perfect crystals.