# Difference between revisions of "Twinning (endemic conditions of)"

### From Online Dictionary of Crystallography

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− | < | + | <font color="blue">Maclage (conditions endémiques)</font> (''Fr''). <font color="black">Geminazione (condizioni endemiche di)</font> (''It''). |

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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. | ||

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'''Rhombohedral lattice''' (''hR'') | '''Rhombohedral lattice''' (''hR'') | ||

− | A ''hR'' lattice (symmetry <math> \bar 3</math>''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 <math> \bar 3</math>''m'' point group of the lattice. | + | A ''hR'' lattice (symmetry <math> \bar 3</math>''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 <math> \bar 3</math>''m'' point group of the lattice. |

## 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 [math] \bar 3[/math]*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 [math] \bar 3[/math]*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°.