A UNIVERSAL TREATMENT OF X-RAY AND NEUTRON-DIFFRACTION IN CRYSTALS .1. THEORY

The reflection power ratio P-H/P-0, transmission power ratio P-T/P-0 a nd absorption power ratio P-A/P-0 for a mosaic crystal plate under asy mmetric Bragg and Laue geometry are obtained by solving power transfer equations employing three dimensionless parameters: an asymmetry fact or b, the ratio xi of the absorption to the scattering cross section, and the reduced thickness A(k) of the crystal. Expressions are given f or the optimum monochromator thickness for asymmetric Laue geometry, a nd the angular dependence of P-H/P-0, P-T/P-0 for Bragg geometry in th e crystals having different xi(0) and A(k0). As a demonstration of the feasibility of this method, the integrated reflection power ratio exp eriment by Mathieson [Acta Cryst. (1975), A31, 769-774] is reanalyzed and good agreement is obtained. The standard formulae for integrated r eflection by a mosaic crystal given in international Tables for X-ray Crystallography [(1972). Birmingham: Kynoch Press] based on the kinema tic approximation are shown to be only the limiting case of the exact solution for xi(0) much greater than 1.