Point Group 53m ()  Practical Electron Microscopy and Database   An Online Book  

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


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The point group 53m () of icosahedral quasicrystals (e.g. AlMnPd, Al_{5.5}Li_{3.3}Cu, Al_{65}Fe_{15}Cu_{20}, Al_{63.5}Cu_{24}Fe_{12.5}, and almost spherical C_{60} molecule) is a 6dimensional (6D) group. This group acts on the 21dimensional space of rank 4 tensors (T_{ijkm} = T_{jikm} = T_{ijmk} = T_{kmij}) with the symmetry of the elasticity tensor. Since this group contains a 2dimesional pointwise invariant subspace, the elasticity tensor has 2 free parameters. Figure 1438 shows the schematic illustration of symmetry operations of point group . Figure 1438. Schematic illustration of symmetry operations of point group .


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