We have conducted a series of scattering experiments at the uranium M4 absorption edge on low-symmetry uranium compounds (U2N3 and U3O8) produced as epitaxial films. At weak and forbidden reflections, we find a resonant signal, independent of temperature, with an energy dependence resembling the imaginary part of the scattering factor. Theory, using the FDMNES code, shows that these results can be reliably reproduced assuming that they originate from aspherical 5f electron charge distributions around the U nucleus. Such effects arise from the intrinsic anisotropy of the 5f shell and from the mixing of the 5f electrons of uranium with the outer 2p electrons of the anions. The good agreement between theory and experiment includes azimuthal scattering dependencies, as well as polarization states of the scattered photons. The methodology reported here opens the way for a deeper understanding of the role of the 5f electrons in the bonding in actinide compounds.

The possibilities provided by the use of circularly polarized X rays in transmission and diffraction geometry for studying the properties of noncentrosymmetric crystals (electronic state, optical activity, absolute chirality, and distribution of chiral domains in multiferroics) are considered.

The use of X-ray synchrotron radiation makes it possible to observe the polarization, spectral, and angular dependences for diffraction reflections. Their theoretical study calls for application of a tensor approach to describe the interaction of X-rays with atoms of matter. Various representations of the tensor atomic scattering amplitude, results of experimental observations of the anisotropy of resonant X-ray scattering, and the relationship of the electric and magnetic multipole moments on atoms with the properties of forbidden resonant reflections are considered.

When carrying out experiments on the P23 beamline of the Petra III synchrotron source (Hamburg, Germany), high efficiency of X-ray acoustic longitudinal resonators for accurate time-resolved control of synchrotron radiation parameters using different diffraction reflections, both allowed and forbidden, is demonstrated by an example of a high-quality ТеО 2 resonator. It is shown that the specific features of ultrasonic strain distribution in these resonators are in full agreement with the previously proposed theoretical models.

Many molecules and crystals are chiral, i.e., can exist as right- and left-handed mirror isomers. It is shown that the absolute configuration of monoatomic chiral crystals, including selenium, tellurium, and β-manganese, can be determined using multi-wavelength diffraction of circularly polarized X-ray radiation.

The possibility of controlled variation of the atomic crystal and electronic structures of a paratellurite crystal under the excitation of intense ultrasonic vibrations has been studied. The resonance diffraction of synchrotron radiation has been used for the first time for such a study. The effect of ultrasonic modulation implemented by means of an acoustic standing wave excited in a high-Q ТеО2 resonator on the structure of the forbidden X-ray 100 reflection has been experimentally demonstrated.

When carrying out experiments on the P23 beamline of the Petra III synchrotron source (Hamburg, Germany), high efficiency of X-ray acoustic longitudinal resonators for accurate time-resolved control of synchrotron radiation parameters using different diffraction reflections, both allowed and forbidden, is demonstrated by an example of a high-quality ТеО2 resonator. It is shown that the specific features of ultrasonic strain distribution in these resonators are in full agreement with the previously proposed theoretical models. DOI: 10.1134/S1063774522070173

This work focuses on the validation of a possible connection of the known Ruddlesden-Popper (RP) phases and the novel concept of the migration-induced field-stabilized polar (MFP) phase. To study this subject, model structures of RP phases in bulk strontium titanate are analyzed by means of density functional theory (DFT). The obtained geometries are compared to experimental MFP data. Good agreement can be found concerning atomic displacements in the pm range and lattice strain inferred by the RP phases. Looking at the energy point of view, the defect structures are on the convex hull of the Gibb's free energy. Although the dynamics to form the discussed defect models are not addressed in detail, the interplay and stability of the described defect model will add to the possible structure scenarios within the near-surface region of strontium titanate. As a result, it can be suggested that RP phases generally favor the MFP formation.

