Cu-precipitation kinetics inα−Fefrom atomistic simulations: Vacancy-trapping effects and Cu-cluster mobility

We present Monte Carlo simulations of the first stages of the coherent precipitation of copper in $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Fe}$. Our method is based on a vacancy mediated diffusion model, which takes into account the dependence of vacancy concentrations and migration barriers on the local atomic environment. These parameters are fitted to ab initio data, calculated within the density functional theory. The simulated precipitation kinetics is compared with experimental one. The Fe-Cu system is characterized by a low mutual solubility, which results in the formation of almost pure copper precipitates, and by a large difference between the vacancy formation energy in bcc iron $(\ensuremath{\sim}2.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ and metastable bcc copper $(\ensuremath{\sim}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$, which leads to strong trapping of vacancies by the precipitates. As a result, precipitates containing up to several tens of copper atoms can be much more mobile than individual copper atoms. This original result is analyzed with a simple model of cluster diffusion, which suggests that the same behavior could be observed in alloys with similar properties.