Application of modern tensor calculus to engineered domain structures. 1. Calculation of tensorial covariants

A systematic approach to calculation of the decomposition of material tensors, including magnetic properties, into tensorial covariants is described.

Application of modern tensor calculus to engineered domain structures. 2. Tensor distinction of domain states

Tensor parameters of domain states in ferroic phase transitions are considered. It is shown how to find both primary and secondary parameters from the decomposition of tensors into covariants.

Unified system of Hermann–Mauguin symbols for groups of material physics. 1. Groups with decomposable lattices

Amendments of classical concepts of space and crystallographic groups are proposed and a unified system of Hermann–Mauguin symbols described which includes subperiodic groups and groups with semicontinuous and continuous lattices. Symbols of subperiodic groups are correlated with symbols of space groups with decomposable lattices.

Some algebraic properties of crystallographic sublattices

Methods are provided to establish the standard form and group structure of a geometric sublattice, and to find the common superlattice of greatest index, and common sublattice of least index, of two such sublattices.

Distinction of magnetic non-ferroelastic domains

Coordinate systems exist in which tensor properties of two magnetic non-ferroelastic domains differ solely by a change in sign.

Quartz aggregates revisited

In quartz aggregates formed by coalescence of preformed crystals in the magma or in hydrothermal solution, monoperiodic twins are common and not restricted to the Zinnwald orientation. For certain values of the axial ratio c/a, diperiodic coincidence in the contact plane will appear, which may be related to the frequency of occurrence of various orientations in low- and high-quartz.

Structures of coincidence symmetry groups

This paper considers the decomposition of a coincidence isometry of a lattice into coincidence reflections and the use of decomposition to study the structure of the coincidence symmetry group.

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups

The article reports on the computer databases and group-theoretical tools related to representations of crystallographic point groups and space groups that are available on the Bilbao Crystallographic Server (https://www.cryst.ehu.es).

Informational entropy of Fourier maps

Information theory has been applied to calculate the amount of information and the informational entropy existing in a Fourier map. These values increase enormously when the number of peaks in the map increases, the greater contribution corresponding to the uncertainty related to the network of chemical bonds.

Comparative crystallographic and hydrogen-bonding analysis of cholestane derivatives

Crystallographic comparison of some geometrical and structural features are described for a series of cholestane derivatives and an analysis is given of X—H⋯A intra- and intermolecular interactions with the aid of distance–scatter plots.