We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modeled by the van Beest–Kramer–van Santen potential [Phys. Rev. Lett. 64, 1995 (1990)]. We find that at density ρ=4.38g∕cm3, spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000K, and we evaluate the nucleation rate J directly at this T via “brute force” sampling of nucleation events in numerous independent runs. We then use parallel, constrained Monte Carlo simulations to evaluate ΔG(n), the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200, and 3300K. By comparing the form of ΔG(n) to CNT, we test the ability of CNT to reproduce the observed behavior as we approach the regime where spontaneous nucleation occurs on simulation time scales. We find that the prediction of CNT for the n dependence of ΔG(n) fits reasonably well to the data at all T studied. Δμ, the chemical potential difference between bulk liquid and stishovite, is evaluated as a fit parameter in our analysis of the form of ΔG(n). Compared to directly determined values of Δμ extracted from previous work, the fitted values agree only at T=3300K; at lower T the fitted values increasingly overestimate Δμ as T decreases. We find that n*, the size of the critical nucleus, is approximately ten silicon atoms at T=3300K. At 3000K, n* decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of ΔG(n) when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of ΔG(n) at 3000K. Finally, we directly evaluate at T=3000K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g., the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2nm. We are thereby able to compare the results for J at 3000K obtained both directly and based on CNT, and find that they agree within an order of magnitude. In sum, our work quantifies how certain predictions of CNT (e.g., for Δμ) break down in this deeply supercooled limit, while others [the n dependence of ΔG(n)] are not as adversely affected.

Saika-Voivod, I., Poole, P. H., & Bowles, R. K. (2006). Test of classical nucleation theory on deeply supercooled high-pressure simulated silica. The Journal of Chemical Physics, 124(22).