The polarizing spectroscopy techniques in visible range optics have been used since the beginning of the 20th century to study the anisotropy of crystals based on birefringence and optical activity phenomena. On the other hand, the phenomenon of X-ray optical activity has been demonstrated only relatively recently. It is a selective probe for the element-specific properties of individual atoms in non-centrosymmetric materials. We report the X-ray Natural Circular Dichroism (XNCD) imaging technique which enables spatially resolved mapping of X-ray optical activity in non-centrosymmetric materials. As an example, we present the results of combining micro-focusing X-ray optics with circularly polarized hard X-rays to make a map of enantiomorphous twinning in a multiferroic SmFe3(BO3)4 crystal. Our results demonstrate the utility and potential of polarization-contrast imaging with XNCD as a sensitive technique for multiferroic crystals where the local enantiomorphous properties are especially important. In perspective, this brings a novel high-performance method for the characterization of structural changes associated with phase transitions and identification of the size and spatial distribution of twin domains.

Examining forbidden reflections provides valuable information on electronic states and the local environment of resonant atoms in crystals. Experimental studies of two forbidden reflections 002 and 100 in TeO2 single crystals were performed at photon energies close to the L1 tellurium absorption edge. It was found that the spectral form corresponding to these two reflections looks almost identical, which is completely unexpected for a highly anisotropic material. Theoretical consideration shows that only one component fxy of the tensor describing dipole-dipole resonance scattering contributes to the 002 reflection, while two components fxy and fxz correspond to the 100 reflection. Numerical calculations show that the latter tensor component is comparable to the first one, but the combination of several geometric factors leads to the fact that its contribution to the spectrum is negligible. This explains the experimentally observed results. The finding shows a way for targeted investigation of single tensor components and makes it possible to compare different spectra and use them the study the physical phenomena in functional materials.

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Multiple-wave X-ray reflections usually aggravate the measurement of Bragg reflections, especially of weak "forbidden" reflections. Accurate analysis of multiple-wave peaks usually allows to avoid this. However, multiple-wave reflections can also provide information about crystal structure, since crystal cell parameters determine the positions of multi-wave peaks. The forbidden reflections 002 and 100 in paratellurite are measured and an approach based on semi-kinematical X-ray scattering used to handle the multiple-wave interferences is shown here.