Algorithms for magnetic symmetry operation search and identification of magnetic space group from magnetic crystal structure

This paper presents algorithms for determining magnetic symmetry operations of magnetic crystal structures, identifying magnetic space-group types from a given magnetic space group (MSG), searching for transformations to a Belov–Neronova–Smirnova setting, and symmetrizing the magnetic crystal structures on the basis of the determined MSGs.

Patch frequencies in rhombic Penrose tilings

An algorithm is presented for an exact calculation of patch frequencies for a family of tilings which can be obtained via dualization.

Background optimization of powder electron diffraction for implementation of the e-PDF technique and study of the local structure of iron oxide nanocrystals

In the case of small nanocrystals (about 4 nm), with a change in electron beam energy the influence of multiple/inelastic scattering on the background signal of powder electron diffraction patterns is evident. Adopting different background removal approaches at lower (80 kV) and higher (300 kV) electron beam energies, e-PDF (electron pair distribution function) G(r) profiles are extracted. From small-box modelling of the structural parameters related to the iron oxide nanoparticles considered, the applicability of the subtraction procedures is discussed.

Optimal estimated standard uncertainties of reflection intensities for kinematical refinement from 3D electron diffraction data

Several models for estimating the standard uncertainties of reflection intensities are analysed for refinement against 3D electron diffraction data. A new model is proposed which results in more accurate structure models.

Perfect precise colorings of plane semiregular tilings

This contribution outlines how to obtain perfect precise colorings of tilings, and illustrates this by obtaining perfect precise colorings of some families of k-valent semiregular planar tilings with k colors.

Distances in the face-centered cubic crystalline structure applying operational research

The face-centered cubic lattice describes the crystalline structure of various materials. Based on two weights assigned to the two types of neighbors among the nodes (representing, e.g., ions), formulae of chamfer distances are computed with the help of the simplex method.

Combinatorial aspects of the Löwenstein avoidance rule. Part III: the relational system of configurations

Maximum independent sets in periodic nets are constructed as homomorphic images of Cayley colour graphs. The method applies to zeolites and aluminosilicates.

Approximating lattice similarity

A method is proposed for transforming unit cells for a group of crystals so that they all appear as similar as possible to a selected cell.

Measuring lattices

Unit cells are used to represent crystallographic lattices. Calculations measuring the differences between unit cells are used to provide metrics for measuring meaningful distances between three-dimensional crystallographic lattices. This is a surprisingly complex and computationally demanding problem. A review is presented of the current best practice using Delaunay-reduced unit cells in the six-dimensional real space of Selling scalar cells S⁶ and the equivalent three-dimensional complex space C³.

Delone lattice studies in C³, the space of three complex variables

The space C³ is explained in more detail than in the original description. Boundary transformations of the fundamental unit are described in detail. A graphical presentation of the basic coordinates is described and illustrated.