Compositions of Al-Based Quasicrystals Interpreted by Cluster Formulae

It is known previously that bulk metallic glass compositions satisfy cluster formulae $[cluster](glue atom)_{1, 3}$ of 24 valence electrons as deduced from our cluster-resonance model. In the present work, it is further shown that compositions of Al-based binary and ternary quasicrystals are also explained by 24-electron cluster formulae of the types $[icosahedron](glue atom)_{0, 1}$, where the icosahedral cluster is identified from a corresponding crystalline approximant according to dense atomic packing and cluster isolation criteria, and the glue atom site is either vacant for an icosahedral quasicrystal or equal to one for a decagonal quasicrystal. Ternary quasicrystals are formulated with the same formulae as their basic binary ones but the icosahedron shell sites are substituted by third elements. The 24-electron cluster formulae are then the chemical and electronic structural units of quasicrystals, mimicking the molecular formulae of chemical substances.