Critical nucleus size for crystallization of supercooled liquids in two dimensions

Using molecular dynamics simulations, we study the crystallization of supercooled liquids in two dimensions in which particles interact with other particles via the Lennard-Jones-Gauss potential. We first prepare supercooled liquids at various temperatures by rapid quenching from the melt. The simulations are performed with a crystalline seed inserted at the center of the initial system. We investigate the time evolution of the inserted nucleus and its surroundings and determine the critical nucleus size n_{c} defined as the smallest nucleus which survives. The results show that n_{c} scales as ∼(T_{m}-T)^{-2} with the melting temperature T_{m}, as expected in the classical nucleation theory. We also obtain the crystallization time at various temperatures as a function of nucleus size and show that the presence of a crystalline seed significantly affects the crystallization time when the temperature is higher than the characteristic temperature T^{*} at which the crystallization time becomes the shortest. This indicates that the crystallization is controlled by thermodynamics in this temperature range. When the temperature is lower than T^{*}, the effect of the inserted nucleus on crystallization is less significant, which indicates that crystallization is controlled by emergence and merging of small crystalline nuclei.