Acta Crystallographica Section A最新文献

A new approach to determining the unit-cell vectors from single-crystal diffraction data based on clustering analysis is proposed. The method uses the density-based clustering algorithm DBSCAN. Unit-cell determination through the clustering procedure is particularly useful for limited tilt sequences and noisy data, and therefore is optimal for single-crystal electron-diffraction automated diffraction tomography (ADT) data. The unit-cell determination of various materials from ADT data as well as single-crystal X-ray data is demonstrated.

Ultrashort X-ray pulses from free-electron laser X-ray sources make it feasible to conduct small- and wide-angle scattering experiments on biomolecular samples in solution at sub-picosecond timescales. During these so-called fluctuation scattering experiments, the absence of rotational averaging, typically induced by Brownian motion in classic solution-scattering experiments, increases the information content of the data. In order to perform shape reconstruction or structure refinement from such data, it is essential to compute the theoretical profiles from three-dimensional models. Based on the three-dimensional Zernike polynomial expansion models, a fast method to compute the theoretical fluctuation scattering profiles has been derived. The theoretical profiles have been validated against simulated results obtained from 300 000 scattering patterns for several representative biomolecular species.

The possible distortions in the spinel structure resulting from rotation of the tetrahedra and octahedra have been investigated by a group-theoretical method. The possibility of the existence of 28 phases of rotation of the tetrahedra and five phases of rotation of the octahedra has been shown. In all these phases the polyhedra are equivalent, but their orientation can be different. Among the phases of the tetrahedra rotation there is one phase of pure rotation, i.e. not accompanied by additional (not rotation) distortions of the structure. Of the five phases of the rotation of the octahedra three phases can be obtained only by pure rotation of the octahedra.

Rod groups (monoperiodic subgroups of the 3-periodic space groups) are considered as a special case of the commensurate line groups (discrete symmetry groups of the three-dimensional objects translationally periodic along a line). Two different factorizations of line groups are considered: (1) The standard L = T(a)F used in crystallography for rod groups; F is a finite system of representatives of line-group decomposition in cosets of 1-periodic translation group T(a); (2) L = ZP used in the theory of line groups; Z is a cyclic generalized translation group and P is a finite point group. For symmorphic line groups (five line-group families of 13 families) the two factorizations are equivalent: the cyclic group Z is a monoperiodic translation group and P is the point group defining the crystal class. For each of the remaining eight families of non-symmorphic line groups the explicit correspondence between rod groups and relevant geometric realisations of the corresponding line groups is established. The settings of rod groups and line groups are taken into account. The results are presented in a table of 75 rod groups listed (in international and factorized notation) by families of the line groups according to the order of the principal axis q (q = 1, 2, 3, 4, 6) of the corresponding isogonal point group.

A new metric is proposed to improve the fidelity of structures refined against precession electron diffraction data. The inherent dynamical nature of electron diffraction ensures that direct refinement of recorded intensities against structure-factor amplitudes can be prone to systematic errors. Here it is shown that the relative intensity of precessed reflections, their rank, can be used as an alternative metric for refinement. Experimental data from erbium pyrogermanate show that applying precession reduces the dynamical transfer of intensity between reflections and hence stabilizes their rank, enabling accurate and reliable structural refinements. This approach is then applied successfully to an unknown structure of an oxygen-deficient bismuth manganite resulting in a refined structural model that is similar to a calcium analogue.

The effects of thermal vibrations on X-ray powder diffraction patterns are discussed. Special considerations for extremely small crystallites are described, including the occurrence of surface and edge vibrational modes, and a restriction on the maximum phonon wavelength. In doing so, a complete temperature diffuse scattering (TDS) model is presented, which includes the influence of these features on: the Debye-Waller parameter; first-order TDS; and higher-order TDS terms. The importance of using an accurate TDS representation is studied as a function of temperature and crystallite size. It is found that a misrepresentation of the TDS for small crystallites can lead to an error in the determined Debye-Waller parameter on the order of 20-40% and a slight overestimation of the peak broadening. While the presented theory is primarily developed considering X-ray scattering, the same expressions are expected to describe the TDS in faster-than-sound neutron powder diffraction measurements.

A simple test based on Bayesian statistics for the presence of minority populations in single-crystal structure refinement is presented. The test is illustrated by analysis of photocrystallographic experiments on single crystals of ruthenium-sulfur-dioxide-based complexes. In data sets collected after irradiation with light, conventional refinements of the populations of different metastable states to values below 4% are shown to be statistically significant. The results also confirm that the photo-induced states are absent from data collected in the dark.

Mean-square displacements were computed within the harmonic approximation from ab initio force constants for binary B-, Tl- and Bi-containing III-V compounds in sphalerite crystal structures in the temperature range from 0 to 1000 K in steps of 1 K. An Einstein model with a temperature-dependent characteristic frequency was used to model the temperature dependence of the mean-square displacements. A Gaussian was fitted to the temperature dependence of the characteristic frequency and parameters of the Gaussian are given. Phonon dispersion relations and densities of states derived during the computation of the mean-square displacements are also shown.