Composition rule of bulk metallic glasses and quasicrystals using electron concentration criterion

This paper aims at establishing a number of electrons/atom (e/a)-based criterion for searching bulk metallic glasses (BMGs) and quasicrystals with large forming abilities in the Zr-based multicomponent alloy systems. After discussions on the diffraction characteristics corresponding to the Fermi surfaces-Brillouin zone interaction in the Zr-based Hume-Rothery phases, the Hume-Rothery matching rule is well explained when the effective e/a value of the matrix element Zr is taken as 1.5. The BMG- and quasicrystal-related phases are pointed out to be a family of nearly e/a-constant phases in a given alloy system. An e/a-constant criterion is then used to predict the ideal composition of the quasicrystals and BMGs in the Zr-Ti-Ni, Zr-Al-Ni, and Zr-Al-Ni-Cu systems, respectively. Nearly pure bulk Zr-Ti-Ni quasicrystals and a series of BMGs with glass-forming abilities greater than that of the known Zr65Al7.5Ni10Cu17.5 alloy are found.