Ostwald ripening in disordered systems

A theory of Ostwald ripening in disordered systems is proposed aimed at describing the ripening in amorphous solids and doped crystals. Whether frozen or caused by impurities, the disorder causes the surface energy to become a random quantity. Ripening in disordered systems is described in terms of the Fokker-Planck equation, in which the effective diffusion coefficient depends on the disorder. In case the disorder is infinitesimal the approach developed reduces to the classic Lifshitz-Slyozov theory, while it predicts considerable deviations from that theory for the case of moderately small disorder. The coarsening rate is found to increase with the disorder increase. Also, the disorder increases the size distribution function in the range of large radii, while shifting its maximum to the left. As a result the distribution becomes broader and more symmetric as compared to that of the classic theory.