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

Abstract

We carry out molecular dynamics (MD) and Monte Carlo (MC) simulations to characterize nucleation in liquid clusters of 600 Lennard-Jones particles over a broad range of temperatures. We use the formalism of mean first-passage times to determine the rate and find that Classical Nucleation Theory (CNT) predicts the rate quite well, even when employing simple modelling of crystallite shape, chemical potential, surface tension and particle attachment rate, down to the temperature where the droplet loses metastability and crystallization proceeds through growth-limited nucleation in an unequilibrated liquid. Below this crossover temperature, the nucleation rate is still predicted when MC simulations are used to directly calculate quantities required by CNT. Discrepancy in critical embryo sizes obtained from MD and MC arises when twinned structures with five-fold symmetry provide a competing free energy pathway out of the critical region. We find that crystallization begins with hcp-fcc stacked precritical nuclei and differentiation to various end structures occurs when these embryos become critical. We confirm that using the largest embryo in the system as a reaction coordinate is useful in determining the onset of growth-limited nucleation and show that it gives the same free energy barriers as the full cluster size distribution once the proper reference state is identified. We find that the bulk melting temperature controls the rate, even though the solid-liquid coexistence temperature for the droplet is significantly lower. The value of surface tension that renders close agreement between CNT and direct rate determination is significantly lower than what is expected for the bulk system.

Analyzing multistep homogeneous nucleation in vapor-to-solid transitions using molecular dynamics simulations

“…Comparing the growth rate obtained by the MD simulations, i.e., di 1/3 c /dt = 0.04σ/τ , with Eq. (2), we obtain where we used i = (4π/3)a 3 n, h = 0.58ε [42], T 0.5ε/k, T m = 0.69ε/k [38], and n = 0.92σ −3 [29]. The diffusion coefficient of the liquid at T 0.5ε/k obtained in [44] was approximately 0.01, which is smaller than our calculated value.…”

“…A study of crystal nucleation in bulk LJ liquid by [39] reported the values of γ = (0.28-0.3)εσ −2 for T 0.45ε/k. In [42], the nucleation rates were obtained by MD simulations of 600 LJ molecules with a potential cutoff radius of 15 σ , and γ was evaluated from the fitting of the obtained nucleation rates as γ = 0.13εσ −2 at T = (0.35-0.485)ε/k, which is smaller than that obtained in our calculation. The reasons for the difference between our calculation of γ and that of [42] may be considered.…”

“…In [42], the nucleation rates were obtained by MD simulations of 600 LJ molecules with a potential cutoff radius of 15 σ , and γ was evaluated from the fitting of the obtained nucleation rates as γ = 0.13εσ −2 at T = (0.35-0.485)ε/k, which is smaller than that obtained in our calculation. The reasons for the difference between our calculation of γ and that of [42] may be considered. First is the temperature difference: in [42], the temperature was maintained with the Nosé-Hoover thermostat.…”

“…The reasons for the difference between our calculation of γ and that of [42] may be considered. First is the temperature difference: in [42], the temperature was maintained with the Nosé-Hoover thermostat. As shown in the Appendix, crystallization occurs earlier in the simulation with the NV T ensemble than with the NV E ensemble because of the higher temperatures in the NV E simulations.…”

“…In [42], T m was set to 0.61 ε/k corresponding to the melting temperature of LJ molecules with a potential cutoff radius of 2.5 σ [39]. However, a higher melting temperature (e.g., T m = 0.69 ε/k with a potential cutoff radius of 6.8 σ ) is preferable because T m depends on the potential cutoff radius [39].…”