On the subgroup structure of the hyperoctahedral group in six dimensions

The subgroup structure of the hyperoctahedral group in six dimensions is studied, with particular attention to the subgroups isomorphic to the icosahedral group. The orthogonal crystallographic representations of the icosahedral group are classified, and their intersections are studied in some detail, using a combinatorial approach which involves results from graph theory and their spectra.

Multiple Bragg reflection by a thick mosaic crystal

To investigate multiple Bragg reflections from a thick and ideally imperfect crystal, the Darwin–Hamilton equations are generalized. Out-of-plane wavevector diffusion causes a noticeable shift and distortion of rocking curves.

Octagonal symmetry in low-discrepancy β-manganese

A low-discrepancy cubic variant of β-Mn is presented, exhibiting local octagonal symmetry upon projection. A comparison of the actual and ideal structure models of β-Mn is made in terms of the newly devised concept of geometrical discrepancy maps. Geometrical discrepancy maps combine predictive and discriminatory powers to appear useful within a wide range of structural chemistry studies.

Fast microstructure and phase analyses of nanopowders using combined analysis of transmission electron microscopy scattering patterns

The usefulness of combined analysis for fast determination of crystallite sizes and shapes of nanoparticle aggregates using electron diffraction patterns is demonstrated.

Strain distributions and diffraction peak profiles from crystals with dislocations

Diffraction profiles for different models of dislocation arrangements are calculated directly by the Monte Carlo method and compared with the strain distributions for the same arrangements, which corresponds to the Stokes–Wilson approximation. The strain distributions and the diffraction profiles are in close agreement as long as long-range order is absent.

Radial spacing distributions from planar point sets

The radial projection method for locally finite planar point sets is explored and numerical examples for different types of order are provided.

Hirshfeld atom refinement for modelling strong hydrogen bonds

Different X-ray refinement methods for modelling hydrogen bonds in the compound L-phenylalaninium hydrogen maleate are compared. It is found that Hirshfeld atom refinement (HAR) produces bond lengths involving hydrogen atoms in agreement with benchmarking results from neutron diffraction, and it is the only X-ray method to obtain a symmetric hydrogen site in the intramolecular hydrogen bond of this compound. Residual-density distributions in HAR are better than in the multipole-based models.

More about systematic errors in charge-density studies

Methods for the detection and visualization of systematic errors in measurement data are developed on the basis of conditional probabilities and applied to artificial and experimental data from the literature.

Analysis of multicrystal pump–probe data sets. I. Expressions for the RATIO model

The application of the RATIO method in processing/analysis prior to structure refinement requires an appropriate ratio model for modeling the light response. Such a model is discussed, taking into account both geometric and thermal light-induced changes.

Phasing in Crystallography: A Modern Perspective