5Fold Rotational Symmetry  Practical Electron Microscopy and Database   An Online Book  

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


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Different from 4fold and 6fold rotational axes, two parallel 5fold rotational axes cannot generate translational symmetry at the same distance of separation as in the original pair and thus no periodicity will result; therefore, they cannot coexist for 5fold as shown in Figure 1458a. Figure 1458a. Two parallel 5fold rotational axes which do not generate translational symmetry. 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, quasicrystals, e.g. with 5fold rotational symmetry, can be formed. Figure 1458b. Twodimensional illustration of a quasicrystal with 5fold rotational symmetry. Note that the typical diffraction patterns of quasicrystals exhibit 5fold or 10fold rotational symmetry.


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