Hit and miss of classical nucleation theory as revealed by a molecular simulation study of crystal nucleation in supercooled sulfur hexafluoride

Classical nucleation theory pictures the homogeneous nucleation of a crystal as the formation of a spherical crystalline embryo, possessing the properties of the macroscopic crystal, inside a parent supercooled liquid. In this work we study crystal nucleation in moderately supercooled sulfur hexafluoride by umbrella sampling simulations. The nucleation free energy evolves from $5.2kBT$ at $T=170K$ to $39.1kBT$ at $T=195K$⁠. The corresponding critical nucleus size ranges from $40molecules$ at $T=170Kto266molecules$ at $T=195K$⁠. Both nucleation free energy and critical nucleus size are shown to evolve with temperature according to the equations derived from the classical nucleation theory. Inspecting the obtained nuclei we show, however, that they present quite anisotropic shapes in opposition to the spherical assumption of the theory. Moreover, even though the critical nuclei possess the structure of the stable bcc plastic phase, the only mechanically stable crystal phase for $SF6$ in the temperature range investigated, they are shown to be less ordered than the corresponding macroscopic crystal. Their crystalline order is nevertheless shown to increase regularly with their size. This is confirmed by a study of a nucleus growth from a critical size to a size of the order of $104molecules$⁠. Similarly to the fact that it does not affect the temperature dependence of the nucleation free energy and of the critical nucleus size, the ordering of the nucleus with size does not affect the growth rate of the nucleus.