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

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