Periodic entanglement I: networks from hyperbolic reticulations

It is well established that crystalline 3-periodic nets can be constructed and systematically catalogued using Delaney–Dress tiling theory. One approach does this by enumerating two-dimensional hyperbolic () tilings and then projects those patterns into three-dimensional Euclidean space () via triply periodic minimal surfaces. We extend this to an investigation of three-dimensional patterns that emerge from a the systematic enumeration of ribbon-like free tilings of .

Periodic entanglement II: weavings from hyperbolic line patterns

In this article, rod packings are generalized to include arrays of more general one-dimensional curvilinear cylinders. Examples are built by projecting free tilings of two-dimensional hyperbolic space into three-dimensional Euclidean space via genus-3 triply periodic minimal surfaces, forming three-dimensional weavings of filaments, which are tightened to a canonical form.

Non-crystallographic nets with finite blocks of imprimitivity for bounded automorphisms

Wreath products of finite permutation groups by translation groups are introduced to describe non-Euclidian symmetries occurring in non-crystallographic nets.

Nonlocality in spherical-aberration-corrected HAADF STEM images

Nonlocality in spherical-aberration-corrected high-angle annular dark-field scanning transmission electron microscope images is theoretically and experimentally examined. A detailed comparison between experimental data and simulations suggests that nonlocality in the thermal diffuse scattering absorption potential cannot be ignored for detailed analysis of materials consisting of several heavy elements.

Impact of anomalous effects on the angular distribution of coherently scattered photons using Monte Carlo simulation

The role of anomalous scattering factors in the angular distribution of coherently scattered photons is explored.

Anisotropic displacement parameters for molecular crystals from periodic Hartree–Fock and density functional theory calculations

An approach to calculating anisotropic displacement parameters based on periodic ab initio calculations is introduced. Calculations on urea, benzene, urotropine and L-alanine are discussed and validated against available experimental results.

Cluster-packing geometry for Al-based F-type icosahedral alloys

A highly stable, periodic approximant to Al-based F-type icosahedral quasicrystals, i-Al–Pd–TM (TM = transition metals), has been synthesized for the first time. A thorough investigation of the crystal structure leads to a universal description of a broader class of complex crystal structures closely related to the quasicrystals.

Incommensurate phases in the statistical theory of the crystalline state

This article is devoted to the elaboration of a mathematical apparatus for studying second-order phase transitions, both commensurate and incommensurate, and the properties of emerging phases on the basis of the approach in equilibrium statistical mechanics proposed earlier by the author.

Quasirandom quasicrystals

Two-dimensional point sets derived from pairs of quasirandom numbers generated by the bit-reversal method introduced by van der Corput exhibit features well known from the quasiperiodic binary substitution tilings derived from the rhombic tilings of Penrose and Ammann–Beenker. The concept of geometric discrepancy, a measure describing the uniformity of distribution of quasirandom sequences or point sets, is discussed from the perspective of structural chemistry.