Non-crystallographic symmetry of liquid metal, flat crystallographic faults and polymorph transformation of the M₇C₃ carbide

The crystal structures of M₇C₃, M₅C₂, M₃C and M₂₃C₆ carbides are determined by the finite projective geometry constructions, namely the Desargues configuration 10₃ and its subconfigurations. The unique mechanism of the liquid-crystal transition and in situ polymorph transformations between these carbides is described within the framework of the same approach.

The phantom derivative method when a structure model is available: about its theoretical basis

The phantom derivative phasing method has been generalized via the study of joint probability distribution functions involving the prior knowledge of a model electron-density map or of a molecular model structure.

Edge-2-transitive trinodal polyhedra and 2-periodic tilings

All trinodal, edge-2-transitive polyhedra and 2-periodic tilings are described.

Diffuse single-crystal scattering corrected for molecular form factor effects

It is shown that chemical short-range order in two-component molecular crystals can be solved directly by separating the influence of the molecular form factor.

Groupoids and labelled quotient graphs: a topological analysis of the modular structure in pyroxenes

A signature of partial symmetry operations acting in ortho­enstatite is evidenced in its labelled quotient graph.

On the Penrose and Taylor–Socolar hexagonal tilings

A uniform geometric/algebraic approach to the Penrose and Taylor–Socolar hexagonal tilings is given, which clarifies their construction and the way in which they are inter-related.

Resonant and non-resonant magnetic scatterings with circularly polarized X-rays: magnetic scattering factor and electron density of gadolinium iron garnet

The energy dependence of resonant magnetic scattering factors revealed antiparallel magnetic moments within the t₂ (3d) orbitals at the Fe K pre-edge. Circular polarization of X-rays is a powerful tool for examining magnetic electrons via both resonant and non-resonant magnetic scatterings simultaneously.

Convex polyhedra with minimum and maximum names

The combinatorial types of convex n-acra with minimum and maximum names for any n ≥ 4 are found. Thus, the latter can be directly calculated from the adjacency matrices of their edge graphs.

International Tables for Crystallography, Volume A, Space-group symmetry

X-ray Diffraction for Materials Research: From Fundamentals to Applications

Symmetry and Physical Properties of Crystals