# Twinning (endemic conditions of)

(Difference between revisions)
 Revision as of 15:10, 17 May 2017 (view source)m (Style edits to align with printed edition)← Older edit Latest revision as of 14:25, 20 November 2017 (view source)m (Tidied translations.) Line 1: Line 1: - Maclage (conditions endémiques) (''Fr''). Geminazione (condizioni endemiche di) (''It''). + Maclage (conditions endémiques) (''Fr''). Geminazione (condizioni endemiche di) (''It''). + When a lattice necessarily contains at least one sublattice that supports either [[twinning by reticular merohedry]] or [[twinning by reticular pseudomerohedry]], it is said that an endemic condition of [[twinning]] does exist. The following cases are known. When a lattice necessarily contains at least one sublattice that supports either [[twinning by reticular merohedry]] or [[twinning by reticular pseudomerohedry]], it is said that an endemic condition of [[twinning]] does exist. The following cases are known.

## Latest revision as of 14:25, 20 November 2017

Maclage (conditions endémiques) (Fr). Geminazione (condizioni endemiche di) (It).

When a lattice necessarily contains at least one sublattice that supports either twinning by reticular merohedry or twinning by reticular pseudomerohedry, it is said that an endemic condition of twinning does exist. The following cases are known.

Rhombohedral lattice (hR)

A hR lattice (symmetry $\bar 3$m) always contains a hP lattice (symmetry 6/mmm). Consequently, the crystal structures based on a hR lattice are endemic candidates to twinning by reticular merohedry via the symmetry elements that occur in the 6/mmm point group of the sublattice, but not in the $\bar 3$m point group of the lattice.

Cubic lattices

The primitive cells of cF and cI lattices are rhombohedric (hR) lattices with α = 60° and 109.47°, respectively; a cP lattice can be seen as a rhombohedric lattice with α = 90°. As said above, a hP sublattice is always embedded in a hR lattice with consequent possibility of favouring twinning by reticular merohedry.

Pseudo cP and hR lattices

The primitive cells of oI and tI lattices always have a = b = c; thus they can either approach a cP (all angles close to 90°) or a hR (all angles close to the same value) lattice and favour twinning by pseudo (reticular) merohedry.

Pseudo hP lattices

The primitive cells of mC and oC lattices have a = b, a condition which brings into existence a hP sublattice when γ is about 120°.