Deep learning applications in protein crystallography

Deep learning applications are increasingly dominating many areas of science. This paper reviews their relevance for and impact on protein crystallography.

Realizations of crystal nets. I. (Generalized) derived graphs

Crystal nets are popular discrete representations of crystal structures, and a recent generalization of voltage graphs allows for a representation of a crystal net as a component of a graph derived from a putative quotient graph labeled by voltages and point groups; this component is realized by successively generating its edges and vertices.

Symmetry groups of two-way twofold and three-way threefold fabrics

The symmetry groups of two-way twofold fabrics and three-way threefold fabrics are derived, including geometric representations of all possible layer symmetry group structures. A method to arrive at a two-way twofold fabric or a three-way threefold fabric with a given symmetry group type is discussed, using tools in color symmetry theory.

Maximal independence and symmetry in crystal chemistry of natural tectosilicates

The distribution of aluminium cations in natural tectosilicates is shown to satisfy the concepts of maximal independence and maximum symmetry.

Hierarchical topological analysis of crystal structures: the skeletal net concept

The skeletal net concept is introduced into the scheme of hierarchical topological analysis of crystal structures to provide the simplest way of describing structure connectivity. Examples, which illustrate the advantages of such analysis, are considered for elements, intermetallics, ionic and coordination compounds, and molecular crystals.

Periodic diffraction from an aperiodic monohedral tiling

The diffraction pattern from the quasicrystalline `hat monotile' is periodic with sixfold chiral symmetry, p6. Triangular patches of discrete satellite reflections appear near the 2/3 2/3 hexagonal reciprocal-lattice locations.

Periodic Borromean rings, rods and chains

The synthesis of molecular Borromean rings and other links is an active area of chemical research. Hypothetical 1-, 2- and 3-periodic molecular structures are described with the Borromean property that, although no two rings or chains are linked, the structures are interlocked and do not fall apart.

Isogonal 2-periodic polycatenanes: chain mail

Two-periodic chain mail polycatenane structures with one kind of vertex are presented. Twenty-four infinite families are identified, with hexagonal, tetragonal or rectangular symmetry.

Algorithm for spin symmetry operation search

An algorithm is presented for determining the spin symmetry operations of a given spin arrangement. Spin symmetry operations of a spin space group act simultaneously on both the spatial and spin coordinates of the spin arrangement.

Identification of Kikuchi lines in electron diffraction patterns collected in small-angle geometry

Some advantages of filtering of digital reflection high-energy electron diffraction (RHEED) patterns are shown.

Permissible domain walls in monoclinic M_AB ferroelectric phases

All the possibilities for permissible (mismatch-free) walls between monoclinic domains of pseudocubic ferroic perovskites are analyzed. Analytical expressions are derived for the orientation of such walls, the orientation relationship between the lattice vectors and the separation between Bragg peaks diffracted from matched domains.

Analytical models representing X-ray form factors of ions

Analytical representations of X-ray form factors for ions are examined based on the inverse Mott–Bethe formula. Twelve sources of form-factor data spanning the period 1961–2023 and representing various ranges and grids in sinθ/λ and different precisions are analysed. Generally, 96.1% of all form factors are exactly reproduced by the analytical models.

Professor Dr Hendrik (Henk) Schenk (1939–2023)

Obituary for Professor Dr Hendrik (Henk) Schenk.