In the general context of the history of the origin of X-ray diffraction analysis in Russia, an interesting episode of the early stage of domestic X-ray structural studies—recording of “hole photographs” by Professor Lebedev of Moscow University in 1896, which can be interpreted as diffractograms of crystals—is highlighted. In authors’s opinion, specifically this scientific result is the starting point of the development of experimental X-ray methods of studying the crystal structure in Russia. Due to this, P.N. Lebedev can be considered as the inspirer of the famous pioneer scientific works of G.V. Wolf and N.E. Uspenskii in this area.

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.

An essay on the 100-year history of the formation and development of the Department of X-ray Diffraction Analysis, subsequently transformed into the Department of Solid State Physics of the Faculty of Physics of Moscow State University, is presented.

The specular reflection of X rays from multilayer crystal structures on the surface of a single crystal under conditions of grazing noncoplanar diffraction is considered. Recurrent relations of a new type are obtained. A high sensitivity of the angular dependence of the specular reflection intensity in the diffraction region to the thickness and number of layers, their deformation, and degree of amorphization is shown.

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.

Some specific features of synchrotron X-ray absorption and scattering in matter are considered as a basis for the methods of studying the electronic, magnetic, phonon, and structural properties of condensed media. Their theoretical description is given within the quasirelativistic approximation of the Dirac equation. This makes it possible not only to describe the experimentally observed phenomena, but also to predict new spin-position effects in resonant scattering.

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.

New spin-dependent components of the cross sections for nonresonant and resonant X-ray scattering by atoms of matter have been found using quasi-relativistic expansion of the Dirac Hamiltonian in the Foldy–Wouthuysen representation. Spin-dependent components of resonant scattering, which are maximum at the K -absorption edge in magnetic materials, contain information about the spin density of p states in the continuous spectrum of material atoms.

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.

: 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.

Analytical expressions are found that in the most general form describe the space–time distribution of the thermal field in an anisotropic crystal during heat exchange with the environment under the influence of synchrotron X-ray radiation or X-ray free-electron laser pulses with an arbitrary space-time structure.

The problem of transmission and reflection of X-rays (0.1 Å ≤ λ ≤ 10 Å) from an infinite amorphous homogeneous wedge-shaped dielectric plate has been analytically solved. The obtained solution is a “zero” step in solving the problem of X-ray diffraction on a semi-infinite amorphous homogeneous dielectric wedge within the heuristic geometric diffraction theory.

The features of the technique of resonant synchrotron-radiation (SR) diffraction are considered. The energy, angular, polarization, and temperature dependences of Bragg reflections at incident radiation energies that are close to the absorption edges of material atoms are studied using this technique. These dependences contain information about the electronic, magnetic, and structural features of the objects under study. The contribution of several scattering channels to the formation of the diffraction spectrum leads to the appearance of interference effects making it possible to obtain information about the scattered radiation phase. Results of some studies of resonant SR diffraction performed at the Kurchatov SR source are presented.

Optical activity in the X-ray range stems from the electric-dipole-electric-quadrupole interference terms mixing multipoles of opposite parity, and can be observed exclusively in systems with broken inversion symmetry. The gyration tensor formalism is used to describe the X-ray optical activity in langasite La3Ga5SiO14 crystal with the P321 space group. An experimental study of the X-ray natural circular dichroism (XNCD) near the Ga K-edge in La3Ga5SiO14 single crystal was performed at ESRF beamline ID12, both along and perpendicular to the crystal optical axis. The combination of the quantum mechanical calculations and high-quality experimental results has allowed us to separate the contributions into X-ray absorption and XNCD spectra of Ga atoms occupying three distinct Wyckoff positions.