Crossover from superdiffusive to diffusive mixing in plastically deformed solids

We derive expressions for the effective diffusion coefficient of Richardsonâ™s pairs in plastically strained solids as a function of the pair separation distance R. We predict that a crossover from superdiffusive to diffusive mixing takes place when R becomes comparable to the coherence length of the shearing events underlying the plastic deformation. Molecular dynamics simulations on nanocrystalline and amorphous systems support this analysis, which thus provides new insight on deformation mechanisms in these systems. Superdiffusive mixing is experimentally observable by monitoring the rate of dissolution of precipitates as a function of their initial size.