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4.5.3.24: Twin lattice

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    365022
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    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. 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* = ∩iHi be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D(LT) the point group of the twin lattice and D(Lind) the point group of the individual lattice. D(LT) 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(Lind).

    • When D(LT) = D(Lind) 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(LT) are differently oriented from the corresponding ones of D(Lind), twinning is by reticular polyholohedry (twin index > 1, twin obliquity = 0) or reticular pseudopolyholohedry (twin index > 1, twin obliquity > 0).
    • When D(LT) ≠ D(Lind) 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).

    4.5.3.24: Twin lattice is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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