An Internally Consistent Approach for Modeling Solid-State Aggregation: II. Mean-Field Representation of Atomistic Processes
A detailed continuum (mean-field) model is presented that captures quantitatively the evolution of a vacancy cluster size distribution in crystalline silicon simulated directly by large-scale parallel molecular dynamics. The continuum model is parameterized entirely using the results of atomistic simulations based on the same empirical potential used to perform the atomistic aggregation simulation, leading to an internally consistent comparison across the two scales. It is found that an excellent representation of all measured components of the cluster size distribution can be obtained with consistent parameters only if the assumed physical mechanisms are captured correctly. In particular, the inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Dynamic clusters with large capture volumes at high temperature, which are the result of rapid cluster shape fluctuations, are shown to be larger than would be expected from static analyses, leading to substantial enhancement of the nucleation rate. Based on these results, it is shown that a parametrically consistent atomistic-continuum comparison can be used as a sensitive framework for formulating accurate continuum models of complex phenomena such as defect aggregation in solids.