Atomic mobility in Cahn’s diffusion model

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Abstract
We propose a simple stochastic model for one-dimensional interdiffusion in a binary A-B solid solution. By an appropriate choice of the activation energy for the interchange of A and B atoms among neighboring planes, we prove the model drives the system to the correct steady states with statistical weights identical to those evaluated by the simplest mean-field thermodynamics. Based on this model an expression is obtained for the interdiffusion flux: The conditions under which the latter reduces to a linear-response-theory type are discussed, and the microscopic expression for mobility coefficient is elucidated. It is found to be a function of the local equilibrium composition and composition inhomogeneity.