TWINNING OF MICAS THEORY

1) Polytypes of the orthorhombic syngony with a hP lattice may undergo twinning by metric merohedry, the twin lattice coinciding with the lattice of the individual. The coset decomposition gives two twin laws  

All the operators corresponding to the same twin law are equivalent under the action of the symmetry operators of the orthorhombic syngony. If the lattice is only oC, twinning is by pseudo-merohedry. The twin lattice (hP) does not coincide exactly with the lattice of the individual, because for the latter the orthohexagonal relation b = 

If the lattice of the individual is oC, the first two cosets in Equation (5) and the first four cosets [Eqn. (6)] correspond to metric merohedry, whereas the others correspond to pseudo-merohedry (ra = ra 0, raj = 0). If the lattice of the individual is mC Class a, the twin laws in Equations (5) and (6) correspond to reticular pseudo-merohedry. The hP twin lattice is a sublattice for the individual, with subgroup of translation 3 the twin index is thus 3. 

The first two [Eqn. (7)] or four [Eqn. (8)] cosets give the twin laws by metric merohedry, the others give the twin laws by reticular merohedry. Twin operators in each coset are equivalent by the action of the symmetry elements of the syngony. 

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