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The electron-density distribution and the contribution to anomalous scattering factors for Fe ions in magnetite have been analyzed by X-ray resonant scattering at the pre-edge of Fe K absorption. Synchrotron X-ray experiments were carried out using a conventional four-circle diffractometer in the right-handed circular polarization. Difference-Fourier synthesis was applied with a difference in structure factors measured on and off the pre-edge (E(on) = 7.1082 keV, E(off) = 7.1051 keV). Electron-density peaks due to X-ray resonant scattering were clearly observed for both A and B sites. The real part of the anomalous scattering factor f' has been determined site-independently, based on the crystal-structure refinements, to minimize the squared residuals at the Fe K pre-edge. The f' values obtained at E(on) and E(off) are -7.063 and -6.682 for the A site and -6.971 and -6.709 for the B site, which are significantly smaller than the values of -6.206 and -5.844, respectively, estimated from the Kramers-Kronig transform. The f' values at E(on) are reasonably smaller than those at E(off). Our results using a symmetry-based consideration suggest that the origin of the pre-edge peak is Fe ions occupying both A and B sites, where p-d mixing is needed with hybridized electrons of Fe in both sites overlapping the neighbouring O atoms.

The anomalous scattering factor (ASF) correction to the relativistic form-factor approximation for Rayleigh scattering is examined in support of its utilization in radiographic imaging. ASF corrected total cross-section data have been generated for a low resolution grid for the Monte Carlo code EGS4 for the biologically important elements, K, Ca, Mn, Fe, Cu and Zn. Points in the fixed energy grid used by EGS4 as well as 8 other points in the vicinity of the K-edge have been chosen to achieve an uncertainty in the ASF component of 20% according to the Thomas–Reiche–Kuhn sum rule and an energy resolution of 20 eV. Such data is useful for analysis of imaging with a quasi-monoenergetic source. Corrections to the sampled distribution of outgoing photons, due to ASF, are given and new total cross-section data including that of the photoelectric effect have been computed using the Slater exchange self-consistent potential with the Latter tail. A measurement of Rayleigh scattering in a dilute aqueous solution of manganese (II) was performed, this system enabling determination of the absolute cross-section, although background subtraction was necessary to remove Kβ fluorescence and resonant Raman scattering occurring within several 100 eV of the edge. Measurements confirm the presence of below edge bound–bound structure and variation in the structure due to the ionic state that are not currently included in tabulations.

Resonant x-ray scattering was used to investigate electronic fluctuations of the octahedral iron atoms in magnetite. We measured the (002) and (006) ``forbidden'' x-ray diffraction reflections permitted by the anisotropy of the iron anomalous scattering factor. The energy and azimuthal angle dependencies of these reflections, and the polarization analysis, are shown and discussed. The results clearly show $p$ and $d$ iron empty states ordering in magnetite at room temperature. Moreover, the octahedral iron atoms are electronically equivalent in a time scale lower than ${10}^{\ensuremath{-}16}\phantom{\rule{0ex}{0ex}}\mathrm{sec}$. Therefore, magnetite should be considered as an itinerant magnet and not as a fluctuating mixed valence material.

Photon scattering from bound electrons of atoms, a component of the elastic photon-atom scattering amplitude called Rayleigh scattering, is discussed. General features of the many-body scattering amplitude and its partitioning into Rayleigh and Delbruck (and nuclear) single-electron transition scattering amplitudes are examined. The use of the state-of-the-art precise second-order S-matrix calculations of Rayleigh scattering in terms of single-electron transition-amplitudes has led to significant progress in our understanding of the scattering process. The importance of relativistic, higher multipole, and bound-bound contributions in calculating anomalous scattering factor deviations from form factor amplitudes must be emphasized. Accurate interpolation of cross sections in the three-dimensional space of scattering angle, photon energy, and atomic number, utilizing the available published S-matrix data, has permitted extensive tabulation of differential scattering cross sections. S-matrix results may be compared with experiments to assess their validity; they may be compared with simpler but more approximate approaches, to identify the extent of the utility of such approaches and to develop simpler prescription schemes which can give results comparable to the S-matrix results. In spite of their many successes, the present second order S-matrix methods also have limitations and shortcomings, observed in certain recent experiments. We describe the explanation of these experiments in terms of a composite theory which also incorporates non-local exchange and correlation effects. We end with a discussion of other future issues.

We have performed resonant X-ray scattering study on PrRu 4 P 12 at the Pr L 2 and L 3 edges. Below the metal–insulator transition temperature ( T MI ≃ 62 K ) , resonant signal appears in the superlattice reflections in addition to the lattice distortion, which demonstrates that different electronic states of the Pr atoms are alternatingly ordered in the BCC unit cell. Polarization analysis of the scattered X-ray shows that the intensity changing the polarization from π to σ is absent or very weak. This means that the difference of the anomalous scattering factor between two Pr atoms in the BCC unit cell, which reflects the character of the intermediate 5d states of the resonant process, is almost isotropic.

