Modern crystallography and its foundations

Authors and readers are reminded of the history and scope of Acta Crystallographica Section A, and simple steps to help maintain its prominence and impact as the premier journal for foundational work in crystallography are outlined.

A cloud platform for atomic pair distribution function analysis: PDFitc

A new web platform is presented for the pair distribution function (PDF) community to use and share advanced PDF analysis software in the cloud.

Spiral tetrahedral packing in the β-Mn crystal as symmetry realization of the 8D E₈ lattice

The 2D projection of all atomic positions in the β-Mn unit cells shows that they are situated on three circumferences containing 2D projections of 90 vertices of the {3, 3, 5} polytope on the same plane. The exhaustive description of the non-crystallographic symmetry of the β-Mn crystal has been achieved by using the 8D E₈ lattice in which both the 4D {3, 3, 5} polytope and cubic 6D B₆ lattice can be inserted.

Macromol­ecular phasing using diffraction from multiple crystal forms

A phasing algorithm for protein crystallography using diffraction data from multiple crystal forms is proposed. The algorithm is evaluated by simulation, and practical aspects and potential for ab initio phasing are discussed.

Gummelt versus Lück decagon covering and beyond. Implications for decagonal quasicrystals

The diversities and commonalities of the two basic decagonal clusters, the Gummelt and the Lück decagons, and of their coverings are discussed.

Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law

The intensity of small-angle X-ray scattering from GaN nanowires on Si(111) depends on the orientation of the side facets with respect to the incident beam. This reminiscence of truncation rod scattering gives rise to a deviation from Porod's law. A roughness of just 3–4 atomic steps per micrometre-long side facet notably changes the intensity curves.

HgH₂ meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

Relativistic structure factors are used to teach a non-relativistic wavefunction relativity using the X-ray constrained wavefunction method, whereby resolution and scaling effects are critically assessed.

The maximum surface area polyhedron with five vertices inscribed in the sphere

It is shown that a polyhedron with the trigonal bipyramidal structure is the unique surface area maximizer among all polyhedra with five vertices inscribed in a sphere.

Algebraic approximations of a polyhedron correlation function stemming from its chord-length distribution

A procedure is reported for obtaining an algebraic approximation of the correlation function of a polyhedron starting from its known chord-length distribution.

Mathematics for Physicists. Introductory Concepts and Methods