Differential geometry: a natural tool for describing symmetry operations

Using differential geometry, a unified description of the symmetry of crystals is presented. This formalism does not require additional dimensions in the modulated case, for which the modulation wave is expressed by a particular parameterization of three-dimensional space.

Point substitution processes for decagonal quasiperiodic tilings

A general construction principle for the inflation rules for decagonal quasiperiodic tilings is proposed.

Phase modulation effects in X-ray diffraction from a highly deformed crystal with variable strain gradient

The concept of interbranch phase modulation of an X-ray wavefield is extended to the case of a large gradient, which depends on the depth inside the crystal. Diffraction (extinction) contrast is also discussed for a strongly deformed specimen containing a single dislocation.

Edge-transitive lattice nets

Properties of periodic edge-transitive nets with one vertex in the primitive unit cell are described.

Using dynamically scattered electrons for three-dimensional potential reconstruction

The use of dynamically scattered electrons for three-dimensional potential reconstruction is described.

Louis Pasteur's discovery of molecular chirality and spontaneous resolution in 1848, together with a complete review of his crystallographic and chemical work

Louis Pasteur's crystallographic and chemical work is described.

International Union of Crystallography Twenty-First General Assembly and International Congress of Crystallography, Osaka, Japan, 23–31 August 2008