X-ray scattering by crystals with local lattice rotation fields

X-ray (or neutron) scattering by crystals with local rotation fields arising from dislocations is treated on the basis of the formalism of the kinematical diffraction theory. Such fields mostly change the intensity distribution of reflections in the azimuthal plane. Scattering intensity in the azimuthal plane for crystals with one or two sets of different-type dislocation walls, causing local rotations in the lattice, is analysed. In this case the intensity distribution is close to Lorentzian in the radial direction and to Gaussian in the azimuthal direction. The expressions for the scattering intensity are valid when averaging over a large statistical ensemble of defects. If this condition is not fulfilled, the intensity distribution in the azimuthal plane will split into several spikes. The mean distance between these spikes in the reciprocal-lattice space is connected with the disorien­tation between the walls. The conditions necessary for such splitting of the reflection into spikes are considered. The values of the limiting disorientation angle for some common scattering volumes and distances between dislocation walls are evaluated.