Difference between revisions of "Twinning by metric merohedry"
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| − | + | <font color="blue">Maclage par mériédrie métrique</font> (''Fr''). <font color="red">Verzwillingung durch metrische Meroedrie</font> (''Ge''). <font color="black">Geminazione per meroedria metrica</font> (''It''). <font color="green">Macla por meroedría métrica</font> (''Sp''). | |
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Twinning by metric merohedry is a special case of [[twinning by merohedry]] which occurs when: | 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 lattice of the individual has accidentally a specialized metric which corresponds to a higher holohedry, |
| − | * the twin operation belongs to this higher holohedry only | + | * 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 | + | 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. | 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== | ==Example== | ||
| − | A monoclinic crystal of point group H = 2 with angle β = 90º has | + | 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 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. | + | * if the twin operation belongs to the orthorhombic holohedry ''D''(''L'') = ''mmm'', twinning is by metric merohedry. |
==Historical note== | ==Historical note== | ||
| − | Friedel (1904, p. 143; 1926, | + | 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. |
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| + | == 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. | ||
[[Category:Twinning]] | [[Category:Twinning]] | ||
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.