Connection between the packing efficiency of binary hard spheres and the glass-forming ability of bulk metallic glasses

Abstract

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate $R$, size ratio $\ensuremath{\alpha}$, and number fraction ${x}_{S}$ of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate ${R}_{c}$, below which jammed hard-sphere packings begin to form ``random crystal'' structures with defects. We find that for systems with $\ensuremath{\alpha}\ensuremath{\gtrsim}0.8$ that do not demix, ${R}_{c}$ decreases strongly with $\ensuremath{\Delta}{\ensuremath{\phi}}_{J}$, as ${R}_{c}\ensuremath{\sim}exp(\ensuremath{-}1/\ensuremath{\Delta}{\ensuremath{\phi}}_{J}^{2})$, where $\ensuremath{\Delta}{\ensuremath{\phi}}_{J}$ is the difference between the average packing fraction of the amorphous packings and random crystal structures at ${R}_{c}$. Systems with $\ensuremath{\alpha}\ensuremath{\lesssim}0.8$ partially demix, which promotes crystallization, but we still find a strong correlation between ${R}_{c}$ and $\ensuremath{\Delta}{\ensuremath{\phi}}_{J}$. We show that known metal-metal BMGs occur in the regions of the $\ensuremath{\alpha}$ and ${x}_{S}$ parameter space with the lowest values of ${R}_{c}$ for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing $\ensuremath{\alpha}$ to increase packing efficiency, while maximizing $\ensuremath{\alpha}$ to prevent demixing.