On the band-structure contribution to the stability of the icosahedral quasicrystals and Frank-Kasper phases in the non-transition metal alloys

The electronic contribution to the energy of icosahedral quasicrystals and related crystalline phases is discussed within a nearly-free-electron approximation. The Penrose approximant is used through the Elser and Henley scheme (1985) for modelling the Frank-Kasper phase atomic structure. The relative position of the Fermi sphere and the wide-gap reciprocal vectors for both structures is analysed. It is shown that the Jones-like arguments concerning the electronic concentration explain the stability of these phases in systems exhibiting the stable quasicrystal formation. Some assumptions about quasicrystalline alloys of other simple metals are suggested.