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. 491492
Section 3.4.2.2.1. Ferroelastic domain state^{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 
The distinction ferroelastic–nonferroelastic is a basic division in domain structures. Ferroelastic transitions are ferroic transitions involving a spontaneous distortion of the crystal lattice that entails a change of shape of the crystallographic or conventional unit cell (Wadhawan, 2000). Such a transformation is accompanied by a change in the number of independent nonzero components of a symmetric secondrank tensor that describes spontaneous strain.
In discussing ferroelastic and nonferroelastic domain structures, the concepts of crystal family and holohedry of a point group are useful (IT A , 2005). Crystallographic point groups (and space groups as well) can be divided into seven crystal systems and six crystal families (see Table 3.4.2.2). A symmetry descent within a crystal family does not entail a qualitative change of the spontaneous strain – the number of independent nonzero tensor components of the strain tensor u remains unchanged.

We shall call the largest group of the crystal family to which the group M belongs the family group of M (symbol FamM). Then a simple criterion for a ferroic phase transition with symmetry descent to be a nonferroelastic phase transition is
A necessary and sufficient condition for a ferroelastic phase transition is
A ferroelastic domain state is defined as a state with a homogeneous spontaneous strain . [We drop the suffix `s' or `(s)' if the serial number of the domain state is given as the superscript . The definition of spontaneous strain is given in Section 3.4.3.6.1.] Different ferroelastic domain states differ in spontaneous strain. The symmetry of a ferroelastic domain state R_{i} is specified by the stabilizer of the spontaneous strain of the principal domain state [see (3.4.2.16)]. This stabilizer, which we shall denote by , can be expressed as an intersection of the parent group G and the family group of (see Table 3.4.2.2):This equation indicates that the ferroelastic domain state R_{i} has a prominent singledomain orientation. Further on, the term `ferroelastic domain state' will mean a `ferroelastic domain state in singledomain orientation'.
The number of ferroelastic domain states is given byIn our example, . In Table 3.4.2.7, last column, the number of ferroelastic domain states is given for all possible ferroic phase transitions.
The number of principal domain states compatible with one ferroelastic domain state (degeneracy of ferroelastic domain states) is given byIn our example, , i.e. two nonferroelastic principal domain states are compatible with each of the two ferroelastic domain states (cf. Fig. 3.4.2.2).
The product of and is equal to the number n of all principal domain states [see equation (3.4.2.19)],The number of principal domain states in one ferroelastic domain state can be calculated for all ferroic phase transitions from the ratio of numbers n and that are given in Table 3.4.2.7.
According to Aizu (1969), we can recognize three possible cases (see also Table 3.4.2.3):

Example 3.4.2.1. Domain states in leucite. Leucite (KAlSi_{2}O_{6}) (see e.g. Hatch et al., 1990) undergoes at about 938 K a ferroelastic phase transition from cubic symmetry to tetragonal symmetry . This phase can appear in singledomain states, which we denote , , . The symmetry group of the first domain state is . This group equals the stabilizer of the spontaneous strain of since Fam( (see Table 3.4.2.2), hence this phase is a full ferroelastic one.
At about 903 K, another phase transition reduces the symmetry to . Let us suppose that this transition has taken place in a domain state with symmetry ; then the roomtemperature ferroic phase has symmetry . The phase transition is a nonferroelastic one [] with nonferroelastic domain states, which we denote and . Similar considerations performed with initial domain states R_{2} and R_{3} generate another two couples of principal domain states , and , , respectively. Thus the roomtemperature phase is a partially ferroelastic phase with three degenerate ferroelastic domain states, each of which can contain two principal domain states. Both ferroelastic domains and nonferroelastic domains within each ferroelastic domain have been observed [see Fig. 3.3.10.13 in Chapter 3.3 , Palmer et al. (1988) and Putnis (1992)].
References
International Tables for Crystallography (2005). Vol. A, SpaceGroup Symmetry, 5th ed., edited by Th. Hahn. Heidelberg: Springer.Aizu, K. (1969). Possible species of `ferroelastic' crystals and of simultaneously ferroelectric and ferroelastic crystals. J. Phys. Soc. Jpn, 27, 387–396.
Hatch, D. M., Ghose, S. & Stokes, H. (1990). Phase transitions in leucite, KAl_{2}O_{6}. I. Symmetry analysis with order parameter treatment and the resulting microscopic distortions. Phys. Chem. Mineral. 17, 220–227.
Palmer, D. C., Putnis, A. & Salje, E. K. H. (1988). Twinning in tetragonal leucite. Phys. Chem. Mineral. 16, 298–303.
Putnis, A. (1992). Introduction to Mineral Sciences. Cambridge University Press.
Wadhawan, V. K. (2000). Introduction to Ferroic Materials. The Netherlands: Gordon and Breach.