# Difference between revisions of "Twin lattice"

### From Online Dictionary of Crystallography

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<Font color="blue"> Réseau de la macle</Font> (''Fr'') <Font color="black"> Reticolo del geminato </Font>(''It'') | <Font color="blue"> Réseau de la macle</Font> (''Fr'') <Font color="black"> Reticolo del geminato </Font>(''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 lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. | + | 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. |

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+ | Let H* = ∩<sub>i</sub>H<sub>i</sub> be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D('''L'''<sub>T</sub>) the point group of the twin lattice and D('''L'''<sub>ind</sub>) the point group of the individual lattice. D('''L'''<sub>T</sub>) 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'''<sub>ind</sub>). | ||

+ | *When D('''L'''<sub>T</sub>) = D('''L'''<sub>ind</sub>) and the two lattices have the same orientation, twinning is by [[twinning by merohedry|merohedry]] ([[twin index]] = 1). When at least some of the symmetry elements of D('''L'''<sub>T</sub>) are differently oriented from the corresponding ones of D('''L'''<sub>ind</sub>), twinning is by [[twinning by reticular polyholohedry|reticular polyholohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or reticular pseudopolyholohedry ([[twin index]] > 1, [[twin obliquity]] > 0). | ||

+ | *When D('''L'''<sub>T</sub>) ≠ D('''L'''<sub>ind</sub>) twinning is by [[twinning by pseudomerohedry|pseudomerohedry]] ([[twin index]] = 1, [[twin obliquity]] > 0), [[twinning by reticular merohedry|reticular merohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or [[twinning by reticular pseudomerohedry|reticular pseudomerohedry]] ([[twin index]] > 1, [[twin obliquity]] > 0). | ||

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==Related articles== | ==Related articles== | ||

[[Mallard's law]] | [[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'''<sub>T</sub>) ⊂ D('''L'''<sub>ind</sub>) was however overlooked. | ||

==See also== | ==See also== |

## Revision as of 10:57, 7 May 2006

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* = ∩_{i}H_{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

## 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*