Length scales in phase coarsening: Theory, simulation, and experiment

The collective interactions occurring within a population of spherical precipitates dispersed throughout a contiguous matrix may be described on the basis of a diffusion screening length. This critical length scale is derived from the quasi-static theory of diffusion-limited phase coarsening of spherical precipitates. This theory predicts as functions of the dispersoid volume fraction the changes in diffusion screening length, the maximum particle size, the population's coarsening rate, and, finally, the affine particle-size distribution. Furthermore, by considering fluctuations observed in the growth rates of individual particles, we formulate a stochastic theory of phase coarsening. Results obtained from simulating phase coarsening using multiparticle diffusion approaches and phase field model are then compared to the kinetic theories. Finally, particle-size distributions and the maximum radii predicted from theory and simulations are shown to agree well with experimental results obtained from measurements performed on δ′ (Al₃Li) precipitates in binary Al-Li alloys.