Experimental observation of carousel-like phason flips in the decagonal quasicrystal Al₆₀Cr₂₀Fe₁₀Si₁₀

Carousel-like successive flippings of groups of atoms inside the decagonal clusters of decagonal quasicrystals were observed experimentally. The observed directionally successive phason flips occur mainly clockwise and occasionally anticlockwise.

On the centennials of the discoveries of the hydrogen bond and the structure of the water molecule: the short life and work of Eustace Jean Cuy (1897–1925)

Eustace J. Cuy (Couyumdjopoulos) was the first scientist to rationalize the bent shape of the water molecule using the Lewis theory of the chemical bond. His work – inspired in part by the discovery of the hydrogen bond by Latimer, Rodebush and Huggins – was published 100 years ago, but had been forgotten after his tragic death at the age of 28.

On Borromean links and related structures

Descriptions are given of optimal piecewise-linear embeddings of families of Borromean structures that can be generated by rotoinversion point-group symmetries. These serve as templates for designed synthesis of polycatenanes.

Piecewise-linear embeddings of knots and links with rotoinversion symmetry

Rotoinversion knots and links are described using the minimum number of sticks. Such structures are attractive targets for molecular synthesis.

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

The presented hybrid approach for a fast and precise determination of the electrostatic potential, electric field and electric field gradient in an infinite crystal, in which the electron-density distribution is represented using a pseudoatom model, combines an efficient Ewald summation technique of the multipoles up to the hexadecapolar level with corrections that account for the nature of the boundary of an infinite periodic lattice at infinity and the short-range electron-density penetration effects.

Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited

An effective theory of lattice vibrations in anisotropic elemental crystals is outlined, based on temperature-dependent spectral cutoffs and varying Debye temperatures. The thermodynamic variables and Debye–Waller B factors of the hexagonal close-packed zinc structure are derived.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory

A theoretical analysis is carried out of the influence of microdefects on the dynamical effects of primary extinction and anomalous absorption in the integrated intensities of coherent and diffuse scattering of X-rays by imperfect crystals in Bragg diffraction geometry.

A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout's identities

The paper describes a method to determine a short unit cell attached to any hyperplane given by its integer vector p. Equivalently, it gives all the solutions of the N-dimensional Bézout's identity associated with the coordinates of p.

Moiré, Euler and self-similarity – the lattice parameters of twisted hexagonal crystals

The moiré lattice parameters are calculated for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides, and the highly complex pattern of solutions is discussed.

Wilson statistics: derivation, generalization and applications to electron cryomicroscopy

This paper provides a rigorous mathematical derivation of Wilson's prediction that the power spectrum of many molecules of biological interest is approximately flat at high frequencies. The analysis elucidates the precise cutoff frequency above which the flat approximation holds and extends the result to other types of statistics with applications to electron cryomicroscopy (cryo-EM).

On incoherent diffractive imaging

Starting from a simple model of stochastic fluorescence emission, a theory is derived of contrast formation and signal-to-noise ratio for incoherent diffractive imaging; its feasibility for plausible experimental parameters is discussed.

On the resolution function for powder diffraction with area detectors

The Caglioti function stemming from 1959 is not well suited to describing the resolution function of modern powder diffraction equipment with large 2D detectors. A new function is derived and verified, replacing the Caglioti function for this very popular geometry.

Teaching Edition of International Tables for Crystallography: Crystallographic symmetry