On the divergence of rays Bragg diffracted by perfect stationary crystals illuminated with collimated polychromatic radiation

The properties of three diffraction geometries, viz symmetric Bragg-case reflection from a crystal surface, symmetric Laue-case transmission through a parallel-sided crystal and asymmetric Bragg-case reflection from a crystal surface, have been examined under the conditions that the crystal (which is assumed to be perfect) is held in fixed orientation relative to an ideally collimated incident beam of white X-rays. Symmetric Bragg-case reflection has the valuable property of invariant direction of reflected rays for all orders of reflection excited, and for strong and weak reflections alike. For the symmetric Laue case, and for the asymmetric Bragg case approximately, for small asymmetry, expressions are given for the angular range of diffracted rays, scaled in terms of the extinction distance of the reflection concerned. The findings have practical applications in the design and interpretation of continuous-radiation topographic experiments.