Nucleation and droplet growth from supersaturated vapor at temperatures below the triple point temperature

Abstract

In 1897 Ostwald formulated his step rule for formation of the most stable crystal state for a system with crystal polymorphism. The rule describes the irreversible way a system converts to the crystal with lowest free energy. But in fact the irreversible way a supercooled gas below the triple point temperature $T_{tr.p.}$ crystallizes via a liquid droplet is an example of Ostwald's step rule. The homogeneous nucleation in the supersaturated gas is not to a crystal, but to a liquid-like critical nucleus. We have for the first time performed constant energy (NVE) Molecular Dynamics (MD) of homogeneous nucleation without the use of a thermostat. The simulations of homogeneous nucleation in a Lennard-Jones system from supersaturated vapor at temperatures below $T_{tr.p.}$ reveals that the nucleation to a liquid-like critical nucleus is initiated by a small cold cluster [S. Toxvaerd, J. Chem. Phys. \textbf{143} 154705 (2015)]. The release of latent heat at the subsequent droplet growth increases the temperature in the liquid-like droplet, which for not deep supercooling and/or low supersaturation, can exceed $T_{tr.p.}$. The temperature of the liquid-like droplet increases less for a low supersaturation and remains below $T_{tr.p.}$, but without a crystallization of the droplet for long times. The dissipation of the latent heat into the surrounding gas is affected by a traditional MD thermostat, with the consequence that droplet growth is different for (NVE) MD and constant temperature (NVT) MD.