# Difference between revisions of "Merohedral"

### From Online Dictionary of Crystallography

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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