According to the adiabatic approximation, the electronic states of atoms in solids are bound up with thermal atomic motion. As a result, thermal-motion-induced ͑TMI͒ anisotropy of x-ray susceptibility can appear for atoms occupying positions with high symmetry. We report evidence for this effect found in the very strong temperature dependence of the 006 forbidden Bragg reflections from a germanium single crystal. The intensity of these reflections increases or decreases drastically as the temperature rises from 30 K to 300 K, in contrast with nonforbidden reflections. It is found that the TMI anisotropy of the structure amplitude scales with the temperature as the mean square of the atomic displacements. This observation is very important for understanding the intricate interplay between phonon and electronic properties of solids. Forbidden x-ray reflections, excited exclusively owing to anisotropy of the atomic susceptibility, can be observed in crystals near x-ray absorption edges. Such reflections are referred to as ATS ͑anisotropy of the tensor of susceptibility͒ reflections. The ATS can violate the glide-plane and screwaxis selection rules for forbidden reflections so that most of them become nonforbidden. The physical reason for this violation is that the anisotropic susceptibility is not invariant under rotations and mirror transformations. The ATS is related to electronic resonant transitions and is caused by distortions of the electronic states in an anisotropic environment. Therefore reflections of this type provide direct evidence for the distortions of electronic states in crystals.Up to now much effort has been spent to study the dynamic changes of the electronic states during thermal motion, phase transitions, or chemical reactions in solids ͑there is no need to explain the evident importance of such studies͒. However, those changes are hardly accessible even with ultrafast optical techniques and the optical probes are often poor indicators of atomic structure. By contrast the x-ray technique developed here, based on ATS reflections, is an effective structural probe sensitive to dynamic changes of local atomic environments. Of course, the time evolution of the distortions cannot be measured in our experiments.ATS reflections have been observed in a NaBrO 3 cubic crystal near the K edge of the Br atoms. 1 Then they were studied for many crystals: TiO 2 , 2 Cu 2 O, 2 Fe 2 O 3 , 3 etc., and even for liquid crystals. 4 The theory of these reflections was developed first in the dipole approximation 5 and then in higher approximations. 6 It was shown recently that ATS reflections can be excited owing to the orbital ordering in colossal magnetoresistance materials, manganites and vanadite. 7-9 Earlier we studied the ATS scattering from Fe atoms, in pyrite 10 (FeS 2 ) and magnetite 11 (Fe 3 O 4 ), where the iron atoms are surrounded by slightly distorted octahedra of sulfur and oxygen atoms, respectively ͑see also a very recent study of magnetite. 12 ͒ The polarization and azimuthal dependences of the measu...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.