Resonant X-ray diffraction in incommensurately modulated crystals. Symmetry consideration of anisotropic anomalous scattering

Symmetry restrictions on the intensities and polarization properties of main reflections and their satellites are found for incommensurately modulated crystals in the case of anisotropic anomalous X-ray diffraction near absorption edges. It is shown that the modulation becomes a source of additional anisotropy for each resonant scatterer and induces a modulated behaviour of the susceptibility tensor. The four-dimensional approach is used to calculate the set of possible reflections. It is found that additional (`forbidden') reflections may appear both in the system of main reflections and in the system of satellites. The anisotropy also results in complex azimuthal and polarization properties of each reflection. The displacive modulation is discussed in detail. The ATS reflections corresponding to the resonant X-ray diffraction near the K-edge of iron in pyrrhotite-5.5C are considered.