Difference between revisions of "Twin lattice"
From Online Dictionary of Crystallography
m |
m (link) |
||
| Line 1: | Line 1: | ||
<Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 双晶格子 </Font>(''Ja'') | <Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 双晶格子 </Font>(''Ja'') | ||
| − | 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 | + | 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 [[twinning (effects of)|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* = ∩<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>). | 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>). | ||
Revision as of 09:15, 5 April 2015
Réseau de la macle (Fr). Reticolo del geminato (It). 双晶格子 (Ja)
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).
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(LT) ⊂ D(Lind) was however overlooked.
See also
Chapter 3.3 of International Tables of Crystallography, Volume D