The kinematical theory of X-ray spherical-wave diffraction

It is shown that the Fraunhofer approximation, used in the kinematical theory of X-ray diffraction, may fail for a wide variety of crystals with different perfection. The kinematical theory describing the diffraction pattern in the general case is developed. The case of spherical-wave diffraction by a plane parallel crystal is considered in detail. The intensity distribution and the diffraction line width are ascertained to be essentially dependent on the region of diffraction in which the observation plane is located. On the other hand, the diffraction pattern geometry is independent of the diffraction region and is determined only by the crystal structure and the optics of diffraction. The geometry of the diffraction pattern recorded by the divergent-beam method is analysed in detail.