Resolution function of an X-ray triple-crystal diffractometer

The resolution function of an X-ray triple-crystal diffractometer is calculated on the assumption that the resolution is controlled by the properties of the monochromating and analysing crystals. The expressions are then evaluated when these crystals have either a mosaic structure or when they are perfect flat crystals with a reflectivity controlled by the Darwin width. Within the Gaussian approximation for the Darwin curve, simple expressions for the resolution are then obtained both for a conventional X-ray source and for an X-ray synchrotron source, although the expressions differ in detail. The expressions are used to discuss the intensity obtained when a triple-crystal diffractometer is used to measure the integrated Bragg reflection intensity, the intensity associated with rods in reciprocal space and the intensity of diffuse scattering.