A novel method for studying thermal motion and point defects in crystals by X-ray resonant diffraction

After an introductory survey of the X-ray resonant anisotropy, we present a novel X-ray method to observe thermal-motion-induced (TMI) and point-defect-induced (PDI) distortions of electronic states of atoms. This method uses the idea that, in general, the local atomic environment becomes less symmetric owing to point defects and/or the thermal vibrations of the atoms in a crystal. As a result of this phenomenon, an additional anisotropy of the resonant scattering factors can occur and "forbidden" Bragg reflections can be excited near the absorption edges. Examples of crystals are discussed (Ge, Y3Fe5O12) where TMI and PDI reflections can be found. The tensor structure factors of the both types of reflections are calculated. According to our theory, the TMI reflection structure factors are proportional to the vibration correlations, u(parallel to)(2) and u(perpendicular to)(2), of neighboring atoms, and it is inferred that u(parallel to)(2) provides the main contribution to the thermal-motion-induced anisotropy of X-ray resonant scattering. The TMI reflections,in Ge were recently observed by Kokubun et al. (Phys. Rev. B64, 073203 (2001)), Kirfel et al. (in press), and Colella et al. (in press) in accordance with our prediction. For the 006 reflection, the intensity increases about 25 times with the temperature increasing from 30 to 735 K. Owing to their resonant character, the PDI reflections allow to separately study both impurity atoms and host atoms of different types. The considered phenomena can provide a very sensitive method for studying point defects because only the atoms that are affected by defects contribute to the PDI reflections.