Bragg diffraction from an Ag/Ni multilayer was used to determine independently both the real and imaginary parts of the anomalous scattering factor (ASF) around the NiLIIIandLIIedges in the soft-X-ray range. Huge resonant variations were observed with f'' reaching 55\,r_o and f' decreasing to −63 r_o at the NiLIIIedge. The independent measurements of f' and f'' are tested for coherency using the Kramers–Kronig relation. The f'' values are also compared with those derived from X-ray absorption methods such as total electron yield and fluorescence yield measurements.

The angle dependence of the elastic photon-atom scattering amplitude is investigated using full relativistic S-matrix calculations for guidance. A simple quantitative approach is developed based on the full nonrelativistic amplitude for Rayleigh scattering from the ground state of a hydrogenic ion and it is successfully applied to neutral atoms of low and intermediate nuclear charge. This framework is useful for scattering of X-rays with energies above the K-shell ionization threshold but below energies where major relativistic corrections are necessary. The generalized anomalous scattering factors presented here go beyond the usual angle-independent anomalous-scattering-factor approximation, permitting a discussion of the full angular dependence of the anomalous scattering factors. Simple formulas, expressed in terms of elementary functions and a lookup table, are presented for these generalized anomalous scattering factors. Numerical examples illustrate that the angle dependence can be substantial. A fairly good representation of full numerical results is achieved.

The X-ray linear absorption coefficient for ZnFe 2 O 4 was measured near the Zn K absorption edge in the energy region between 9 and 11 keV. The result was used for determining the imaginary part of the anomalous dispersion factors f''(E) as a function of energy E. The real part of the anomalous scattering factor f'(E) was also estimated from the f''(E) data through the dispersion (Kramers-Kronig) relation. The experimental f' (E) values agree almost within the error bars with the data calculated by the Cromer-Liberman scheme, except for the energy region about 400 eV above the absorption edge.

Partial Patterson maps containing peaks from anomalous scatterers only can be derived from powder diffraction data. For each anomalous scatterer, three data sets are needed: one off the edge and another two at two wavelengths close to the edge. The method presented is based essentially on the wavelength dependence of the real part of the anomalous scattering factor.

An analytic-calculation method enabling the evaluation of the real part of the anomalous scattering factor f\ifmmode\bar\else\textasciimacron\fi{}' from attenuation measurements in the x-ray range is presented. This method utilizes a power law to fit the variation of the experimentally observed mass attenuation coefficients as a function of the photon energy. It uses an analytic expression involving Gauss hypergeometric functions to calculate the dispersion term. A derivation of the relativistic correction to the dispersion term shows it to be smaller than the one used in the scattering-factor tabulation. The calculations using this method are tested for seven elements of medium Z: Pd, Ag, Cd, In, Sn, I and Xe, between 15 and 45 keV. Since they compare favorably with the ab initio calculation, the present approach can be considered as an advantageous alternative to the full calculation.

Two kinds of 4×1 superstructures are found for Yb/GaAs(001) contacts with different Yb thicknesses. Different Schottky-barrier height values are also found for these samples. To clarify the role of Yb atoms in the 4×1 structure, an X-ray anomalous dispersion effect has been used in the grazing-incidence X-ray diffraction geometry. Diffraction intensities measured in the X-ray energy range near the Yb L III absorption edge show a characteristic variation, which reflects the energy dependence of the real part of the anomalous scattering factor (f ’ ) for Yb atoms. As a result, for all the samples, Yb atoms are found to order in 4×1 structures. By comparison of the calculated diffraction intensities with observed intensities, two (4×1) structural models are found for the thin and thick Yb-layer samples, respectively.

The importance of photon scattering data, including elastic scattering, is well known. The state-of-the-art precise method for estimating elastic scattering cross-sections of x- and γ-rays using the S-matrix is briefly discussed. Since the estimation of cross-sections using the S-matrix is very computer intensive, other alternatives to obtaining cross-sections with the same precision as that of the S-matrix are discussed. It is concluded that the modified form factor with angle-independent anomalous scattering factor could be used for photon energies below and near the K-threshold photoeffect energies. For other energies it is suggested that one should use the recently interpolated tables of cross-sections (within an accuracy of better than 1% with S-matrix values) of all elements of the periodic table within the range 13 ≤ Z ≤ 104 and at photon energies at suitable intervals between 50 and 1500 keV for 55 different scattering angles θ between 0 and 180°. Future issues which require further investigation are also indicated.

Z-dependent energy-independent corrections to the relativistic anomalous-scattering factors tabulated by a number of workers are given. These corrections are most significant for medium-Z and high-Z atoms, but are experimentally observable even in low-Z elements. Examples of use of the correction factors are provided for the real anomalous-scattering factor f' and for the differential elastic scattering cross section do'/dO.

