International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 3.3, p. 477
Section 3.3.12. Domain structures (by V. Janovec)^{a}Institut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and ^{b}Mineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany |
Domain structure is a special kind of twinning which results from lowering of crystal symmetry at a phase transition. A homogeneous phase with higher symmetry (called the parent phase) breaks into a non-homogeneous twinned phase (ferroic phase) with lower symmetry in which the twin partners (domains) are related by twinning operations that are crystallographic operations disappearing at the transition (for different terminology used in twinning and domain structures, see Table 3.4.2.4 ).
Domains have lower symmetry than the parent phase. As a result, domains acquire additional physical properties called spontaneous properties. When observed by certain apparatus (e.g. a microscope), anisotropic domains exhibit different properties and thus can be observed and identified in direct space. This distinction of domains in direct space by means of their spontaneous properties thus provides important additional information to the examination of twinning of the material by diffraction methods.
It turns out that symmetry lowering at the transition exactly determines which spontaneous quantities are distinct in the two different domains of a domain twin. Unfortunately, this useful consideration cannot be performed with twins which originate from means other than a phase transition, e.g. growth twins. It is, however, possible to check whether the nonexistent high-symmetry parent phase can be substituted by a so-called composite symmetry of the twin, even though a phase of the crystal with this symmetry does not exist in reality. This means that we treat a twin as a domain twin resulting from a nonexistent (hypothetical) phase transition.
This is why it is expedient to have at one's disposal tables of possible phase transitions from all possible composite symmetries. These tables can be found in Sections 3.4.3 and 3.4.4 of Chapter 3.4. Several examples show how these tables can be utilized in twin analysis.