Identification of a coherent twin relationship from high-resolution reciprocal-space maps

The theory and algorithm are presented for the assignment of ferroelastic domains to the individual components of split Bragg peaks in high-resolution reciprocal-space maps. The formalism of mechanical compatibility of ferroelastic domains is further developed for the analysis of the geometry of the reciprocal space. The application of the algorithm to the reciprocal-space maps of tetragonal BaTiO₃ and rhombohedral PbZr_1−xTi_xO₃ crystals is demonstrated.

Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudo­symmetries and its optimal image-quality enhancement

Information-theoretic crystallographic symmetry classifications distinguish between genuine symmetries and strong Fedorov-type pseudo­symmetries in noisy crystal patterns in two dimensions. Because these classifications require neither visual comparisons of image pairs nor subjective interpretations of `symmetry deviation quantifiers' by human beings, they enable the optimal crystallographic processing of an experimental image that results in a significantly enhanced signal-to-noise ratio of a microscopic study of a crystal.

A Metropolis Monte Carlo algorithm for merging single-particle diffraction intensities

A Monte Carlo implementation of the expand–maximize–compress algorithm is presented and compared with the standard implementation.

Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO₄)ⁿ⁻ tetrahedra

Chains of TO₄ⁿ⁻ tetrahedra are represented as chain graphs in which tetrahedra are represented as vertices and the linkage between tetrahedra is represented as edges. Topologically distinct chain graphs are generated for all possible chain stoichiometries (up to a boundary number of tetrahedra) using the formalisms of graph theory, making possible the comparison of observed chain arrangements with all topologically possible chain arrangements.

Isogonal piecewise-linear embeddings of 1-periodic knots and links, and related 2-periodic chain-link and knitting patterns

1- and 2-periodic structures are described built from single threads, or from multiple threads with parallel or collinear axes. The work has relevance to the manufacture of mechanically interlocked polymers.

nmfMapping: a cloud-based web application for non-negative matrix factorization of powder diffraction and pair distribution function datasets

A web application for non-negative matrix factorization of powder X-ray diffraction and pair distribution function datasets is presented, with examples.

Ab initio reconstruction from one-dimensional crystal diffraction data

Methods for reconstructing electron densities from diffraction amplitudes alone, measured from single 1D crystals, are described and illustrated by simulation. Ab initio phasing is demonstrated using an iterative projection algorithm.

Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. I. Theory

A general formalism to determine the surface unit cell of a three-dimensional crystallographic lattice is presented.

Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. II. Experimental results

Organic epitaxy is studied experimentally in terms of the correlation of the involved two- and three-dimensional crystallographic lattices.

From affine A₄ to affine H₂: group-theoretical analysis of fivefold symmetric tilings

The non-crystallographic affine group H₂ is constructed as the subgroup of the affine Coxeter–Weyl group A₄. It is applied on the projections of the Voronoi cells of root and weight lattices of A₄ leading to fivefold tessellations of the plane, which could be useful in the classification of quasicrystals.

Lessons in Enumerative Combinatorics