Resonant X-Ray Diffraction: Forbidden Bragg Reflections Induced by Atomic Displacements

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 Pnma with resonant atoms in 4(c) position is discussed in detail.