E.N. Ovchinnikova

Resonant X-ray diffraction: `forbidden' Bragg reflections induced by thermal vibrations and point defects

In general, the local atomic environment becomes less symmetric owing to point defects and thermal vibrations of atoms in crystals. It is shown that, as a result of this phenomenon, an additional anisotropy of the resonant scattering factors can occur and the forbidden Bragg reflections can be excited near absorption edges. Examples of crystals are presented (Ge, K2CrO4, C-15 type) where such thermal-motion-induced (TMI) and point-defect-induced (PDI) reflections can be observed. The tensor structure factors of both types of reflection are computed. Owing to their resonant character, the PDI reflections allow both impurity atoms and host atoms of different types to be studied separately. The considered phenomena can provide a very sensitive method to study point defects because only the atoms distorted by defects produce contributions to the PDI reflections.

Chirality-induced 'forbidden' reflections in X-ray resonant scattering

It is shown that additional Bragg reflections can appear exclusively owing to the local chirality associated with the left-right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these reflections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole-quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail (alpha-Fe2O3, LiNbO3 etc.). For instance, the interference between the dipole-quadrupole and quadrupole-quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, reflections observed recently in hematite.

X-ray spectroscopy of thermally distorted electronic states in crystals

AbstractA new type of x-ray spectroscopy is proposed which can detect the thermal-motion-induced distortions of atomic electronic states in crystals. It is shown that those distortions can cause extra Bragg reflections (so-called forbidden reflections) and that their intensity should grow with increasing temperature. The reason is that the thermal displacements, which change the symmetry of atomic environment, can modify the tensor amplitude of x-ray resonant scattering. In the first approximation, the structure factor of extra reflections is proportional to the reflection vector H and to the mean-square thermal displacement

Combined effects of magnetic structure and local crystal fields in anisotropic X-ray anomalous scattering

\overline {u_j u_k }

Numerical simulation of experimental resonance absorption spectra and diffraction of synchrotron radiation in yttrium iron garnet

for optical phonons. It is demonstrated that the forbidden resonant reflections, observed recently in Ge, could be caused by the thermal motion.

Absolute Intensity and Phase of the Resonant X-ray Scattering from a Germanium Crystal

Three experimental techniques sensitive to the sign of the Dzyaloshinskii-Moriya interaction are discussed: neutron diffraction, Mössbauer γ-ray diffraction, and resonant x-ray scattering. Classical examples of hematite (α-Fe2O3) and MnCO3 crystals are considered in detail.

Investigation of X-Ray Natural Circular Dichroism in a CsCuCl 3 Single Crystal: Theory and Experiment

The X-ray extinction conditions are studied for the cases when both magnetic interaction and crystalline fields cause the anisotropy of X-ray scattering amplitudes near the absorption edge. It is demonstrated that the simultaneous existence of those two anisotropies, referred to as the combined anisotropy, can result in excitation of additional Bragg reflections otherwise forbidden by extinction rules. To show this, the structure amplitudes of reflections are computed and two Laue (L) groups are compared: one, L m , which corresponds to the anomalous X-ray scattering in the presence of magnetic structure and another one, L g , which takes into account the anisotropic atomic environment. Both groups can contain additional reflections and differ from the Laue group, L p , associated with the usual potential X-ray scattering. The cross of these groups is considered and it is shown that several extinctions, typical for the L P group, still remain in L q and L m . Nevertheless, the new reflections may appear instead of those extinctions when the combined anisotropy is taken into account. In this case, the diffraction pattern is characterized by the L C group. Then, the transformation of L q into L C under the phase transition is studied. It is shown that the additional reflections, not typical for L m , can appear in the diffraction pattern below the magnetic ordering temperature T M . Two cases are discussed: (i) L q above T M contains the same reflections as L C and (ii) L q contains the extinctions corresponding to the additional reflections in L C . Several examples are considered for real magnetic crystals.

X-Ray Natural Circular Dichroism in Langasite Crystal at the Ga and La Edges

We discuss how measurements of x-ray circular intensity differentials (XCIDs) could be used to probe the Voigt-Fedorov vector part of optical activity (OA) due to electric dipole-electric quadrupole (E 1E 2) interferences. The first experiment was carried out on a single crystal of zincite (hexagonal ZnO: class 6mm). XCID spectra were recorded in the x-ray resonant diffraction regime near the Zn K edge using the (300) reflection at Bragg angles near 45°. In the x-ray range, the effective operator responsible for the vector part of OA can be assigned to the vector product \mathbf {L} \times {\bOmega }_{L}-{\bOmega }_{L} \times {\mathbf {L}} \propto {\mathbf {n}} , in which L and ΩL are time-reversal odd operators associated with the orbital angular momentum and the orbital anapole respectively, whereas n is a true time-reversal even electric dipole. This is consistent with the pyroelectric properties of zincite crystals.