Temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals

This paper reports temperature- and energy-dependent phase shifts of resonant multiple-beam X-ray diffraction in germanium crystals, involving forbidden (002) and weak (222) reflections. Phase determination based on multiple-beam diffraction is employed to estimate phase shifts from (002)-based {(002)(375)(373̅)} four-beam cases and (222)-based { (222)(5̅33̅)} three-beam cases in the vicinity of the Ge K edge for temperatures from 20 K up to 300 K. The forbidden/weak reflections enhance the sensitivity of measuring phases at resonance. At room temperature, the resonance triplet phases reach a maximum of 8° for the four-beam cases and -19° for the three-beam cases. It is found that the peak intensities and triplet phases obtained from the (002) four-beam diffraction are related to thermal motion induced anisotropy and anomalous dispersion, while the (222) three-beam diffraction depends on the aspherical covalent electron distribution and anomalous dispersion. However, the electron-phonon interaction usually affects the forbidden reflections with increasing temperatures and seems to have less effect on the resonance triplet phase shifts measured from the (002) four-beam diffraction. The resonance triplet phase shifts of the (222) three-beam diffraction versus temperature are also small.