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.
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