Paratellurite TeO 2 crystals under the application of a strong electric field demonstrate significant changes of the shape of allowed reflections, which are associated with the migration of oxygen vacancies to the surface layers [1]. Similar effect was found earlier in strontium titanate SrTiO 3 and got the name of “migration-induced field-stabilized polar phase” [2]. An experiment was carried out at P23 beamline of PETRA III synchrotron, devoted to the study of the changes in the forbidden reflections 002 and 100 in TeO 2 under applied electric field. These reflections are forbidden in conventional X-ray scattering, but can be observed at the energies close to absorption L-edges of Te, due to appearance of dipole-dipole resonant contribution to the atomic factor of Te. The experiment was carried out at the incident radiation energy, close to L 1 edge of Te 4938 eV. For both reflections the azimuthal dependence and energy spectrum were measured with and without application of electric field. For 002 reflection electric field magnitude was 500 and 750 V/mm, for 100 reflection it was 750 and 1050 V/mm. We have observed a change of azimuthal dependence (Fig.1) caused by the violation of a symmetry in electric field in accordance with the predictions of preliminary theoretical calculations. Also we have observed a change of the energy spectrum at the magnitude It is assumed that this change is caused by appearance of oxygen vacancies in the environment of Te. For reflection this change of the energy spectrum was even more obvious. is justified because in this experimental geometry migration of is

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.

Absorption spectra of two orthogonal linearly polarized X-rays in a single CeCoGe3 crystal were measured at the ID12 beamline of the ESRF for the energies near the K-edges of Ge, Co and near the L-23 edges of Ce. The X-ray natural linear dichroism (XNLD) was revealed in the vicinity of all the absorption edges, which indicates a splitting of electronic states in a crystalline field. Mathematical modelling in comparison with experimental data allowed the isotropic and anisotropic parts of atomic absorption cross section in CeCoGe3 to be determined near all measured absorption edges. The calculations also show that the "average" anisotropy of the cross section close to the Ge K-edge revealed in the experiment is less than the partial anisotropic contributions corresponding to Ge atoms in two different Wyckoff positions.

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.

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.

We propose a new method to determine the absolute structure of chiral crystals, which is based on the chiral asymmetry of multiple scattering diffraction. It manifests as a difference in the azimuthal dependence of the forbidden Bragg reflection intensity measured with left and right circularly polarized X-ray beams. Contrary to the existing ones, the suggested method does not use X-ray anomalous dispersion. The difference between the Renninger scans with circularly polarized X-rays has been experimentally demonstrated for the 001 reflection intensities in the right- and left-handed quartz single crystals. A Jmulti-based code on model-independent three-wave-diffraction approach has been developed for quantitative description of our experimental results. The proposed method can be applied to various structures including opaque, organic and monoatomic crystals, even with only light elements. To determine the type of isomer, the Renninger plot of a single forbidden reflection is sufficient.

: 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 TeO 2 single crystals were performed at photon energies close to the L 1 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 f xy of the tensor describing dipole-dipole resonance scattering contributes to the 002 reflection, while two components f xy and f xz 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.

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 componentfxyof the tensor describing dipole-dipole resonance scattering contributes to the 002 reflection, while two componentsfxyandfxzcorrespond 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.

It has been shown that channels of resonant X-ray scattering with a change in polarization can be present in allowed Bragg reflections. The measurement of the energy and azimuthal dependences of Bragg reflections with a change in polarization makes it possible to study resonant diffraction in crystals of symmorphic groups, which are often used to describe the symmetry of functional materials. This can be effectively used to study structural changes in phase transitions or external impacts, as well as to separate contributions to resonant scattering from crystallographically nonequivalent positions of atoms. A sharp increase in the intensity of the scattering of π-polarized radiation into s-polarized radiation has been demonstrated by the simple example of lowering the symmetry of the SrTiO3 crystal as a result of the transition from the cubic phase to the tetragonal one. It has also been shown that the study of the circular X-ray dichroism of Bragg reflections can be used instead of the polarization analysis of scattered radiation.