COARSENING OF ELASTICALLY INTERACTING COHERENT PARTICLES .1. THEORETICAL FORMULATION

The problem of Ostwald ripening in binary systems possessing a nonzero volume fraction of elastically and diffusionally interacting particles is examined. Under the assumption that the partial molar volumes of the two components are equal, the elastic and diffusion field equations decouple. This leads to a formulation of the coarsening problem which requires a solution of a multiparticle diffusion problem. The elastic stresses are incorporated into this formulation through the diffusional boundary conditions. The concentration in the matrix phase at the particle-matrix interface is obtained from the assumption of local thermodynamic equilibrium. Assuming particle sphericity, the multiparticle diffusion problem is solved under a quasistatic approximation using the method of irreducible multipole tensors. Instantaneous radial growth rates and migration rates of the particles are obtained which, in conjunction with a simple time-integration procedure, can be used to simulate coarsening in either stressed or unstressed systems.