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May 2010 issue
Cover illustration: A collage of related patterns that are formed via tilings of the hyperbolic plane. Two-dimensional `universal tilings' (e.g. UQC473) of hyperbolic space can be wrapped onto a three-periodic minimal surface (e.g. the gyroid), forming a curvilinear `Epinet tiling' (EGC473) whose edges relax to give a `Systre net', sqc14527. This approach to net enumeration is described in Ramsden et al. [Acta Cryst. (2009), A65, 81-108]. Further examples are collected at https://epinet.anu.edu.au.
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Opechowski–Guccione-like symbols of magnetic space groups with a centred conventional cell are proposed for which a set of generators of the group can be read off the symbol, as for the Belov–Neronova–Smirnova symbols.
All homogeneous sphere packings were derived that refer to the trivariant orthorhombic lattice complexes with mirror symmetry. Examples of corresponding crystal structures are given.
Morphological properties of single biomacromolecules based on molecular enclosing forms indexed by an appropriate `form lattice' are related to the symmetry of the crystal where the molecules are periodically packed.
The differentiation of the human rhinovirus into serotypes, all having very similar structures and the same architecture, is shown to be related to the packing of the viruses in the crystal and to its space-group symmetry.
Crystallographic face forms (crystal forms) {hkl} are interpreted as sets of symmetry-equivalent X-ray reflections. The eigensymmetry (inherent symmetry) of these forms is used to derive general results on diffraction intensity relations (i) in non-centrosymmetric crystals exhibiting anomalous scattering and (ii) of overlapping twin-related reflections in crystals twinned by merohedry.
The difference electron density has been reformulated via the use of the joint probability distribution functions of three isomorphous crystal structures.
The effect of neglecting anharmonic nuclear motion on the residual density distribution and on isoresidual density representations in real space from theoretical data corresponding to 100 K experimental data is demonstrated. A shashlik pattern indicates neglect of third-order anharmonic motion coefficients in real space, while in the residual density analysis plot it appears as triangular shaped shoulders even for a resolution of 1.15 Å−1.
An analytical formula for diffuse scattering in quasicrystals is given.
An analytical formula for neutron magnetic diffuse scattering in quasicrystals is given.
The tangent-bundle formalism provides a representation of symmetry operations particularly useful for the determination of the intrinsic translation part in operations without a fixed point. Moreover, space-group operations appear to be independent of any origin point.
High-angle scattering of high-energy electrons by a dopant atom is investigated using Bloch waves. Bloch wave transitions leading to high-angle scattering are identified and an `atom focusing' effect of the dopant atom, similar to channelling, is observed for the first time.
Interference fringes in multiple Bragg–Laue mode and mirage fringes from a bent Si single-crystal strip were observed as a function of bending strain. The calculated intensities based on the dynamical theory of diffraction including hyperbolic ray trajectories and using the strain parameter determined by the mirage fringes reproduce the characteristic features of the interference fringes well.
Methods of construction and research of self-similar quasiperiodic tilings of the complex plane on tiles with fractal boundaries are developed.
short communications
A general expression of the polarization factor of multi-diffracted beams, which can be easily coded into a computer program, is derived.
