Origin and application of the Lorentz factor in X-ray diffraction

This review treats the role of the Lorentz factor in quantitative analysis of X-ray diffraction data. The origin of the Lorentz factor, its derivation and practical implementations for a variety of modern X-ray diffraction methods are discussed.

Symmetric vertex- and edge-transitive 3-periodic nets

We show that most crystal structures found in nature correspond to symmetric or supersymmetric nets, which are tolerable (tessellate). Remarkably, we find only one reported structure based on a symmetric net that is decussate (untileable).

Surface-driven size scaling of the lattice parameter, Debye–Waller coefficient and microstrain in nanocrystals

This work develops three surface-driven nanoscale models for the diffraction-derived lattice parameter, Debye–Waller coefficient and microstrain, clarifying why their size dependences are not equally universal. Atomistic simulations and literature data show that lattice parameter trends depend strongly on capillarity, chemistry and defects, whereas the Debye–Waller coefficient and microstrain follow more robust surface-disorder and surface-stress gradient scaling laws.

Tiles from projections of the root and weight lattices of A_n

The 2D faces of the Voronoi cell of the lattice A₄* are of two types: regular hexagons and squares in 4D, but project into two types of hexagons and two types of rhombuses with edges of two lengths in proportion to the golden ratio.

A parsimonious structure model for the icosahedral quasicrystal Cd_5.7Yb

The paper presents a parsimonious structure model for the icosahedral Cd_5.7Yb quasicrystal. It employs only spherical and elliptical occupation domains, which significantly decreases the number of parameters and the required calculation effort. Still, the model describes the characteristic structural features with considerable accuracy.