The kinetics of ostwald ripening in stressed solids: The low volume fraction limit

Abstract

The thermodynamics of non-hydrostatically stressed solids has been used to examine the influence of misfit strains, interfacial stress, and coherency stress on the kinetics of coarsening in an elastic solid with a vanishingly small volume fraction of noninteracting spherical precipitates. The following results are obtained: 1.1. The dimensionless form of the governing equations for Ostwald ripening in a coherent solid, when expressed in the comparison state, is isomorphic with that of the classical LS theory.2.2. The exponents of the temporal power laws for the mean radius, the number density of precipitate particles, and the supersaturation obtained in the long-time asymptotic limit are identical to those of the LS theory.3.3. The amplitudes of the temporal power laws are different from those of LS and are dependent on the signs and magnitudes of the precipitate misfit, interfacial stress, and solute expansion coefficient.4.4. The kinetics of coarsening are altered by the elastic stress primarily through the coupling of misfit and interfacial stress. Only the coefficient for the decay of the supersaturation depends on the solute expansion coefficient.5.5. A new expression for the dependence of the precipitate misfit on time during coarsening has been obtained. If the solute expansion coefficient of the matrix is not zero, the misfit is predicted to approach its equilibrium value as t−1/3.6.6. The analysis shows that decreasing the magnitude of the precipitate misfit may either increase or decrease the coarsening kinetics.