Theoretical and Computational Studies of Three-dimensional Phase Separation

The diffusive interactions occurring within a population of precipitates dispersed throughout a contiguous matrix may be described on the basis of a diffusion screening length. Screening theory predicts as functions of the dispersoid volume fraction the changes in diffusion screening length, maximum particle size, coarsening rate, and the scaled particle-size distribution. Furthermore, by considering fluctuations observed in the growth rates of individual particles, we report on developments of a stochastic theory of phase separation. Also, particle-size distributions and the maximum particle radii predicted as a function of time from theory and simulations are shown to agree well with experimental results obtained from measurements performed on Al$_{3}$Li precipitates in binary Al-Li alloys. Lastly, we calculated the spatial correlation function of these microstructures. We revealed through data analysis the relationship between the critical length scale for diffusion-mediated coarsening and spatial correlations in the microstructure.