Self-consistent formulation of configurational kinetics close to equilibrium: The phenomenological coefficients for diffusion in crystalline solids

We present a new microscopic kinetic theory for the calculation of the phenomenological coefficients for matter transport in alloys. The theory is based on the master equation which gives the evolution with time of the distribution function of the system. While at equilibrium the distribution function depends on the configurational Hamiltonian, in the general case it is expressed by a time-dependent effective Hamiltonian. The zero-order self consistent approximation consists in considering only the effective pairwise interactions. Kinetic equations are written to zero order for a stationary state close to equilibrium, from which we infer the analytical expression of the transport coefficients (both diagonal and off-diagonal) in a homogeneous binary solid solution with a vacancy diffusion mechanism. These expressions depend on the configurational Hamiltonian pairwise interactions, the attempt jump frequencies, the alloy composition and the correlation factor for selfdiffusion which reflects the crystallographic structure. They are then compared with Monte Carlo values, obtained from the fluctuation—dissipation theorem. The agreement for the bcc structure is better than 20% over the whole composition range, for a positive as well as a negative heat of mixing. In the pure material, the theory yields the exact value of the correlation factor. Comparisons with the Manning relations and the other microscopic approaches are discussed.