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Chemistry LibreTexts

Pseudo symmetry

A crystal space can in general be divided in N components S1 to SN. When a coincidence operation φ(Si)→Sj brings the i-th component Si to coincide with the j-th component Sj, for any i and j, φ is a symmetry operation of the space group.

Sometimes, φ brings Si close to, but not exactly on, the position and orientation of Sj: in this case the operation mapping Si onto Sj is not crystallographic but the linear and/or rotational deviation from a space group operation is limited. For this reason, it is preferable to describe the crystallographic operation φ as a pseudo symmetry operation.

Pseudo symmetry operations for the lattice play an important role in twinning, namely in the case of twinning by pseudomerohedry and twinning by reticular pseudomerohedry.