# Long-Lived Non-Equilibrium Interstitial-Solid-Solutions in Binary Mixtures

## TL;DR

This study investigates the formation and stability of non-equilibrium interstitial solid solutions in binary mixtures of hard spheres, revealing long-lived trapped small particles and contrasting with previous equilibrium predictions.

## Contribution

It demonstrates that in certain binary mixtures, small particles become trapped in interstitial sites, forming long-lived non-equilibrium structures unlike previously predicted equilibrium solutions.

## Key findings

- Small particles occupy up to 14% of interstitial sites.
- Small particles are trapped in octahedral holes, not hopping further.
- Long-lived non-equilibrium structures observed in experiments and simulations.

## Abstract

We perform particle resolved experimental studies on the heterogeneous crystallisation process of two compo- nent mixtures of hard spheres. The components have a size ratio of 0.39. We compared these with molecular dynamics simulations of homogenous nucleation. We find for both experiments and simulations that the final assemblies are interstitial solid solutions, where the large particles form crystalline close-packed lattices, whereas the small particles occupy random interstitial sites. This interstitial solution resembles that found at equilibrium when the size ratios are 0.3 [Filion et al., Phys. Rev. Lett. 107, 168302 (2011)] and 0.4 [Filion, PhD Thesis, Utrecht University (2011)]. However, unlike these previous studies, for our system sim- ulations showed that the small particles are trapped in the octahedral holes of the ordered structure formed by the large particles, leading to long-lived non-equilibrium structures in the time scales studied and not the equilibrium interstitial solutions found earlier. Interestingly, the percentage of small particles in the crystal formed by the large ones rapidly reaches a maximum of around 14% for most of the packing fractions tested, unlike previous predictions where the occupancy of the interstitial sites increases with the system concentration. Finally, no further hopping of the small particles was observed.