Difference between revisions of "Merohedral"

From Online Dictionary of Crystallography

Merohedral is the adjectival form of merohedry and indicates a crystal that does not possess the full point symmetry of its lattice.

Discussion

In the literature, the term merohedral twinning is often improperly used instead of twinning by merohedry. A merohedral crystal may undergo several different types of twinning and for this reason the term "merohedral twinning" is misleading, as the following example shows.

A crystal belonging to the geometric crystal class 2 is merohedral because its lattice has at least symmetry 2/m. There are thee minimal supergroups of order four of the point group 2 which correspond to three different twins.

1. Twinning by reflection across the (010) plane or by inversion: this corresponds to twinning by merohedry, twin point group 2/m';
2. Twinning by reflection across the (100) or (001) plane: this corresponds to twinning by pseudomerohedry, twinning by reticular merohedry, or twinning by reticular pseudomerohedry if β ≠ 90º, or to twinning by metric merohedry if β = 90º; the twin point group is m ′ 2 m
3. Twinning by rotation about [100] or [001]: direction: this corresponds to the same types of twinning as case 2) above but the twin point group is 2′ 2 2′.

Case 1 above would be a "merohedral twin of a merohedral crystal" while cases 2 and 3 would be "non-merohedral twins of a merohedral crystal". To avoid any terminological awkwardness, the adjective merohedric has been suggested with reference to twins, but the use of the category names like twinning by merohedry remains preferable