A Symmetry in Asymmetry I Quasi Crystalline State of Matter

2 A Symmetry in Asymmetry I Quasi Crystalline State of Matter 

We have seen in Chap. 3 (Fig. 10.3) that there cannot be any crystalline substance with fivefold of sjunmetry as the motifs having that symmetry cannot make any compact structme, and same is true for sevenfold, eightfold, or tenfold rotation S5rmmetries. It was accepted in classical crystallography 

Since 1984, many stable and also metastable quasi crystals have been found, and these are often binary or ternary intermetallic alloys with aluminum as one of the primary component. Some of these stable quasi crystals with aluminum as a major component are 

In addition to these stable state quasi crystals, there are much more binary and ternary alloys that form metastable quasi crystalline states. 

The growth morphology of the stable decagonal quasi crystals Al-Ni-Co or Al-Mn-Pd shows that they grow as decaprismaic (ten prism faces with the tenfold axis as rotation axis). Al-Cu-Fe quasi crystals, which are icosahedral quasi crystals, grow with triacontahedral shape, which exhibit 30 rhombic faces perpendicular to the twofold rotation axes. Though the interpretation of the patterns involves more mathematical complexicity, the experimental 

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