Merohedry metric

Syngonic Complete Merohedry Syngonic Selective Merohedry Metric Complete Merohedry Metrie Seleetive Merohedry ... 

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 ... 

Polytypes of the monoclinic and triclinic syngony with an hP lattice may undergo twinning by metric merohedry. For the monoclinic syngony the coset decomposition gives five twin laws, each with four equivalent twin operators ... 

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. 

Syngonic Merohedry Class 1 Syngonic Merohedry class IIA Metric Merohedry elass IIB Pseudo- merohedry Reticular merohedry Reticular pseudo- merohedry... 

This shows that the structure has metric orthorhombic symmetry to a good approximation. The comparison of the Rjnt values makes clear that the correct Laue group is only monoclinic, but because of the higher metric symmetry there is the possibility of twinning by pseudo-merohedry The additional twofold axis, which is present in the orthorhombic system but not in the monoclinic one, is the twin law. To describe this axis in the monoclinic system three matrices need to be multiplied ... 

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