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'Forbidden' reflections are observed in synchrotron radiation diffraction when the energy of incident radiation is close to the absorption edges in crystals. In the present paper, a new method for calculating the intensity of thermal-motion-induced forbidden reflections is proposed. It includes two steps: simulation of the temporary atomic displacements with the help of the ab initio molecular dynamics followed by quantum-mechanical calculations of the resonant scattering amplitude for various configurations. This technique is applied to the calculation of the 600 reflection thermal behavior in Ge and gives an adequate quantitative fitting of experimental data. The proposed simulation method of the thermal-motion-induced forbidden reflections is suitable for any crystal structure and promises to explain many results obtained up to now in synchrotrons., UDC 539.26 Introduction Resonant X-ray diffraction has emerged in the last two decades as a powerful method for studying structural and magnetic properties of crystals (17), (20), (28), (36), (49). [...]

The displacements of atoms from their equilibrium sites with high symmetry are accompanied by the appearance of the additional components of the resonant susceptibility tensor and become a source of additional anisotropy of resonant X-ray scattering. As a result, forbidden Bragg reflections can appear near absorption edges, which are absent far from the edges in a regular crystal. These reflections can be induced by dynamic thermal atomic vibrations or by static displacements because of modulation and point defects. A theoretical approach is suggested that allows the calculation of the susceptibility tensor and a set of forbidden reflections, in the case of small atomic displacements. This approach is based on the calculation of the displacements using the mechanic representation of space groups. The example of a space group Prima with resonant atoms in 4(c) position is discussed in detail. [ABSTRACT FROM AUTHOR]

Focuses on chirality-induced forbidden reflections or anisotropy of the tensor of the susceptibility in X-ray resonant scattering. Structure amplitudes of Bragg reflections; Distinction between the global anisotropy/chirality of a crystal and the local atomic anisotropy/chirality accessible only via X-ray diffraction.

Studies the Bragg reflections induced by thermal vibrations and point defects. Tensor structure factors of thermal-motion-induced and point-defect-induced reflections; Occurrence of anisotropy of the tensor susceptibility reflections in non-magnetic crystals.

Examines resonant X-ray scattering in the presence of several anisotropic factors. Different phenomenological approaches used to obtain the explicit form of the susceptibility tensor; Coexistence between charge and orbital ordering with anisotropy of local atomic environment and magnetic ordering.

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. [ABSTRACT FROM AUTHOR]