Ab initio calculations of the forbidden Bragg reflections energy spectra in wurtzites versus temperature

Thermal-motion induced (TMI) scattering is caused by the influence of atomic displacements on electronic states in crystals and strongly depends on temperature. It corresponds to dipole-dipole resonant x-ray scattering, but is usually accompanied by dipole-quadrupole scattering. The phenomenological theory supposes the dipole-quadrupole term to be temperature independent (TI). As a result, the transformation of the energy spectra with temperature observed experimentally in ZnO and GaN corresponds to the interference between the TMI and TI terms. In the present paper the direct confirmation of this theoretical prediction is given. Ab initio molecular dynamics was used to simulate the sets of atomic sites at various temperatures followed by quantum mechanical calculation of resonant Bragg reflection energy spectra. The results of simulation are in excellent coincidence with experimental energy spectra of forbidden reflections and confirm the earlier phenomenological conjecture about the interference between the TI dipole-quadrupole and TMI dipole-dipole contributions to the resonant atomic factor.