Molecular Dynamics Studies of the Melting Kinetics of Superheated Crystals

Molecular dynamics (MD) simulations have long had an important role in the study of equilibrium and nonequilibrium phase transitions. However, the effects of finite system sizes and periodic boundary conditions on such simulation are still not fully understood. In the present paper, we investigate this issue using simulations of the homogeneous melting of superheated crystals, specifically the effect of system size on the delay time before melting (which we call "melting time"). Because melting is a random and relatively rare event, we perform a systematic and extensive MD simulation study of a simple molecular system, solid-phase argon in a perfect fcc crystal superheated above the melting point. Using extensive replicate simulations, we first confirm that the distribution of melting times is accurately characterized by a gamma distribution. Next, we use the model of melting being triggered by random dislocations to derive an equation for the mean melting time as a function of system size and show that this model well-matches our MD data over a range of periodic boxes containing from 256 to 296,352 argon atoms. This equation shows that the system-size effect is inversely proportional to the number of atoms (or equivalently, proportional to L-3 with L being the side length of the periodic box) and could be used as a correction factor for melting times calculated in finite systems. We also study the effects of temperature on melting and find that the mean melting time exponentially decreases to a nonzero asymptotic value with increasing temperature. We observe that the melting time distributions shift toward more Gaussian-like forms of the gamma distribution (i.e., with larger values of the shape parameter) at elevated temperatures. Finally, we also present the results of the melting of water ice I-h to show that our findings apply to molecules and melting processes more complex than simple Lennard-Jones systems.