An error in the article by Mkrtchyan et al. [Acta Cryst. (2025), A81, 438–448] is corrected.

A technical update of the Becker–Coppens [Acta Cryst. (1974), A30, 129–147] recipe for estimating extinction factors in spherical crystallites or grains is provided, addressing limitations in scenarios with higher Bragg angles or stronger extinction effects, as well as providing improved precision in general. The work utilizes modern computing capabilities and improved recipes are provided for easy community adoption.

The Cayley graph of a crystallographic group, although depending only on intrinsic information from the group, often allows the derivation of interesting combinatorial and geometric properties of crystal structures on which the group acts [Baburin (2026). Acta Cryst. A82, 18–31].

P3 is a linearized description of unit-cell parameters, created from the usual lengths and angles of the unit cell. It provides a useful metric for comparing unit cells and a convenient base for displaying and comparing unit cells.

Natural quasicrystals from the Khatyrka meteorite reveal that hypervelocity impacts can generate and preserve quasiperiodic phases under extreme non-equilibrium conditions. Their occurrence highlights the role of quasicrystals as robust markers of shock processes, offering new insights into the collisional and chemical evolution of planetary bodies.

The study introduces new primitive icosahedral quasicrystals in Zn–Mg–Li–(Dy, Ho, Er, Tm) systems. Quasicrystals are studied with an X-ray diffraction technique resolving the local atomic structure.

This study presents a comprehensive characterization of the symmetry structures of tilings on a Klein bottle, arising from tilings of the Euclidean plane with crystallographic symmetry groups containing a subgroup of type pg.

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.

IUCr Journals subscription prices for 2026.

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.

Measurement of diffuse scattering data and subsequent three-dimensional difference pair-distribution function (3D-ΔPDF) analysis of correlated disorder are compared for in-house and synchrotron sources.

Crystal Palace is a new Windows program for parametric analysis of least-squares and atomic coordination with estimated standard uncertainties. It allows the easy analysis of how crystal structures change with temperature, pressure or composition.

An approach is presented to calculate topological coordination numbers (tCNs) obeying the principle of coordination reciprocity from solid angles subtended by the interatomic surfaces of electron density (QTAIM) atomic domains. The tCN approach characterizes a compound's coordination situation as a set of sub-coordination scenarios with associated weights, which is considered a suitable input for future AI applications on structure–property relationships.

The variance of 1/d2hkl positions for different lattice relaxation schemes is calculated and compared with literature formulas for anisotropic peak broadening in powder diffraction.

A new phasing method capable of solving crystal structures, from small molecules to macromolecules, is conceived and tested by a feasibility study.

The report of the Executive Committee for 2023 is presented.

In memory of George Sheldrick.

Pair distribution function (PDF) analysis can provide important local structure insights; however, its application in thin films is limited to those on amorphous substrates. We report a novel data processing approach and program, IsoDAT2D, which demonstrates the feasibility of using unsupervised machine learning algorithms to access PDF data from thin films on single-crystal substrates.

The structure of the α-helix is determined by a helical substructure of the 4D tube polytope with the symmetry group ±[O×D20]; this substructure has a screw axis 40/11 with the angle of rotation of 99°. This polytope belongs to the family of tube polytopes with the starting groups ±1/2[O×C2n], which determine the screw axes of the α-helices included in superhelices.

Twisted homophase bilayers exhibit remarkable physical properties absent in their constituent monolayers. Quiquandon & Gratias [Acta Cryst. (2025), A81, https://doi.org/10.1107/S2053273324012087] develop a crystallographic framework for rigorous description of the structure of bilayers, including systems without a coincidence lattice.

Sine Larsen, former President and former General Secretary and Treasurer of the IUCr, is remembered.

Obituary for Rajagopala Chidambaram

Several types of possible hexagonal double-layer honeycombs are described and analyzed from the point of view of their topology, symmetry and wax economy, including the newly discovered honeycomb with minimal use of wax.

A description is provided of infinite families of high-symmetry 1-periodic chains, including linked polygons as well as linked polyhedra. Examples of both Hopf-linked and Borromean-linked chains are presented.

We present an algorithm for unit-cell determination from a set of randomly oriented electron diffraction patterns and demonstrate its performance for two known structures (copper perchlorophthalocyanine and lysozyme) and one as-yet uncharacterized structure.

Bayesian machine learning, trained by physics-based simulations, is used to separate the effects of temperature and mechanical loading within in situ diffraction data.

The quasiperiodic nature of moiré patterns in homophase twisted bilayers is analyzed to understand the underlying basic periodicities and symmetries of homophase twisted bilayers built on any 2D structure.

This article describes the re-formulation of Bloch waves using physical optics theory for more efficient simulation of large electron diffraction data sets.