On the origin of multi-component bulk metallic glasses: Atomic size mismatches and de-mixing

The critical cooling rate $\mathcal{R}_c$, below which liquids crystallize upon cooling, characterizes the glass-forming ability (GFA) of the system. While pure metals are typically poor glass formers with $\mathcal {R}_c>10^{12}\, {\rm K/s}$, specific multi-component alloys can form bulk metallic glasses (BMGs) even at cooling rates below $\mathcal {R}\sim 1\, {\rm K/s}$. Conventional wisdom asserts that metal alloys with three or more components are better glass formers (with smaller ${\cal R}_c$) than binary alloys. However, there is currently no theoretical framework that provides quantitative predictions for $\mathcal{R}_c$ for multi-component alloys. We perform simulations of ternary hard-sphere systems, which have been shown to be accurate models for the glass-forming ability of BMGs, to understand the roles of geometric frustration and demixing in determining $\mathcal {R}_c$. Specifically, we compress ternary hard sphere mixtures into jammed packings and measure the critical compression rate, below which the system crystallizes, as a function of the diameter ratios $\sigma_B/\sigma_A$ and $\sigma_C/\sigma_A$ and number fractions $x_A$, $x_B$, and $x_C$. We find two distinct regimes for the GFA in parameter space for ternary hard spheres. When the diameter ratios are close to $1$, such that the largest ($A$) and smallest ($C$) species are well-mixed, the GFA of ternary systems is no better than that of the optimal binary glass former. However, when $\sigma_C/\sigma_A \lesssim 0.8$ is below the demixing threshold for binary systems, adding a third component $B$ with $\sigma_C < \sigma_B < \sigma_A$ increases the GFA of the system by preventing demixing of $A$ and $C$. Analysis of the available data from experimental studies indicates that most ternary BMGs are below the binary demixing threshold with $\sigma_C/\sigma_A < 0.8$.