Impact of diffusion on concentration profiles around near-critical nuclei and implications for theories of nucleation and growth

In order to better understand the interplay of diffusion and interfacial processes in nucleation phenomena we have performed kinetic Monte Carlo simulations of a lattice gas model with realistic but generic microscopic dynamics. These simulations are used to probe the complete dynamic range extending from diffusion-limited through interface-limited kinetics. Most phenomenological theories describing nucleation, growth and/or coarsening focus on either the diffusion-limited or interface-limited regime. Calculations are performed on initially monodisperse clusters placed into solutions of uniform concentration. In agreement with predictions, our simulations show the appearance of regions of enhanced solute concentration around clusters smaller than the critical size, and of solute depletion around clusters larger than the critical size. The range and magnitude of these effects are largely controlled by the ratios of the rate of free diffusion to those of interfacial attachment and detachment processes. Furthermore, these simulations show that the rate of cluster growth depends strongly on the diffusion rate and correlates well with the local solute concentration at the cluster surface, over the entire dynamic range studied. In “diffusion-limited” phenomenological models the solute concentration at the cluster surface is assumed to be determined by the radius of the cluster, through a local-equilibrium condition. Our results indicate that in the intermediate regime in which the rates of diffusion and interfacial processes are similar, such assumptions are qualitatively incorrect and so models that assume either fully diffusion-limited or fully interface-limited growth and coarsening should not be used. We show, in particular, that the recently proposed “coupled-flux model” correctly and naturally describes the underlying physics over the complete dynamic range and therefore is generally preferable.