Abstract

It is shown that the Darwin equations, which describe the effect of multiple Bragg reflexion in mosaic crystals and have previously been obtained by heuristic arguments, arise naturally in a systematic solution of the neutron transport equation. With a method similar to that developed for calculating multiple-scattering corrections for neutron inelastic scattering in liquids, an approximate expression for the secondary extinction factor is obtained, which is applicable to a crystal of arbitrary size and shape. The results are compared with exact results for a plane slab, with Hamilton's Acta Cryst. (1963), 16, 609-611 results for a cylinder and with Becker & Coppens's Acta Cryst. (1974), A30, 129-147 results for a sphere.