Computer Simulation of Precipitate Coarsening: A Unified Treatment of Diffusion and Reaction Controlled Ostwald Ripening

In Ion Beam Synthesis (IBS) 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 behaviour, 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 an 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.