Three-dimensional domain growth on the size scale of the capillary length: Effective growth exponent and comparative atomistic and mean-field simulations

The evolution of diffusively interacting nanoclusters is investigated by combined atomistic (kinetic lattice Monte Carlo method based on the nearest-neighbor Ising model) and mean-field (numerical integration of the governing reaction-diffusion equations) simulations. By expressing Monte Carlo parameters in terms of macroscopic thermodynamic quantities a well-defined interface between both methods is derived. Based on extensive Monte Carlo studies of the Gibbs-Thomson equation an explicit expression for the intrinsic capillary length is presented. Starting with
high-temperature quenches, the evolution of nanoclusters is first studied by the atomistic model. The observed transient dynamics of coarsening is explained uniquely on the basis of the ratio of the capillary length to the mean cluster size. Using input data from the atomistic model, Ostwald ripening is also studied in parallel with the mean-field model. In a detailed study, the similarities and differences of both approaches are discussed and explained in terms of their statistical and deterministic natures. It is demonstrated that in contrast to the commonly applied linearized version of the Gibbs-Thomson relation in the mean-field approach only the use of the full exponential form provides a reasonable matching with the atomistic model.