Multiscale simulations on the coarsening of Cu-rich precipitates in α-Fe using kinetic Monte Carlo, molecular dynamics and phase-field simulations

Abstract The coarsening kinetics of Cu-rich precipitates in an α-Fe matrix for thermally aged Fe–Cu alloys at temperatures above 700 °C is studied using a kinetic Monte Carlo (KMC) simulation and a phase-field method (PFM). In this work, the KMC approach adequately captures the early stage of the system evolution which involves nucleation, growth and coarsening, while the PFM provides a suitable framework for studying late-stage coarsening at large precipitate volume fraction regimes. Hence, both models complement each other by transferring the results of KMC along with precipitate–matrix interface energies from a broken-bond model to a quantitative PFM based on a grand chemical potential formulation and the CALPHAD database. Furthermore, molecular dynamics simulations provide information on the structural coherency of the precipitates and hence justify the sequential parameter transfer. We show that our PFM can be validated quantitatively for the Gibbs–Thomson effect and that it also predicts the coarsening kinetics correctly. It is found that the kinetics closely follow the LSW (Lifshitz–Slyozov–Wagner) law, whereas the coarsening rate constant increases with an increase in volume fraction of precipitates.