Accurate room-temperature structure analyses have been carried out on the two well known structures of cuprite, Cu20, and corundum, a-A1203, using synchrotron radiation, in order to assess the accuracy of single-crystal X-ray diffraction data that can be obtained with such a source. The two compounds were chosen since results can be rigorously cross checked against deposited data from careful X-ray tube measurements which have been analyzed in terms of electron-density distributions. The synchrotron data were collected on the five-circle diffractometer at HASYLAB in the dedicated mode of DORIS II (3.7 GeV) within normal beam time allowance at the same wavelengths as the tube experiments. The final Cu20 data set included 21 'forbidden' reflections whose intensities cannot be measured using tube radiation. The intensities of these latter reflections turned out to be predominantly determined by the anisotropic vibration of Cu. Refinements using multipole expansion, models yielded agreement indices R = 0-0173 and 0.0078 for Cu20 and A1203, respectively. Structure factors as well as static-model deformation properties including electric-field gradients are compared with the corresponding literature results. Most findings are in satisfactory agreement implying that high-quality diffraction data can be obtained with a synchrotron-radiation source within reasonable time, provided proper attention is given to the experiment and the data-reduction procedure. In particular, the use of synchrotron radiation allows recording of weak and very weak reflection intensities with an accuracy that could never be achieved in conventional tube experiments. An additional data collection on Cu20 in parasitic mode (5.3 GeV) shows that under less-favorable conditions data can also be collected at a synchrotron-radiation source with an accuracy sufficient for standard structure analyses.
AbstractA new multisolution method for direct phase determination [Bricogne (1984). Acta Cryst. A40, 410-445] has been implemented and tested on small crystal structures. It consists of an organized search for those combinations of phases associated with a 'basis set'
Symmetry and physical aspects of 'forbidden' reflections excited by a local polarization anisotropy of the X-ray susceptibility are surveyed. Such reflections are observed near absorption edges where the anisotropy is caused by distortions of the atomic electronic states owing to interaction with neighbouring atoms. As a consequence, they allow for extracting nontrivial information about the resonant atom's local environment and their physical conditions. The unusual polarization properties of the considered reflections are helpful to distinguish them from other types of 'forbidden' reflections. When such reflections are excited, it is, for example, possible to determine not only the intrinsic anisotropy of an atomic form factor but also additional anisotropy induced by thermal motion, point defects and/or incommensurate modulations. Even the local 'chirality' of atoms in centrosymmetric crystals is accessible. Unsolved key problems and possible future developments are addressed.
The room-temperature electron-density distribution in natural anhydrite, CaSO4, has been studied by both X-ray and neutron diffraction. Conventional refinements of the data sets yielded RXw --0.020 and RNw = 0.025. The X-ray intensities were also used for high-order refinements, a refinement based on a point-charge model for the representation of positive residual charge accumulations, and a multipole expansion refinement. All these refinements were performed to study and to reduce parameter bias arising from bonding effects. The multipole expansion model yielded the significantly improved R w = 0.0116. The resulting (X--X) and (X-N) dynamic deformation density maps showed features qualitatively in agreement. Special attention was given to the charge distribution within and around the [SO4] 2-anion. The observed bond density distribution is different from earlier results obtained from comparable sulfate derivatives and from the [8206 ]2anion, indicating a considerable 3d population of the S atom.
ExperimentalThe anhydrite investigated was a natural mineral specimen from Stassfurt, Federal Republic of Germany, taken from the Institute's museum. The chemical
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