Evolution of nanocluster ensembles: Computer simulation of diffusion and reaction controlled Ostwald ripening

The Ion Beam Synthesis (IBS) of nanoclusters can be controlled by the flux and the fluence of ions as well as by the implantation and/or annealing temperature. The evolution of the precipitates, mainly described by their particle radius distribution (PRD), the number of remaining particles and the critical radius, depends on these parameters. However, the evolution is expected to behave different for systems like SiO2 and CoSi2 clusters in Si, because they are characterized by quite different ratios of diffusion to reaction constants. Here we present a unified model of Ostwald ripening of nanoclusters, which describes the pure diffusion and reaction controlled limits as well as all intermediate, mixed processes. Expressing the exact solution of the adiabatic diffusion equation by multipole moments we derive the governing equation for the evolution of an ensemble of nanoclusters in the leading monopole approximation. Whereas in the diffusion controlled regime we have the well known infinite range 1/r interaction among the nanoclusters, 1/r(2) interactions come into play in the reaction limited regime. Computer simulations for ensembles of several thousands of nanoclusters demonstrate the evolution for typical cases.