Computer simulation of precipitate coarsening: A unified treatment of diffusion and reaction controlled Ostwald Ripening

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Abstract
In Ion Beam Synthesis of nanoclusters the postimplantation annealing step causes major redistribution of the implanted impurity atoms by Ostwald Ripening (OR). The diffusion-reaction equations describing OR are highly nonlinear. Therefore, analytical studies are restricted to special cases like the asymptotic behavior, the diffusion or reaction controlled limit, low cluster concentration, etc. An alternative to analytical studies of OR is the numerical integration of the diffusion-reaction equations. Using this method we take into account the diffusion and reaction control of OR, i.e. we present for the first time a unified treatment for the whole range of and in between the diffusion and reaction controlled limits. Based on a local mean field theory, our model starts with a multipole expansion of the concentration field, which satisfies the stationary diffusion equation. Using appropriate boundary conditions on the precipitates we derive self-consistently the governing equations for the evolution of the clusters. Alternatively to Ewald's summation method we apply a Yukawa-like screening of precipitates. The dependence of the particle radius distribution (PRD), the critical radius and the density of nanoclusters on process parameters will be discussed.

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