Rotation Axis (1, 2, 3, 4 and 6 (C_{n})) in Crystallography  Practical Electron Microscopy and Database   An Online Book  

Microanalysis  EM Book https://www.globalsino.com/EM/  


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In reality, not all rotational symmetries are allowed in crystals. The only rotational symmetries possible in crystal lattices are 2, 3, 4 and 6, because it is impossible to fill space with other symmetries (e.g. 5, 7 …). However, this restriction does not apply to molecular symmetry, for instance, Creactive protein has 5fold rotational symmetry, GroEL has 7fold, etc. On the other hand, quasicrystals, e.g. with 5fold rotational symmetry, can be formed.
Figure 1622. (a) 2, (b) 3, (c) 4 and (d) 6rotational symmetries. As an example, the three space groups C2/m, C2 and Cm have the same systematic forbidden reflections which are caused by the Ccentering (h+k = 2n+1). The other symmetry operations in the three space groups, e.g. 2fold rotation axis (2) and mirror plane (m) in the C2/m space group, do not cause forbidden reflections. Rotation axes are observed directly with ZOLZ and HOLZ lines in CBED patterns when the beam is aligned with the rotation axis.


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