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ISSN: 2053-2733

March 2015 issue

Highlighted illustration

Cover illustration: Bravais described his complete set of space-filling lattices in 1850, but new insights into the hierarchical relationship between the Bravais lattices described in this issue [Grimmer (2015). Acta Cryst. A71, 143-149; see also Flack (2015). Acta Cryst. A71, 141-142] will give scientists powerful new tools in predicting new structures and understanding phase transitions, such as the magnetic ordering in haematite (shown as a backdrop). Image courtesy of K. M. Ø. Jensen, Columbia University.

advances

scientific commentaries


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Crystallographers need to understand better the Bravais lattice.

research papers


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The partial order among Bravais types of lattices obtained by considering special cases is derived from their space-group symmetry and applied to continuous equi-translation phase transitions.

foundations

research papers


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The affine and Euclidean normalizers of the subperiodic groups are derived and listed.

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Decorated generalized Penrose tiling is described as a potential quasilattice for models of decagonal quasicrystals. Its advantage over the conventional Penrose tiling is that its long-range order can be continuously changed if the tile decoration is fixed.

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A simple approach to estimate temperature-dependent isotropic motion of hydrogen atoms is proposed. The model is validated against experimental data.

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A general technique has been introduced for the projection of the hypercubic lattices into two- and three-dimensional subspaces with dihedral and icosahedral residual symmetries, respectively. Eigenvalues and corresponding eigenvectors of the Cartan matrix (Gram matrix) determine the projected subspace and symmetry of the aperiodic tilings.

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In order to characterize molecular-replacement search spaces, the structure of Sohncke groups is examined. It is observed that proteins most often crystallize in Sohncke groups with small torsion subgroups.

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The mimetic twinning of aragonite is explained by the high degree of pseudo-symmetry of the crystallographic orbits and the action of the twin operation on the structure slices which form the composition surface.

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Residuals from artificial and from published data are tested against the hypothesis of being identically distributed. An anharmonic motion model reduces the number of rare events in the lowest resolution range.

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Linear relations between numbers of k-faces of non-principal primitive parallelohedra are obtained from Dehn–Sommerville relations for simple polytopes.

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Given a subgroup H of the symmetry group G of an object, an H-invariant coloring of the object has a color group which is a subgroup of G containing H. A method is described for determining whether this subgroup is G, H or some intermediate subgroup.

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Correlations between different local topological properties of the electron density due to nuclear vibrations are analysed via computational statistics.

short communications


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Cartesian real spherical harmonics for l ≤ 20 and the corresponding normalization factors for the deformation density functions with an accuracy to 35 significant figures have been generated using the Wolfram Mathematica software and converted to a Fortran90 code.

book reviews


obituaries


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Obituary for Hans Wondratschek.
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