Recoil resolution and particle stability under irradiation

The stability of a dispersion of particles may be affected by resolution due to radiation recoil. Simple models of the diffusion of solute that recoils into the matrix allow an estimate of when this process will be important, leading either to the complete dissolution of the particles or to inverse coarsening in which small particles grow and large particles shrink. We first find the concentration profile for which solute diffuses back to a particle as fast as it is expelled by recoils. The transient concentration profiles in the matrix demonstrate the time required to approach steady state. The solution for a single particle is then used to calculate the rate of inverse coarsening by the diffusion of solute from the region near large particles to the region near small particles. The rate of growth or shrinkage depends directly on the recoil rate and the recoil distance cubed. It depends only weakly on the particle spacing and not at all on the diffusion coefficient