The geometry of X-ray multiple diffraction in crystals

A derivation of the geometrical distribution of multiply diffracted X-ray beams in single crystals is presented. Included is a brief survey of the geometrical and analytical methods, with some new concepts and constructions, which are useful in the interpretation and prediction of X-ray multiple diffraction phenomena. Applications include the analysis of Kossel patterns, calculation of angles of diffraction, and precision determination of lattice parameters and wavelengths, for which appropriate formulae and procedures are given.