Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space

Mean-field theory has been widely applied in modelling the kinetics of microstructure evolution. Considering a free energy contribution by microstructure entropy, a Fokker-Planck equation for precipitation kinetics is variationally derived from thermodynamic principles. Using dimensionless transformation into the Lifshitz-Slyozov-Wagner space, the Fokker-Planck equation is effectively solved within a fixed radius interval and an explicit Euler scheme, which is computationally advantageous. Through comparisons with the Ni-12.5 Al at. % alloy, it is shown that the Fokker-Planck equation can represent the typical stages of precipitation kinetics, i.e., nucleation, growth, and coarsening.