Composition optimization of Zr55Cu30Al10Ni5 bulk metallic glass using cluster formula approach

Compositions of typical binary and ternary bulk metallic glasses have previously been interpreted via a cluster formula approach, i.e., a good glass former is formulated by a nearest-neighbor cluster matched with one or three glue atoms, with a free electron number per unit formula approaching 24. In this study, a classical quaternary glass composition Zr ₅₅Cu ₃₀Al ₁₀Ni ₅, representative of bulk metallic glasses of complex chemistry and dual-glassy structure, is interpreted and optimized using a dual-cluster formula approach, i.e., a chemical formula representing two single-cluster formulas. First, the number of atoms in the dual-cluster formula is estimated from combinations of all possible single-cluster formulas of the major devitrification phase CuZr ₂, which ranges from 28 to 34. Second, the free electron number of each element is estimated using the Cu-Zr single-cluster formulas. Third, the reference composition Zr ₅₅Cu ₃₀Al ₁₀Ni ₅ is approximated into integer forms of 27 to 36 atoms and their free electron numbers are calculated using the assigned free electron numbers of the elements. The so-formulated compositions are examined for glass forming abilities via copper-mold arc melting. The atomic densities, the critical temperatures, the HV hardness, the volume fractions of the glassy phase in the ingots, and the activation energies of crystallization all point to a 32-atom chemical formula Zr ₁₇Cu ₁₀Al ₃Ni ₂ (Zr _53.13Cu _31.25Al _9.38Ni _6.25) as the optimal glass former, with its electron number per unit formula falling slightly below 48. This work confirms the 24-electron rule for single-cluster formulas and provides an easy route towards understanding the complex chemistries of bulk metallic glasses via multiple single-cluster formulas.