# Twinning by metric merohedry

### From Online Dictionary of Crystallography

Maclage par mériédrie métrique (*Fr*). Verzwillingung durch metrische Meroedrie (*Ge*). Geminazione per meroedria metrica (*It*). Macla por meroedría métrica (*Sp*).

Twinning by metric merohedry is a special case of twinning by merohedry which occurs when:

- the lattice of the individual has accidentally a specialized metric which corresponds to a higher holohedry,
- the twin operation belongs to this higher holohedry only.

If *H* is the individual point group, *D*(*H*) the corresponding holohedry and *D*(*L*) the point group of the lattice, twinning by metric merohedry corresponds to *D*(*L*) ⊃ *D*(*H*) ⊇ *H*.

Twinning by metric merohedry can be seen as the degeneration of twinning by reticular merohedry to twin index 1, or of twinning by pseudomerohedry to twin obliquity zero.

## Example

A monoclinic crystal of point group *H* = 2 with angle β = 90º has an orthorhombic lattice. It may undergo two types of twinning by merohedry:

- if the twin operation belongs to the monoclinic holohedry
*D*(*H*) = 2/*m*, twinning is the classical twinning by merohedry, also termed*twinning by syngonic merohedry*; - if the twin operation belongs to the orthorhombic holohedry
*D*(*L*) =*mmm*, twinning is by metric merohedry.

## Historical note

Friedel (1904, p. 143; 1926, pp. 56-57) called metric merohedry **mériédrie d’ordre supérieur** (higher order merohedry) but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.

## References

- Friedel, G. (1904).
*Étude sur les groupements cristallins.*Extrait du*Bulletin de la Société de l'Industrie minérale*, Quatrième série, Tomes III et IV. Saint-Étienne, Société de l'imprimerie Théolier J. Thomas et C., 485 pp. - Friedel, G. (1926).
*Leçons de Cristallographie.*Berger-Levrault, Nancy, Paris, Strasbourg, XIX+602 pp.