Refraction in general asymmetric X-ray Bragg diffraction.

When the surface of a single-crystal monochromator is not parallel to the diffracting crystallographic planes, the diffracted beam is generally deviated from the plane of diffraction and the angle between the diffracted beam and the diffracting planes is different from the angle between the incident beam and the diffracting planes. The angular diffraction regions for the incident and diffracted beams are also different. This is the manifestation of the refraction occurring during Bragg diffraction. Very simple formulae are presented which describe this situation in a general case (e.g. for a rotated-inclined X-ray monochromator). These formulae allow sagittally focusing monochromators for synchrotron radiation to be easily designed, based on X-ray diffraction-refraction phenomena. Some important properties of such types of monochromators are deduced.