3.4 Domain structures

This chapter is devoted to the crystallographic aspects of static ferroic domain structures. The exposition is based on well defined concepts and rigorous relations that follow from the symmetry lowering at the ferroic phase transition. Necessary mathematical tools are explained in Section 3.2.3 and important points are illustrated with simple examples. Synoptic tables provide useful ready-to-use data accessible even without knowledge of deeper theory. Three main concepts needed in a rigorous analysis (both in a continuum and a microscopic description) of any domain structure are thoroughly discussed. (1) Domain states (orientation states or structural variants) representing inner structures of domains are classified according to their characteristic properties (ferroelastic, ferroelectric etc.) and their hierarchy (primary, secondary, principal, basic etc.). A synoptic table is given with all possible symmetry lowerings at ferroic transitions and contains the numbers of ferroic, ferroelectric and ferroelastic domain states, Aizu's classification and the representation characterizing the principal domain states. (2) Relations between domain states (twin laws) determine domain distinction, switching of domain states in external fields and properties of interfaces (domain walls) between coexisting domains. Tables give for each possible transition all independent twin laws and for each twin law the number of equal and distinct tensor components of material tensors up to rank 4 in two coexisting domains of a domain twin. (3) The basic properties of domain twins and domain walls are determined by their symmetry, which is expressed by crystallographic layer groups. The fundamental significance of this description is explained and illustrated. Synoptic tables give for each twin law the possible orientations of compatible domain walls and their symmetries. Keywords: Aizu classification; Dauphine twins; coherent domain walls; dichromatic complexes; domain pairs; domain states; domain structures; domain twins; domain walls; ferroelastic domain pairs; ferroelastic domain states; ferroelastic domain structures; ferroelastic domain twins; ferroelastic domain walls; ferroelastic single-domain states; ferroelectric domain states; ferroelectric domain structures; ferroic domain states; ferroic domain structures; ferroic transitions; layer groups; morphic tensor components; non-ferroelastic domain pairs; non-ferroelastic domain states; non-ferroelastic domain structures; non-ferroelastic domain twins; non-ferroelastic domain walls; non-ferroelastic phases; non-ferroelectric domain states; non-ferroelectric phases; parent clamping approximation; physical property tensors; stabilizers; switching; symmetry descent; twin laws; twinning group