Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

Abstract

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modelled by the BKS potential. We find that at density ρ = 4.38 g/cm 3 , spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T = 3000 K, 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 ∆G(n), the free energy to form a crystalline embryo containing n silicon atoms, at T = 3000, 3100, 3200 and 3300 K. By comparing the form of ∆G(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 ∆G(n) fits reasonably well to the data at all T studied. ∆µ, the chemical potential difference between bulk liquid and stishovite, is evaluated as a fit parameter in our analysis of the form of ∆G(n). Compared to directly determined values of ∆µ extracted from previous work, the fitted values agree only at T = 3300 K; at lower T the fitted values increasingly overestimate ∆µ as T decreases. We find that n * , the size of the critical nucleus, is approximately 10 silicon atoms at T = 3300 K. At 3000 K, n * decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of ∆G(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 ∆G(n) at 3000 K. Finally, we directly evaluate at T = 3000 K 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 0.2 nm. We are thereby able to compare the results for J at 3000 K 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 ∆µ) break down in this deeply supercooled limit, while others [the n-dependence of ∆G(n)] are not as adversely affected.

Nucleation barriers in tetrahedral liquids spanning glassy and crystallizing regimes

“…Below, we compare our results for a against β| μ|, as some studies suggest a very good correspondence, 8,9,41 and justify our assumption that b is equal to βγ up to a constant factor which depends on the shape and density of the crystallites. Recently, it has been shown for a soft-core colloidal model that the procedure we follow here for determining n may not be sufficient for describing crystal-like structures, but that the scaling represented by Eq.…”

“…On the other hand, it is somewhat perplexing that such a large rescaling is required at all. In a few previous studies, comparison between a and β μ has shown that in some cases a close correspondence is observed, 8,9,41 while, in principle, the value of a should vary with the definition crystallike particles. There are several potential reasons why such a disagreement can be found.…”

Crystallization of Lennard-Jones nanodroplets: From near melting to deeply supercooled

“…After a very short time, ∆n 2 (t) enters a diffusive regime [52], i.e., it becomes linear in time, and one obtains in this regime,…”

Phase diagram of a tetrahedral patchy particle model for different interaction ranges

“…The presented equilibrium phase diagram will serve as a starting point for studies of crystal nucleation in tetrahedral liquids. [16][17][18][19] …”