Generalization of the Lifshitz-Slyozov-Wagner coarsening theory to non-dilute multi-component systems

The coarsening of precipitates in a matrix with a non-zero volume fraction is treated by assuming that the exchange of matter between the precipitates occurs by diffusion in the matrix within finite zones surrounding the precipitates. The thermodynamic extremal principle is used for the derivation of evolution equations for the precipitate radii. Accordingly, non-steady-state and steady-state distribution functions are deduced, depending on the system parameter characterizing the finite diffusion zones. The distribution functions tend exactly to the established Lifshitz-Slyozov-Wagner distribution for a zero volume fraction of the precipitates. The steady-state distribution functions are expressed by means of distinct volume-fraction-dependent parameters, which are presented by analytical expressions and in diagrams. To treat non-steady-state systems, ensembles of up to 106 precipitates can easily be handled by standard computational methods.