Twin lattice

Réseau de la macle (Fr) Reticolo del geminato (It)

A twin operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent (twinning (effects of). The (sub)lattice that is formed by the (quasi)restored nodes is the twin lattice. In case of non-zero twin obliquity the twin lattice suffers a slight deviation at the composition surface.

Let H* = ∩_iH_i be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D(L_T) the point group of the twin lattice and D(L_ind) the point group of the individual lattice. D(L_T) either coincides with D(H*) (case of zero twin obliquity) or is a proper supergroup of it (case of non-zero twin obliquity): it can be higher, equal or lower than D(L_ind).

• When D(L_T) = D(L_ind) and the two lattices have the same orientation, twinning is by merohedry (twin index = 1). When at least some of the symmetry elements of D(L_T) are differently oriented from the corresponding ones of D(L_ind), twinning is by reticular polyholohedry (twin index > 1, twin obliquity = 0) or reticular pseudopolyholohedry (twin index > 1, twin obliquity > 0).
• When D(L_T) ≠ D(L_ind) twinning is by pseudomerohedry (twin index = 1, twin obliquity > 0), reticular merohedry (twin index > 1, twin obliquity = 0) or reticular pseudomerohedry (twin index > 1, twin obliquity > 0).

Related articles

Mallard's law

History

The definition of twin lattice was given in: Donnay, G. Width of albite-twinning lamellae, Am. Mineral., 25 (1940) 578-586, where the case D(L_T) ⊂ D(L_ind) was however overlooked.

See also

Chapter 3.3 of International Tables of Crystallography, Volume D