Mean field theories for the description of diffusion and phase transformations controlled by diffusion

A self-consistent mean field (SCMF) theory starting from an atomic diffusion model can predict most of the correlation effects induced by the vacancy diffusion mechanism while being coherent with thermodynamics. For that purpose a time dependent effective Hamiltonian is introduced into the non-equilibrium distribution function. Such effective Hamiltonian makes a new hierarchy of approximations to appear in parallel to the thermodynamic mean-field approximations. We explain how each level of approximation is related to correlation effects and how kinetics of phase transformation results from both thermodynamics and diffusion properties. A first example is the radiation induced segregation (RIS) at grain boundary (GB) in austenitic steels where thermodynamics is shown to play an important role under irradiation. In a second example, we demonstrate how mean-field approximations combined with mesoscopic theories like the classical nucleation theory can describe the kinetics of precipitation, leading to a prediction of the cluster size distributions in the solid solution and of the steady state nucleation rates in agreement with kinetic Monte Carlo simulations.