Isotopy classification of three-dimensional embedded nets

The article by Power et al. [Acta Cryst. (2020), A76, 275–301] on the isotopy classification of crystal nets is discussed.

Isotopy classes for 3-periodic net embeddings

Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type.

Texture corrections for total scattering functions

The Debye scattering equation (DSE) is generalized and augmented in order to account for moderate texture effects, yielding the differential cross section as a function of atomic coordinates and texture coefficients subject to symmetry constraints. Implications for the evaluation of the pair distribution function (PDF) as a direct transform of powder diffraction data from textured samples are also discussed.

Wedge reversion antisymmetry and 41 types of physical qu­antities in arbitrary dimensions

Physical quantities in arbitrary dimensional space can be classified into 41 types using three antisymmetries within the framework of Clifford algebra.

Comparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surface

Features of azimuthal plots for RHEED and its new counterpart, RHEPD, are discussed. The plots, for both electrons and positrons, are determined using dynamical diffraction theory.

Groupoid description of modular structures

The application of groupoids to modular crystal structures is presented.

An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films

A method is described for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films comprising various crystal orientations and/or polymorphs by measuring reciprocal-lattice vectors.

Geometric realizations of abstract regular polyhedra with automorphism group H₃

A method is adapted to generate a full rank realization of an abstract regular polyhedron with automorphism group H₃.

SPIND-TC: an indexing method for two-color X-ray diffraction data

An auto-indexing method for two-color X-ray diffraction data is presented, which has been tested on both simulated and experimental protein diffraction data. The indexing yield is increased significantly compared with the previous approach using conventional indexers.

Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid

To describe multiple Bragg reflection from a thick, ideally imperfect crystal, the transport equations are reformulated in three-dimensional phase space and solved by spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially for finite detectors.

Testing of a `hard' X-ray interferometer for experimental investigations

A new type of X-ray LLL interferometer, a `hard' interferometer, which has both a base and a `ceiling', is tested for experimental investigations. The tested interferometer has no preliminary uncontrollable moiré and can be used for object and deformation investigations.

Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models

Structure-mining finds and returns the best-fit structures from structural databases given a measured pair distribution function data set. Using databases and heuristics for automation, it has the potential to save experimenters a large amount of time as they explore candidate structures from the literature.

Domain formation and phase transitions in the wurtzite-based heterovalent ternaries: a Landau theory analysis

A Landau theory for the wurtzite-based heterovalent ternary semiconductor ZnSnN₂ is developed and a first-order reconstructive phase transition is proposed as the cause of observed crystal structure disorder. The model implies that the phase transition is paraelectric to antiferroelectric.

New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution

The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect.

The Fedorov–Groth law revisited: complexity analysis using mineralogical data

Using mineralogical data, it is demonstrated that chemical simplicity measured as an amount of Shannon information per atom on average corresponds to higher symmetry measured as an order of the point group of a mineral, which provides a modern formulation of the Fedorov–Groth law.