Golden Mean analysis of bulk metallic glasses with critical diameter over half-inch for their mole fractions of compositions

Eighteen bulk metallic glasses (BMGs) with critical diameters over ∼15 mm in Pd-, Zr-, Mg-, Y-, La-, Pt- and Ca-based multicomponent alloys were analyzed for their mole fractions of compositions with Golden Mean (ϕ ∼ 1.618). The results proved that the 18 BMG compositions are describable with mϕ−n or mΦ−n where Φ−n is ϕ−(n+1) plus ϕ−(n−1) and m and n are positive integers. The maximum difference in fractions between the analyzed and experimental compositions was 0.038. The irrational nature of ϕ makes the compositions of the 18 BMGs different from those of the stoichiometric intermetallic compounds and near eutectic compositions, leading to the high glass-forming ability. The possible prototypes of the 18 BMGs have the ability to form critically-percolated local atomic arrangements for both Metal–Metal and Metal–Metalloid types of BMGs. Golden Mean analysis provides a new alloy design for fractions of alloying elements owing to its irrationality.