A test of Hume-Rothery rules for stable quasicrystals

Abstract

The stability of the icosahedral quasicrystals has been studied in terms of Hume-Rothery rules i.e., atomic size factor, electronegativity and valence electron concentration. It has been confirmed that most of the stable quasicrystals can be understood within the frame work of the Hume-Rothery rules. Even more interestingly, it is found that stable quasicrystals are strict electron compounds, which only form at sharp valence electron concentration. All of the stable quasicrystals commonly have the corresponding valence electron concentration, but the dependence of stability on the atomic size factor is different among the groups. Qualitatively, the most relevant criterion for the formation of stable quasicrystals is that the alloy should have a definite valence electron concentration. On top of this, a high stability of the quasicrystal is observed when the atomic size factor is favored.