Twinning

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Oriented association and twinning

Crystals (also called individuals or components) or domains belonging to the same phase form an oriented association if they can be brought to coincidence by a translation, rotation, inversion or reflection. Individuals related by a translation form a parallel association; domains related by a translation form antiphase domains. Individuals or domains related by a reflection, inversion or rotation form a twin called, respectively, reflection twin, inversion twin or rotation twin.

A mapping relating differently oriented crystals cannot be a symmetry operation of the individual: it is called a twin operation and geometric element about which it is performed, associated with this operation, is called twin element. Mallard's law states that the twin element is restricted to a direct lattice element: it can thus coincide with a lattice node (twin centre), a lattice row (twin axis) or a lattice plane (twin plane).

The symmetry of a twin (twin point group) is obtained by extending the intersection point group of the individuals in their respective orientations by the twin operation.

Classification of twins

Twins are classified following Friedel's reticular (i.e. lattice) theory of twinning (see: G. Friedel Lecons de Cristallographie, Nancy (1926) where reference to previous work of the author can be found; see also Friedel's law). This theory states that the presence, either in the lattice or a sublattice of a crystal, of (pseudo)symmetry elements is a necessary, even if not sufficient, condition for the formation of twins. In presence of the reticular necessary conditions, the formation of a twin finally still depends on the matching of the crystal structures at the contact surface between the individuals.

The following categories of twins are described under the listed entries.

• twinning by merohedry
• twinning by pseudomerohedry
• twinning by reticular merohedry
• twinning by reticular pseudomerohedry
• twinning by metric merohedry
• twinning by reticular polyholohedry
• hybrid twins
• plesiotwins
• allotwins
• selective merohedry

Related articles

• twinning (effects of)
• twin index
• twin lattice
• twin law
• twin obliquity
• corresponding twins
• twinning (endemic conditions of)
• Twinning (effects of)

See also

• Chapter 1.3 of International Tables of Crystallography, Volume C
• Chapter 3.3 of International Tables of Crystallography, Volume D