Direct observation of charge ordering in magnetite using resonant multiwave x-ray diffraction.

Charge disproportion at octahedral Fe sites in magnetite was observed at low temperature using two inversion-symmetry related three-wave resonant x-ray diffraction, 022-311 and 002-̅3̅1, near the iron K edge. Both of the three-wave cases involve the (002) forbidden-weak reflection. The self-normalized three-wave to two-wave (002) diffraction intensity ratio automatically cancels the self-absorption effect and leads to direct determination of charge disproportion for magnetite below 120 K. This approach provides a more direct and effective way for extracting charge-ordering information.

Multiple wave diffraction anomalous fine structure.

A new method, multiple-wave diffraction anomalous fine structure, combining the x-ray multiple-wave diffraction and diffraction anomalous fine structure techniques, is proposed. The real part of dispersion correction Deltaf' and fine structure chi function can be obtained directly by multiple diffraction analysis without using Kramers-Krönig relations and kinematical fitting of diffracted intensity. Better wave vector sensitivity of the fine structure is expected. The multiple-wave diffraction anomalous fine structure experiment for a GaAs single crystal is reported as an example.

X-ray multiple-wave coherent interaction in a quasi-two-dimensional material NbSe2-2H.

The first observation of the X-ray multiple-wave interaction in an incommensurate charge-density-wave (CDW) modulated structure at low temperatures is reported for an example of a quasi-two-dimensional material, NbSe(2)-2H. Via the coherent interaction between the X-ray waves propagating in the CDW-modulated structure and the host structure, the phase-dependent intensity variations of a CDW reflection were detected. In accord with a centrosymmetric structure, the phases of the structure-factor triplets of two CDW reflections and a Bragg reflection of the host structure were determined to be either 0 or 180 degrees, and not to vary with temperature. Relative phase differences of the two CDW reflections are also deduced.

Phase-dependent polarization aspects of three-wave X-ray diffraction: an iterative Born approximation.

The iterative Born approximation is derived for three-wave dynamical X-ray diffraction. Dependence of the three-wave diffraction profiles of the diffracted wave on the polarization state of a linearly polarized incident wave is theoretically and experimentally investigated. General conditions of the phase sensitivity as well as the asymmetry of diffraction profiles are obtained from this approximation and compared with direct dynamical calculations. Reasonable qualitative agreement between the results obtained from this iterative approach and the exact dynamical calculation is shown. A new feature of reversing asymmetry of an intensity profile with respect to phase change is theoretically predicted.

Multiple diffraction data analysis for macromolecular crystals in stereoscopic multibeam imaging.

A detailed analysis of multiple diffraction data collected by the stereoscopic multibeam imaging technique from a tetragonal lysozyme crystal is reported. Calculations based on the dynamical theory are employed to account for diffraction profiles obtained with Bragg-angle scan in stereoscopic imaging and the conventional azimuthal scan in Renninger arrangement. The formation of a multibeam intensity profile and the relationship and mutual influence between the two scans are investigated. A simple practical method of quantitative estimation of the reflection phases of structure-factor multiplets from the experimental data obtained with two inversion-symmetry-related diffractions is proposed. The procedures for data handling and for distinguishing "partial" diffraction images from "full" diffraction images are also developed considering multibeam diffraction geometry and experimental conditions. These procedures thus provide a practical way of reconstructing diffraction profiles for experimental phase determination for macromolecular crystals.