The decoration of cluster centers, while not modifying the surface plane selection rule established for Tsai-type quasicrystals and approximants, affects the superstructure type stabilized at the surface.

The internal space expansion with variable system size is investigated for three different oxide quasicrystal systems. Patches of 7800, 4800 and 3600 vertices are examined in Ba–Ti–O/Pt(111), Eu–Ti–O/Pd(111) and Sr–Ti–O/Pd(111), respectively. This internal space inspection provides unique structural information for quasicrystalline systems, which goes far beyond a tiling analysis in the physical space.

A practical approach is proposed for constructing short presentations for Euclidean crystallographic groups on given generating sets.

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To describe the structural phase transitions P42/mnm(R) ↔ P21/c(M1) ↔ P1(T) ↔ C2/m(M2) observed experimentally in VO2 and its solid solutions, the two-component order parameter model is newly proposed.

Deformation defects in structurally disordered glasses are much more difficult to detect and characterize than defects in crystals. Here we show how well defined geometric indicators of local plasticity in glasses can be measured using scanning small-beam diffraction.

Denoised X-ray diffraction images by total variation regularization were used to improve the accuracy of X-ray structure analysis of a small-molecule crystal.

A new approach for generating training data for solving the phase problem with deep learning is proposed. Models trained on such data are better at generalizing the solution for structures outside the training domain.

The torsion instability of chiral selenium nanorods from the trigonal bulk phase was theoretically predicted. Two types (chiral/achiral) of selenium nanorods from the tetragonal bulk phase were constructed and studied.

We describe an efficient algorithm to compute the bridge length estimating the size of a complete isoset invariant, which classifies all periodic point sets under Euclidean motion.

We describe the supersymmetric nets, including some that are interlinked and interwoven.

The kisrhombille tiling is the dual of one of the eight semi-regular tilings and is composed of right-angled triangles in 12 different orientations. In this paper, two triangles are considered neighbors if they share an edge. Paths in the grid are sequences of triangles where each triangle (except the first) follows one of its neighbors. Digital distance is defined and calculated based on the number of steps in a shortest path between any pair of triangles.

The Commission on Crystallographic Nomenclature has concluded that, in some rare, carefully justified circumstances, Z, the number of formula units in the unit cell, may be a fraction.

A probabilistic theory of the quartet invariants is presented, which is capable of estimating quartet phases by exploiting the prior information contained in the Patterson map.

We provide a systematic account using symmetry and coordinates to explore symmetric (vertex- and edge-transitive) 3-periodic weavings of piecewise linear threads and 3-coordinated nets.

Machine learning based sorting of synthetic serial electron diffraction patterns into 2D zonal patterns and patterns representing intersections of multiple Laue zones is demonstrated. The extracted zonal patterns can be used for the determination of unit-cell parameters.

An algorithm is described to recover super-temporal resolution dynamics of X-ray scattering profiles of photo-excited biomolecules in solution from pump–probe X-ray solution scattering data.

Scanning tables for the layer groups are presented, listing the crystal symmetries for all rational lines in all layer groups (describing monolayer crystals). This has applications for linear defects and domain walls in 2D materials.

Direct derivation of anisotropic atomic displacement parameters is possible using molecular dynamics simulations of supercells at finite temperature.

Carrozzini et al. [(2025), Acta Cryst. A81, 188–201] propose a hybrid phasing strategy where coarse phase estimates for a subset of strong reflections – potentially ML-derived – serve as seeds for dual-space ab initio methods. This can enhance structure solution for large non-centrosymmetric systems.

We have studied the constraints that the spin group symmetry imposes on the most important crystal tensors, on the basis of a generalization of the Neumann principle to spin point groups. Some examples of real materials are presented, and their tensor forms under the spin and magnetic point groups are compared.

A `new theory for X-ray diffraction' proposed by Fewster in 2014 is shown to be based on a conceptual error. Residual intensity away from Bragg peaks is also discussed.

The double-slit Laue symmetrical case dynamical diffraction of X-rays in a crystal influenced by a constant temperature gradient is investigated. The dynamical diffraction double-slit interference fringes are formed; for the period of the fringes an expression is obtained, which depends on the modulus of the temperature gradient and is polarization sensitive.

A novel theory for the one-phase semi-invariant estimates is presented. The theoretical approach uses the Patterson map as prior information.