Thermal-motion-induced resonant reflections at the Ge K-edge: calculation of the intensity dependence on atomic displacements

Abstract

In the Ge-structure, the forbidden Bragg reflections hk0 (h + k = 4n + 2) can be excited at the Ge K-edge due to both dipole-quadrupole scattering and dipole-dipole scattering of thermally vibrating atoms. The dipole-dipole contribution is referred to as TMI (Thermal Motion Induced) and is caused by the dependence of the atomic tensor form factors on the relative atomic displacements. This effect explains the strong increase of the 600 forbidden reflection intensity with temperature observed in experiments. In the present paper, both the dipole-quadrupole and the TMI contributions to the structure factor of the 600 reflection are calculated using the FDMNES code. Two models are considered, one assuming only displacements of the scattering atom, the other assuming all atoms in a supercell randomly displaced. Both approaches reveal a strong dependence of the dipole-dipole contribution to the tensor atomic factor on the atomic displacements and thus give a qualitative explanation of the temperature behavior of the forbidden reflection 600 observed in Ge.