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

TL;DR

This study uses molecular dynamics and Monte Carlo simulations to analyze nucleation and crystallization in Lennard-Jones nanodroplets across various temperatures, confirming classical nucleation theory predictions and revealing structural pathways.

Contribution

It provides a detailed comparison of MD and MC methods in predicting nucleation rates and critical embryo sizes, highlighting the role of embryo structure and surface tension effects.

Findings

Classical Nucleation Theory accurately predicts nucleation rates down to the metastability limit.

Crystallization initiates with hcp-fcc stacked nuclei, with structural differentiation at critical sizes.

Surface tension values needed for CNT agreement are lower than bulk expectations.

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.