Revisiting La0.5Sr1.5MnO4 lattice distortion and charge ordering with multi-beam resonant diffraction.

Sinusoidal wave type distortions of La0.5Sr1.5MnO4 in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction (MRXD) with (7/4 7/4 0) fractional primary diffraction. Two four-beam diffractions with opposite asymmetry were measured at 6.5545 keV and compared with the curves simulated by the dynamical X-ray diffraction theory. This approach provides the possibility of resolving the distortion modes which are perpendicular to the momentum transfer by a single azimuthal scan. The paper also demonstrates the sensitivity of MRXD profiles versus incident X-ray energy in the vicinity of the Mn K edge to the charge disproportion between the two manganese sites, reconfirming the small charge disproportion feature.

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.