Synchrotron diffraction studies have been carried out for single crystals of ferrimagnetic M‐type ferrites at the BL‐3A of the Photon Factory. Resonant x‐ray magnetic scattering (RXMS) and x‐ray magnetic circular dichroism (XMCD) at the Fe K edge were utilized to examine the magnetic order of 3d states through the hybridized 4p states. A magnetic satellite reflection of 0 0 8+(2/3) was observed for BaTiCoFe10O19 with the resonant enhancement The magnetic anomalous scattering factor f″m of BaFe12O19 was estimated as 0.23 at E = 7128.2 eV in the least‐squares procedure to use the difference of asymmetrical ratios. The crystal structure with spin arrangement has been determined for BaFe12O19, which coincides with the Gorter model.

X-ray dynamical diffraction induced only by the imaginary part of the scattering factor was measured using a Ge perfect crystal. The 844 integrated reflecting intensities near the K-absorption edge were measured in both the Bragg and the Laue cases. The intensities show the characteristic variations for the scattering factor having no real part, which agree well with theoretical predictions. There remains a slight difference between the theoretical [Fukamachi & Kawamura (1993). Acta Cryst. A49, 384–388] and the experimental energy position at which this occurs, which is related to the fine structure of the anomalous scattering factor above the absorption edge.

Molecular oxygen on Earth is generated from photosynthesis by cyanobacteria, algae and plants, where water molecules are split by Photosystem II (PSII). PSII catalyzes light-induced water oxidation leading to the production of protons, electrons and molecular oxygen. The catalytic center of oxygen evolving complex (OEC) in PSII is composed of four Mn atoms and one Ca atom organized in a Mn4CaO5-cluster, which cycles through several different redox states to accomplish the catalytic process. Cyanobacterial PSII is a multi-subunits membrane protein complex composed of 17 membrane-spanning subunits, 3 membrane-extrinsic subunits and about 80 co-factor molecules with a total molecular weight of 350 kDa as a monomer. We reported the PSII structure at 1.9 Å resolution prepared from Thermosynechococcus vulcanus (PDB code: 3ARC)[1]. We determined unambiguously the positions of the atoms in OEC using the electron density map corresponding to each of five metal atoms and five oxygen atoms, for the first time. However, the valences of each of the four Mn atoms and their participation in the redox reactions in OEC are not fully understood. In order to uncover the catalytic mechanism of light-induced water oxidation by OEC, it is important to determine the valence of each Mn atom as well as to solve the detailed structure. In this study, we analyze the electronic state of each Mn atom in OEC by X-ray crystallographic analysis using Mn K-absorption edge wavelength. The Mn K-absorption edge depends on the oxidation number, and the anomalous scattering factor changes greatly for the Mn atoms in different oxidation states. We collected the anomalous difference data from PSII crystals using the wavelength (~1.8921 Å) on the Mn K-absorption edge at beamline BL38B1 and BL41XU of SPring-8 in Japan. The calculated anomalous difference Fourier map indicated different intensities among the four Mn atoms in OEC. This may suggest the different electronic state among the four Mn atoms in OEC. However, there is a possibility that these Mn atoms are reduced by X-ray exposures to some extent, and so the valences of these Mn atoms were not determined completely. We will discuss the relationship between peak heights of the anomalous difference Fourier map and the valence among the four Mn atoms in OEC.

Resonant X ray scattering has been used to investigate charge localization on the octahedral iron atoms in magnetite below and above the Verwey temperature. We have measured the DAFS spectra of the 002 and 006 `forbidden' Bragg reflections permitted by the anisotropy of the iron anomalous scattering factor. We performed ab initio calculations which are in fair agreement with the experiment in the near edge region and demonstrate the sensitivity of the DAFS spectra to tiny structural and electronic changes. No change is observed, in the energy and azimuthal dependences, when the sample is cooled down below the Verwey temperature. Charge ordering can be definitely excluded and different charge localization schemes discarded. Ab initio simulations, performed by using the refined crystallographic structure proposed for the room temperature phase, do not show a good agreement with the experiment in the extended region of the DAFS spectrum. This point is being investigated.

The multiwavelength anomalous dispersion (MAD) method is increasingly being used to determine protein crystal structures. In theory, data collection at two wavelengths is sufficient for the determination of MAD phases, but three or even more wavelengths are used most often. In this paper, the results of the phasing procedure using only two wavelengths for proteins containing different types of anomalous scatterers are analyzed. In these cases, it is shown that this approach leads to interpretable maps, similar in quality to those obtained with data collected at three wavelengths, provided that the wavelengths are chosen so as to give a large contrast in the real part of the anomalous scattering factor f. The consequences for a rational MAD data-collection strategy are discussed.

Resonant X-ray scattering study was carried out to investigate an anomalous ordered state ( T A =6.5 K ) in the filled skutterudite PrFe4P12. At the Pr-LIII absorption edge, we observed resonant features in h+k+l=odd reflections, which are forbidden in the BCC structure above TA. Because these reflections contain the difference of anomalous scattering factor between two Pr atoms in the BCC unit cell, and the ordered state is attributed to the ordering of two different electronic states of Pr.