Difference between revisions of "Pseudo symmetry"
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| − | <font color="blue">Pseudo symétrie</font> (<i>Fr</i>) | + | <font color="blue">Pseudo symétrie</font> (<i>Fr</i>). <font color="black">Pseudo simmetria</font> (<i>It</i>). <font color="purple">擬対称</font> (<i>Ja</i>). |
| − | A crystal space can in general be divided in ''N'' components S<sub>1</sub> to S<sub>''N''</sub>. When a coincidence operation φ(S<sub>''i''</sub>)→S<sub>''j''</sub> brings the ''i'' | + | A crystal space can in general be divided in ''N'' components ''S''<sub>1</sub> to ''S''<sub>''N''</sub>. When a coincidence operation φ(''S''<sub>''i''</sub>)→''S''<sub>''j''</sub> brings the ''i''th component ''S''<sub>''i''</sub> to coincide with the ''j''th component ''S''<sub>''j''</sub>, for any ''i'' and ''j'', φ is a symmetry operation of the [[space group]]. |
| − | Sometimes, φ brings S<sub>''i''</sub> close to, but not exactly on, the position and orientation of S<sub>''j''</sub> | + | Sometimes, φ brings ''S''<sub>''i''</sub> close to, but not exactly on, the position and orientation of ''S''<sub>''j''</sub>; in this case the operation mapping ''S''<sub>''i''</sub> onto ''S''<sub>''j''</sub> is [[Noncrystallographic symmetry|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]]. | 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]]. | ||
Revision as of 13:34, 16 May 2017
Pseudo symétrie (Fr). Pseudo simmetria (It). 擬対称 (Ja).
A crystal space can in general be divided in N components S1 to SN. When a coincidence operation φ(Si)→Sj brings the ith component Si to coincide with the jth 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.