International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 3.4, p. 535

## Section 3.4.4.5. Ferroelastic domain twins and walls. Ferroelastic twin laws

V. Janoveca* and J. Přívratskáb

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic, and bDepartment of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic
Correspondence e-mail:  janovec@fzu.cz

#### 3.4.4.5. Ferroelastic domain twins and walls. Ferroelastic twin laws

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As explained in Section 3.4.3.6, from a domain pair of ferroelastic single-domain states with two perpendicular equally deformed planes p and one can form four different ferroelastic twins (see Fig. 3.4.3.8). Two mutually reversed twins and have the same twin symmetry and the same symmetry of the twin pair . The ferroelastic twin laws can be expressed by the layer group or, in a less complete way (without specification of reversibility), by the twin symmetry . The same holds for two mutually reversed twins and with a twin plane perpendicular to p.

Table 3.4.4.6 summarizes possible symmetries of ferro­elastic domain twins and corresponding ferroelastic twin laws . Letters V and W signify strain-dependent and strain-independent (with a fixed orientation) domain walls, respectively. The classification of domain walls and twins is defined in Table 3.4.4.3. The last column contains twinning groups of ordered domain pairs from which these twins can be formed. The symbol of is followed by a symbol of the group given in square brackets. The twinning group specifies, up to two cases, a class of equivalent domain pairs [orbit ] (see Section 3.4.3.4). More details on particular cases (orientation of domain walls, disorientation angle, twin axis) can be found in synoptic Table 3.4.3.6. From this table follow two general conclusions:

• (1) All layer groups describing the symmetry of compatible ferroelastic domain walls are polar groups, therefore all compatible ferroelastic domain walls in dielectric crystals can be spontaneously polarized. The direction of the spontaneous polarization is parallel to the intersection of the wall plane p and the plane of shear (i.e. a plane perpendicular to the axis of the ferroelastic domain pair, see Fig. 3.4.3.5b and Section 3.4.3.6.2).

 Table 3.4.4.6| top | pdf | Symmetry properties of ferroelastic domain twins and compatible domain walls
Classification
V   , , ,
V
W , , , , , , , ,
V SI
W   , , ,
W SI
V , , , , , , , , ,
W SI
W   , , ,
W SI
W SR , , , , , , ,
W SR
V SR   , , , ,
W SR
W SR   , ,
W SR
m V AI   , ,
m V AI
m V   ,
V
W SR , , , , , , ,
W SR
W , , , , , , ,
W SI
W SR , , , ,
W SR
• (2) Domain twin formed in the parent clamping approximation from a single-domain pair and the relaxed domain twin with disoriented domain states have the same symmetry groups and .

This follows from simple reasoning: all twin symmetries in Table 3.4.4.6 have been derived in the parent clamping approximation and are expressed by the orthorhombic group or by some of its subgroups. As shown in Section 3.4.3.6.2, the maximal symmetry of a mechanically twinned crystal is also . An additional simple shear accompanying the lifting of the parent clamping approximation cannot, therefore, decrease the sym­metry derived in the parent clamping approximation. In a similar way, one can prove the statement for the group of the twin pairs and .