Melting kinetics of small crystalline clusters in the liquid by molecular dynamics

Molecular Dynamics techniques for monitoring the dissolution and growth kinetics of small crystalline clusters in a liquid are developed for the Stillinger-Weber potential. Crystalline regions of 400 to 800 atoms are embedded into equilibrated liquids of 3600 to 7200 atoms to create initial cluster configurations. The sizes of these crystalline clusters are monitored as a function of time as they dissolve into the surrounding liquid. Temperatures from 5 to 20% above and 40% below the equilibrium melting temperature were studied. These simulated kinetics were then compared with predications of small cluster dynamics derived from classical nucleation models.; The problem of identifying and quantifying the extent of a solid region embedded in a liquid is discussed. Several explicit algorithms for separating the system into solid and liquid regions were developed and assessed for their ability to identify physically reasonable cluster sizes and shapes. A criterion based on both the three body component of the potential energy and the local coordination was found to be most successful in tracking cluster sizes.; Two methods developed for the construction of the initial atomic configurations are described. Effects of these methods on the dynamics of the systems are reported. During initial stages of melting, kinetic results are greatly influenced by the details of the initial configuration. However, latter stages of dissolution are relatively insensitive to the initial conditions and permitted determination of dissolution rates for clusters below 200 atoms.; Dissolution rates were determined from the size histories of a number of similar clusters through development of an absorbing Markov chain analysis. These rates, obtained from clusters of a variety of initial sizes and shapes, were compared to rates predicted by classical nucleation theory. Both quantitative and qualitative differences were found. In order to reconcile the qualitative differences, it was necessary to include an explicit size dependence in the interfacial free energy term of the driving force. For small clusters, the apparent driving force for dissolution is reduced and requires that the interfacial energy decrease as the size of the clusters decreases. This result is consistent with results obtained in other Molecular Dynamics simulations where interfacial excess properties are explicitly determined.; The temperature dependence of the dissolution rates was also used to estimate the activation energy for atomic detachment. The value obtained, 0.4 eV, is very similar to that found for self-diffusion of atoms in the bulk liquid and indicates that diffusive motion is a major component of the crystal growth/melting mechanism.