Difference between revisions of "Merohedral"
From Online Dictionary of Crystallography
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| − | '''Merohedral''' is the adjectival form of [[merohedry]] and indicates a crystal that does not possess the full point symmetry of its lattice. | + | '''Merohedral''' is the adjectival form of [[merohedry]] and indicates a crystal that does not possess the full point symmetry of its lattice. Merohedral twins are the result of [[Twinning|twinning]] by merohedry. |
==Discussion== | ==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 | + | 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 | + | A crystal belonging to the [[geometric crystal class]] 2 is merohedral because its lattice has at least symmetry 2/''m''. There are three 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''′. |
| − | #Twinning by rotation about [100] or [001] | + | #Twinning by rotation about the [100] or [001] direction: this corresponds to the same types of twinning as case 2 above but the twin point group is 2′22′. |
| − | Case 1 above would be a | + | 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 | + | 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. |
==See also== | ==See also== | ||
Revision as of 16:26, 15 May 2017
Merohedral is the adjectival form of merohedry and indicates a crystal that does not possess the full point symmetry of its lattice. Merohedral twins are the result of twinning by merohedry.
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 three 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′2m′.
- Twinning by rotation about the [100] or [001] direction: this corresponds to the same types of twinning as case 2 above but the twin point group is 2′22′.
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.