Twinning by pseudo-merohedry

The cell of the true space group must be transformed into the apparent cell to use the description of the twin operation in this Laue group. Then the cell must be re-transformed into the true Laue group. 

In contrast to the two first t5rpes of twinning (twiiuiing by merohedry and pseudo-merohedry), in the remaining two t5rpes not every reflection is affected by the twinning. This means that the twinning may be detectable from the diffraction 

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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 ... 

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 =... 

Orthogonal plytyps. In the Trigonal model, the lattice is hP (o = 0) in the true structure for orthorhombic polytypes the lattice is normally oC but pseudo-/ / (co 0). For subfamily B and mixed-rotation polytypes the limiting symmetry is hP and there is only one independent orientation of the w.r.l. Twinning is either by complete merohedry or by pseudo-merohedry and does not modify the geometry of the diffraction pattern. 

In the following sections we present examples of how to refine twinned structures with SHELXL. All files you may need in order to perform the refinements yourself are given on the CD-ROM that accompanies this book. The first example is a case of merohedral twinning that will acquaint you with the basics of practical twin refinement. The second example describes a typical pseudo-merohedral twin such as every crystallographer will encounter sooner or later. Two different examples for twinning by reticular merohedry are given next and the chapter ends with two cases of non-merohedral twinning. 

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