An exact solution in the dynamical diffraction theory of lamellarly distorted crystals

An exact solution of dynamical diffraction was found for a lamellarly distorted infinite crystal. Here the deviation of the lattice spacing was assumed to have the form D₀ tanh αx where the spatial variable x is normal to the net plane concerned. The problem is reduced to solving an ordinary differential equation of second order. The linearly independent solutions (LIS) are represented in a very symmetric manner with the use of the U function defined here. They are essentially hypergeometric functions with three complex parameters which are specified in terms of the diffraction condition and the lattice distortion. The analytical properties of the LIS's and their physical interpretation are described. Rocking curves are calculated for both the Darwin and Ewald cases. The theory can be applied to a variety of monotonic lattice distortions.