A digital distance on the kisrhombille tiling

The kisrhombille tiling is the dual of one of the eight semi-regular tilings and is built up by right-angled triangles in 12 orientations. In this paper, an appropriate coordinate system is presented and the digital distance is defined and computed by the number of steps of neighboring triangles, where two triangles are considered to be neighbors if they share at least one point on their border.

The single-atom R1: a new optimization method to solve crystal structures

A new optimization method based on a new concept of single-atom R1 (sR1) for solving crystal structures is presented.

N-representable one-electron reduced density matrix reconstruction with frozen core electrons

An improved method of one-electron reduced density matrix reconstruction from structure factors and directional Compton profiles is tested on a urea crystal. Novel restrictions accounting for molecular symmetry and freezing of core electrons are introduced.

Bond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO₄)ⁿ⁻ tetrahedra

It is shown that all possible topologically distinct chain graphs of tetrahedra may be embedded into 3D Euclidean space. In minerals, separations between linked T cations are 3.06 (15) Å and between unlinked T cations are >3.71 Å, and these distances constrain the ability of embedded chain graphs to occur as structural entities in crystals. Software (GraphT-T) allows this embedding to be tested for stereochemical viability.

GraphT–T (V1.0Beta), a program for embedding and visualizing periodic graphs in 3D Euclidean space

The program GraphT–T (V1.0Beta) has been developed to embed graphical representations of observed and hypothetical chains of (SiO₄)⁴⁻ tetrahedra into 2D and 3D Euclidean space.

Permissible domain walls in monoclinic ferroelectrics. Part II. The case of M_C phases

Following the previous work [Biran & Gorfman (2024). Acta Cryst. A80, 112–128], all the possibilities for permissible (mismatch-free) walls between monoclinic domains of pseudocubic ferroelectric perovskites of M_C type are analyzed. The study yields analytical expressions for the orientation of such walls, the orientation relationship between the lattice vectors and for the separation between Bragg peaks diffracted from matched domains.