106-particle molecular-dynamics study of homogeneous nucleation of crystals in a supercooled atomic liquid

Molecular-dynamics simulations of 15 000 and ${10}^6$ particles have been performed to study the onset of crystallization in supercooled Lennard-Jones liquids. The calculations were performed by suddenly cooling an equilibrated liquid and calculating the subsequent time evolution of the system (at constant energy and volume with periodic boundary conditions). The configurations at evenly spaced times along the trajectory were subjected to an analysis that consisted of a short steepest-descents energy minimization toward an inherent structure followed by a Voronoi analysis to identify crystalline regions. The sequence of these quenched configurations was analyzed to study the time evolution of the solidlike regions. Several observations are consistent with the existence of a free-energy barrier to crystallization, as described by classical nucleation theory, including an identification of a critical nucleus size. Critical nuclei by our analysis and under the conditions of this simulation consist of 10 to 20 particles in face-centered cubic and hexagonal close-packed environments. A steady-state distribution of sizes of precritical clusters is observed at intermediate times, but the first critical and postcritical nuclei form and there is a significant amount of crystallization before this steady-state distribution is achieved.