Algorithm for distance list extraction from pair distribution functions

The atomic pair distribution function (PDF) represents the structure of a material as a list of distances between pairs of atoms. This article presents an algorithm that can extract the distance list from a measured PDF in a highly automated manner without prior knowledge of the structure.

Robust minimal matching rules for quasicrystals

An algorithmic procedure is proposed for extraction of physically meaningful matching rules directly from the phased diffraction data of a quasicrystal.

XGANDALF – extended gradient descent algorithm for lattice finding

A description and evaluation are given of XGANDALF, extended gradient descent algorithm for lattice finding, an algorithm developed for fast and accurate indexing of snapshot diffraction patterns.

Relativistic quantum crystallography of di­phenyl- and di­cyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Contributions of different physical effects (thermal smearing, relativity, electron correlation, basis set, environment and/or atomic contributions) to the structure factors of heavy-element compounds are inspected. Relativistic Hirshfeld atom refinement yields an almost perfect agreement with reference geometries in this theoretical pilot study, showing the usefulness of the employed methodology.

Anomalous X-ray diffraction from ω nanoparticles in β-Ti(Mo) single crystals

Anomalous X-ray diffraction was used to study the energy dependence of diffuse scattering around the reciprocal-lattice point h = [006]_β of a Ti–15Mo single crystal. The diffuse scattering as well as its energy dependence around an Mo K absorption edge were qualitatively explained by a numerical model of ω particles which elastically deform the surrounding β matrix.

Local and global color symmetries of a symmetrical pattern

Given a symmetrical pattern consisting of disjoint congruent symmetric motifs, a method is described for arriving at a coloring of which is perfect and transitive under its global symmetry group G and where the coloring of each motif is also perfect and transitive under its own group of symmetries (local symmetries of ). The coloring of is coordinated with the property that the symmetry of that is both a global and local symmetry effects the same permutation of the colors of and the corresponding motif, respectively.

Coordination shells and coordination numbers of the vertex graph of the Ammann–Beenker tiling

A growth form and an asymptotic formula for the coordination sequence of the vertex graph of the Ammann–Beenker tiling are obtained.

A new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactors

A novel method is introduced for in situ X-ray total scattering experiments. Two examples of the method as applied to non-classical nucleation and crystal growth studies are discussed.

Using the singular value decomposition to extract 2D correlation functions from scattering patterns

The truncated singular value decomposition is applied to extract the underlying 2D correlation functions from small-angle scattering patterns.

X-ray diffraction in superabsorbing crystals: absorption intrinsic width

This article presents an analytical description of the X-ray diffraction peak profile of superabsorbing crystals. For thick crystals, the absorption intrinsic profile is described by a Lorentzian and characterized by an absorption intrinsic width.

The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigenda

Three equations in Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] are corrected.