Pseudo symmetry

Pseudo symétrie (Fr). Pseudo simmetria (It). 擬対称 (Ja).

A crystal space can in general be divided in N components S₁ to S_N. When a coincidence operation φ(S_i)→S_j brings the ith component S_i to coincide with the jth component S_j, for any i and j, φ is a symmetry operation of the space group.

Sometimes, φ brings S_i close to, but not exactly on, the position and orientation of S_j; in this case the operation mapping S_i onto S_j 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.