X-ray spectroscopy of thermally distorted electronic states in crystals

A new type of x-ray spectroscopy is proposed which can detect the thermal-motion-induced distortions of atomic electronic states in crystals. It is shown that those distortions can cause extra Bragg reflections (so-called forbidden reflections) and that their intensity should grow with increasing temperature. The reason is that the thermal displacements, which change the symmetry of atomic environment, can modify the tensor amplitude of x-ray resonant scattering. In the first approximation, the structure factor of extra reflections is proportional to the reflection vector H and to the mean-square thermal displacement <(u(j)u(k))over bar> for optical phonons. It is demonstrated that the forbidden resonant reflections, observed recently in Ge, could be caused by the thermal motion. (C) 1999 American Institute of Physics. [S0021-3640(99)01012-9].