Institut Jean Barriol
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"Merohedral Twinning" vs. "Merohedric Twinning"

The terms "merohedral twinning" and "non-merohedral twinning" are nowadays frequently used in the literature about crystal twinning. They are meant to separate twinning by merohedry (where the twin lattice coincides with the lattice of the individual) from all the other types of twinning (twinning by pseudo-merohedry, reticular merohedry, reticular pseudo-merohedry etc. - for details on the classification of twinned crystals see this page).

The choice of the adjective "merohedral" is actually unfortunate when it is used to indicate a type of twinning, because "merohedral" has a different, although closely related, meaning. The use of the same word to indicate two different concepts should always be avoided.

The meaning of "merohedral"

Merohedral, in contrast to holohedral, identifies a crystal whose point group is a subgroup of the point group of its lattice. Thus, a point group is said holohedral or merohedral depending on whether it corresponds or not to the symmetry of a lattice.

The following table shows holohedral and merohedral crystallographic point groups in the three-dimensional space.

Holohedral and merohedral crystallographic point groups in the three-dimensional space
Crystal family Bravais lattice-type Lattice system Holohedral point group Merohedral point groups
*S means one face centred.
Cubic cP, cF, cI Cubic m-3m 23
Hexagonal hP Hexagonal 6/mmm 6
hR Rhombohedral -3m 3
Tetragonal tP, tI Tetragonal 4/mmm 4
Orthorhombic oP, oS*, oF, oI Orthorhombic mmm 222
Monoclinc mP, mS* Monoclinc 2/m 2
Triclinic aP Triclinic -1 1

"Merohedral" vs. "Merohedric"

A merohedral crystal may undergo twinning by merohedry: the twin operation then belongs to the lattice of the individual. To replace "twinning by merohedry" with "merohedral twinning" is incorrect, because "merohedral" indicates the symmetry of the individual, not the type of twinning. When that same crystal undergoes another type of twinning, the use of "non-merohedral" is even more misleading - the crystal is still merohedral! To avoid this type of confusion, the adjective merohedric was introduced long ago to specifically indicate the type of twinning. Unluckily, in some languages (ex. German) the two English adjectives translate in the same way, and this may be one of the reasons for the persistence in the literature of the use of "merohedral" in two different meanings.

Finally, it should be noted that sometimes an ugly hybrid term appears too: "merohedrical", just to make the terminological situation even more confused and confusing.


Suppose that you have to deal with an individual crystal whose point group is H = 2, without specialized metric (the angle β is not accidentally 90º). It is evidently a merohedral crystal. It may undergo twinning by merohedry with respect to its holohedry, K = 2/m, supergroup of order two of H. This is a twin by merohedy, or merohedric twin. To call it a "merohedral twin of a merohedral crystal" is simply confusing. But even worse is the case when the same crystal has a pseudo-orthorhombic lattice (the angle β is close to 90º) or a (pseudo) orthorhombic sublattice. In this case, the individual may undergo twinning with respect to K = 222 or K = mm2 - which are again supergroups of order two of H - without passing through the monoclinic holohedry. Twinning is by pseudo-merohedry, reticular merohedry or reticular pseudo-merohedry, that is a non-merohedric twin. To call it a "non merohedral twin of a merohedral crystal" means to make confusing something that by its nature is instead very clear.

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