# Twinning by metric merohedry

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 Revision as of 17:46, 17 May 2017 (view source)m (Style edits to align with printed edition)← Older edit Latest revision as of 14:30, 20 November 2017 (view source) (Tidied translations and added German and Spanish (U. Mueller)) Line 1: Line 1: -

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

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## Latest revision as of 14:30, 20 November 2017

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.