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.

Tensor distinction of pairs of completely transposable domain states in multiferroics