A Local Order Parameter-Based Method for Simulation of Free Energy Barriers in Crystal Nucleation

Abstract

While global order parameters have been widely used as reaction coordinates in nucleation and crystallization studies, their use in nucleation studies is claimed to have a serious drawback. In this work, a local order parameter is introduced as a local reaction coordinate to drive the simulation from the liquid phase to the solid phase and vice versa. This local order parameter holds information regarding the order in the first- and second-shell neighbors of a particle and has different well-defined values for local crystallites and disordered neighborhoods but is insensitive to the type of the crystal structure. The order parameter is employed in metadynamics simulations to calculate the solid-liquid phase equilibria and free energy barrier to nucleation. Our results for repulsive soft spheres and the Lennard-Jones potential, LJ(12-6), reveal better-resolved solid and liquid basins compared with the case in which a global order parameter is used. It is also shown that the configuration space is sampled more efficiently in the present method, allowing a more accurate calculation of the free energy barrier and the solid-liquid interfacial free energy. Another feature of the present local order parameter-based method is that it is possible to apply the bias potential to regions of interest in the order parameter space, for example, on the largest nucleus in the case of nucleation studies. In the present scheme for metadynamics simulation of the nucleation in supercooled LJ(12-6) particles, unlike the cases in which global order parameters are employed, there is no need to have an estimate of the size of the critical nucleus and to refine the results with the results of umbrella sampling simulations. The barrier heights and the nucleation pathway obtained from this method agree very well with the results of former umbrella sampling simulations.