Twinning by metric merohedry

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<p><font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>). <font color="black"> Geminazione per meroedria metrica</font>(<i>It</i>).
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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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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.