Difference between revisions of "Merohedral"
From Online Dictionary of Crystallography
m (typo (missing space)) |
m (typo (4, not two!)) |
||
| Line 4: | Line 4: | ||
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. | 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 supergroups of order | + | 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. |
#Twinning by reflection across the (010) plane or by inversion: this corresponds to [[twinning by merohedry]], twin point group 2/''m'''; | #Twinning by reflection across the (010) plane or by inversion: this corresponds to [[twinning by merohedry]], twin point group 2/''m'''; | ||
#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'' ′ | #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'' ′ | ||
Revision as of 12:09, 20 December 2016
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.
- Twinning by reflection across the (010) plane or by inversion: this corresponds to twinning by merohedry, twin point group 2/m';
- 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 ′
- 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