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. 3.4, pp. 521527
Section 3.4.3.6.4. Ferroelastic domain pairs with compatible domain walls, synoptic table^{a}Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ18221 Prague 8, Czech Republic, and ^{b}Department of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic 
As we have seen, for each ferroelastic domain pair for which condition (3.4.3.54) for the existence of coherent domain walls is fulfilled, there exist two perpendicular equally deformed planes. On each of these planes two ferroelastic twins can be formed; these two twins are in a simple relation (one is a reversed twin of the other), have the same symmetry, and can therefore be represented by one of these twins. Then we can say that from one ferroelastic domain pair two different twins can be formed. Each of these twins represents a different `twin law' that has arisen from the initial domain pair. All four ferroelastic twins can be described in terms of mechanical twinning with the same value of the shear angle .
Table 3.4.3.6 presents representative domain pairs of all classes of ferroelastic domain pairs for which compatible domain walls exist. The first five columns concern the domain pair. In subsequent columns, each row splits into two rows describing the orientation of two associated perpendicular equally deformed planes and the symmetry properties of the four domain twins that can be formed from the given domain pair. We explain the meaning of each column in detail.

The first three columns specify domain pairs.
Example 3.4.3.7. The rhombohedral phase of perovskite crystals. Examples include PZNPT and PMNPT solid solutions (see e.g. Erhart & Cao, 2001) and BaTiO_{3} below 183 K. The phase transition has symmetry descent .
In Table 3.4.2.7 we find that there are eight domain states and eight ferroelectric domain states. In this fully ferroelectric phase, domain states can be specified by unit vectors representing the direction of spontaneous polarization. We choose with corresponding symmetry group .
From eight domain states one can form domain pairs. These pairs can be divided into classes of equivalent pairs which are specified by different twinning groups. In column of Table 3.4.2.7 we find three twinning groups:
These conclusions are useful in deciphering the `domainengineered structures' of these crystals (Yin & Cao, 2000).
References
Erhart, J. & Cao, W. (2001). Effective symmetry and physical properties of twinned perovskite ferroelectric single crystals. J. Mater. Res. 16, 570–578.Yin, J. & Cao, W. (2000). Domain configurations in domain engineered 0.995Pb(Zn_{1/3}Nb_{2/3})O_{3}–0.045PbTiO_{3} single crystals. J. Appl. Phys. 87, 7438–7441.