Helicity-dependent resonant X-ray scattering in CuB2O4.

Exploitation of X-ray circular polarized beams to study forbidden Bragg reflections and new information that could be obtained in these experiments are discussed. It is shown that the intensities of such reflections can be different for the right- and left-circular polarizations (i.e. exhibiting circular dichroism) even for the dipole-dipole resonant transitions involved in the scattering process. This difference can be observed only in crystals having no center of inversion. Here, this approach is used to study helicity-dependent resonant diffraction in copper metaborate CuB2O4 single crystal, which is non-centrosymmetric but achiral. Nonetheless, a strong circular dichroism has been observed for hh0 forbidden reflections in the vicinity of the Cu K-edge. This effect is shown to originate from dipolar transitions in Cu atoms occupying the 8(d) Wyckoff position only.

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.

Numerical simulation of the forbidden Bragg reflection spectra observed in ZnO.

Thermal motion induced (TMI) scattering is a unique probe of changes in electronic states with atomic displacements in crystals. We show that it provides a novel approach to extract atomic correlation functions. Using numerical calculations, we are able to reproduce the temperature-dependent energy spectrum of the 115 'forbidden' Bragg reflection in ZnO. Our previous experimental studies showed that the intensity growth of such reflections over a wide range of temperatures is accompanied by a dramatic change in the resonant spectral lineshape. This is the result of the interplay between the temperature-independent (TI) and temperature-dependent TMI contributions. Here, we confirm that the TI part of the resonant structure factor can be associated with the dipole-quadrupole contribution to the structure factor and show that the temperature-dependent part arises from the zinc and oxygen vibrations, which provide additional temperature-dependent dipole-dipole tensor components to the structure factor. By fitting the experimental data at various temperatures we have determined the temperature dependences of autocorrelation and correlation functions.