Twinning by metric merohedry
From Online Dictionary of Crystallography
Revision as of 14:30, 20 November 2017 by BrianMcMahon (Tidied translations and added German and Spanish (U. Mueller))
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.
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.
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.
- 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.