SPHERICAL WAVE APPROACH TO ELECTRON FOCUSING PROCESSES IN EXAFS

A novel method based on the spherical wave formalism is presented to account the low-angle electron scattering processes in EXAFS. The usually used plane wave approximation is shown to be inappropriate when the electron forward scattering should be accounted. The developed formulae are used to obtain X-ray absorption spectra (XAS) of some crystals

CRYSTAL POTENTIAL AND SIZE EFFECTS IN XANES K-SPECTRA OF ALKALI HALIDES

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Interpretation of Pre-Edge Fine Structures (PEFS) of K Edge of Vanadium in VOPO4, 2H2O

A method based on the local density approximation and on the multiple scattering wave calculation taking into account screened X-ray core hole potential for the final state has been used to analyze the experimental XANES spectra of the VOPO4.2H2O xerogel. The effect of cluster size on the computations has been analyzed concluding that the pre-edge depends only on the first shell formed by the six nearest oxygen atoms. In VOPO4.2H2O structure, the absorbing VO6 octahedron is surrounded by PO4 tetrahedra. Thus VO6 octahedra are not linked with each other excluding solid state effect in the pre-edge region. In contrast, edge region is sensitive to the cluster size. Computations show that at least a cluster of V5P4O26 must be taken into account to reproduce, in rather good agreement, the edge part of the absorption spectrum

Interpretation of Pre-Edge Fine Structures (PEFS) of K Edge of Titanium in Rutile TiO2

A method based on the local density approximation and on the multiple scattering wave calculation taking into account screened X-ray hole potential for the final state has been used to analyze the experimental XANES spectra of the TiO2 rutile. The effect of cluster size on the computations has been analyzed concluding that taking into account atoms forming all neighboring octahedra lead to a reasonable agreement between theoretical and experimental spectra. In the crystal structure containing only slightly distorted regular octahedra in ground state, only two peaks corresponding to 1 s -> t2g and eg transitions are obtained. In contrast, due to the effect of the core hole potential calculated self consistently, the locally projected 3d density (DOS) is shifted down by about 3 eV giving rise to quadrupole transition. The 3d DOS arising from neighboring octahedra is not shifted by the core hole potential and contains non-centrosymmetric wave functions arising from solid state effect giving rise to dipole transitions. Temperature vibrations of atoms decrease the symmetry of the system thus making dipolar transitions to t2g and eg of absorbing octahedron allowed, this increases the intensities of the two first peaks A1 and A2 in the pre-edge region

Pre-Edge Fine Structure (PEFS) of the K-XAS for the 3d Atoms in Compounds: A New Tool for Quantitative Atomic Structure Determination

The two mechanisms are shown to be mainly responsible for the formation of the K-XAS PEFS for the 3d-atoms in the compounds: p-d mixture (PDM) which makes allowed the ls-electron transitions to the absorbing atom 3d-states influenced by the screened hole potential and the ls-electron transitions to the unoccupied 3d-states of the neighbouring atoms. The intensities of the PDM induced peaks strongly depend on the displacement of the absorbing atom from the center of inversion symmetry and on the X-ray polarization vector e direction. Taking into account this dependence and employing the experimental Ti K-XAS for the PbTi03 monocrystal measured for different temperatures and directions of the vector e the ferroelectric phase transition in this crystal has been studied

Resonant diffraction in FeS2: Determination of the x-ray polarization anisotropy of iron atoms.

For pyrite, FeS2, both the imaginary and real parts of the anisotropy of the iron atomic scattering factor are experimentally determined as functions of the x-ray energy near the iron K-edge and compared with ab initio calculations. The anisotropy appears due to the deformations of the electronic states induced by the asymmetric atomic environment and thus provides a quantitative measure of these deformations. As a consequence, reflections expected to be forbidden by screw-axis or glide-plane symmetry operations can be excited, with structure factors being proportional to the anisotropy. The azimuthal angle dependencies and energy spectra of such anisotropy-induced "forbidden" reflections are studied and the phase of the anisotropy is determined from interferences of the forbidden reflections with different multiple-wave reflections. The energy dependencies of the real and imaginary parts of the anisotropy are shown to be in good agreement with theoretical results obtained from two different approaches, i.e., the full multiple-scattering method employing a cluster muffin-tin potential and pseudopotential ab initio calculations. It is found that the anisotropy in pyrite is much more sensitive to the Fe environment than the average absorption coefficient

Atomic displacement effects in near-edge resonant “forbidden” reflections.

A survey of atomic displacement effects in the resonant scattering of synchrotron radiation is presented. It is shown that the dynamical displacements, associated with thermal vibrations, provide the thermal-motion-induced (TMI) “forbidden” reflections, while static displacements (e.g. induced by impurities) provide the point-defect-induced (PDI) “forbidden” reflections. Both kinds of reflections occur owing to perturbation of valent electrons wave functions by atomic displacements. The results of numerical calculations of TMI forbidden reflections in Ge and ZnO are compared with experimental data