The intensity distribution observed with a multi-crystal X-ray diffractometer

Expressions are obtained for the intensity distributions which are observed when Bragg reflections are studied using an X-ray multi-crystal diffractometer. The expressions are obtained for both Bragg and Laue geometry at the sample, and assuming that the monochromator, sample and analyser elements are all perfect crystals. Detailed calculations are made of several configurations with both laboratory-based and synchrotron sources, and the results are compared with experimental measurements. The comparison shows that the theory gives reliable results not only for the half-widths of the distributions, but also for the tails of the distributions resulting from the dynamical effects in one or more of the crystals.