Resonant X-ray diffraction: `forbidden' Bragg reflections induced by thermal vibrations and point defects

In general, the local atomic environment becomes less symmetric owing to point defects and thermal vibrations of atoms in crystals. It is shown that, as a result of this phenomenon, an additional anisotropy of the resonant scattering factors can occur and the forbidden Bragg reflections can be excited near absorption edges. Examples of crystals are presented (Ge, K₂CrO₄, C-15 type) where such thermal-motion-induced (TMI) and point-defect-induced (PDI) reflections can be observed. The tensor structure factors of both types of reflection are computed. Owing to their resonant character, the PDI reflections allow both impurity atoms and host atoms of different types to be studied separately. The considered phenomena can provide a very sensitive method to study point defects because only the atoms distorted by defects produce contributions to the PDI reflections.