On the temperature dependence of H-U_iso in the riding hydrogen model

The temperature dependence of hydrogen U_iso and parent U_eq in the riding hydrogen model is investigated by neutron diffraction, aspherical-atom refinements and QM/MM and MO/MO cluster calculations. Fixed values of 1.2 or 1.5 appear to be underestimated, especially at temperatures below 100 K.

The wingspan of mathematical crystallography

The current activities of the IUCr Commission on Mathematical Crystallography are described and the articles in this virtual special issue on mathematical crystallography are introduced.

Unification and classification of two-dimensional crystalline patterns using orbifolds

The discrete groups of isometries of the two-dimensional sphere, flat (euclidean) plane and the hyperbolic plane are described and unified using orbifolds. A simple classification schema for orbifolds is proposed that allows systematic exploration of the vast wealth of hyperbolic examples. The article also tabulates space groups that form by decorating simpler triply periodic minimal surfaces with so-called crystallographic hyperbolic orbifolds.

Unveiling the origin of a nonequilibrium dynamic process detected by X-ray photon correlation spectroscopy via a finite element analysis approach

Using a three-dimensional finite element analysis approach, a stress-relaxation mechanism was identified to account for the slow, nonequilibrium dynamics of a composite material observed using X-ray photon correlation spectroscopy.

The staurolite enigma solved

The relative frequency of occurrence of staurolite twins is explained by the quasi-restoration of the cationic substructures in terms of the pseudo-eigensymmetry of the corresponding crystallographic orbits.

Ambiguity of structure determination from a minimum of diffraction intensities

It is demonstrated that the ambiguity of determination of two- and three-dimensional crystal structures from an algebraic minimum of error-free intensities increases exponentially with the increasing structure size. This exponential dependence becomes steeper with increasing dimensionality.

Faces of Platonic solids in all dimensions

A polytope is called Platonic if it has faces of one kind in every dimension, 0 (vertices), 1 (edges), 2 (faces), …. The three-dimensional Platonic solids/polytopes have been known since antiquity: tetrahedron, octahedron, cube, dodecahedron and icosahedron. Platonic solids in any dimension n < ∞ were identified in the 20th century. In this paper a simple recursive method of decoration of the Coxeter–Dynkin diagram is used to describe the faces of all types and dimensions.

A multiple-common-lines method to determine the orientation of snapshot diffraction patterns from single particles

Using a multiple-common-lines method, the orientations of high- and low-signal diffraction patterns can be accurately recovered.

Crystallographic data of double antisymmetry space groups

Crystallographic data of double antisymmetry space groups are presented.

Changes of physical properties in multiferroic phase transitions

Nonmagnetic, magnetic and toroidal properties are given for all 1601 Aizu species of point-group pairs, highlighting the differences in property coefficients between each pair of groups.

Report of the Executive Committee for 2012