Mean Field Kinetics: a Sound Framework for Understanding Diffusion in Alloys

摘要

Different techniques for simulating the kinetics of phase transformations are compared on their capability to reproduce the diffusion properties of alloys. The common framework is the linear formalism of the Thermodynamics of Irreversible Processes (TIP). After a critical review of the phenomenological models, the atomic point of view is presented with a focus on the correlation effects produced by a vacancy diffusion mechanism. Calculating the correlation factors in pure metal and in dilute alloys is mainly a mathematical exercise. In concentrated alloys, mean-field theories are now efficient enough to go beyond the approximate "random alloy" of Manning. They start from a microscopic description of the alloy where atoms are distributed on a rigid lattice and interact through a configurational Hamiltonian. The jump frequencies being an activated process depend on the local environment through the interaction energies such that the large range of frequencies is produced by a small number of thermodynamic and kinetic parameters. Until a recent self-consistent mean-field formulation, the correlation effects were not included in the mean-field equations. This new formulation starts from the master equation which gives the evolution with time of the distribution function of the system and introduces a time-dependent effective Hamiltonian. A simple illustration of this kinetic theory is the calculation of the transport coefficients. The general kinetic equations are linearized for a stationary state close to equilibrium and analyzed within the framework of the Thermodynamics of Irreversible Processes from which the transport coefficients are identified (both diagonal and off-diagonal terms of the Onsager matrix). In the particular case of a pure material, the same theory yields the exact value of the correlation factor.