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Difference between revisions of "Twin lattice"

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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''. It corresponds to the crystal lattice in [[twinning by merohedry]] and to a sublattice of the crystal (individual) in [[twinning by reticular merohedry]].
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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 ([[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* = &cap;<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>).
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*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).
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*When D('''L'''<sub>T</sub>) &ne; 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).
  
The symmetry of the twin lattice has to be compared with the intersection symmetry of the individuals in their respective orientation, which in general is a subgroup of the group of the individual. As a consequence, the symmetry of the twin lattice may be higher, equal or lower than the symmetry of the individual lattice.
 
  
 
==Related articles==
 
==Related articles==
 
[[Mallard's law]]
 
[[Mallard's law]]
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==History==
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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>) &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* = ∩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).


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(LT) ⊂ D(Lind) was however overlooked.

See also

Chapter 3.3 of International Tables of Crystallography, Volume D