Intrinsic diffusion simulation for single-phase, multicomponent systems

A one-dimensional, finite difference simulation based on Darken’s treatment of intrinsic diffusion for single-phase, multicomponent systems is described. For the study of intrinsic diffusion using semi-infinite diffusion couples for binary systems, the input to the simulation includes the initial concentration distributions, the molar volume and the intrinsic diffusion coefficients for the two components as a function of composition. The simulation provides as the output all the results that are obtained from a typical interdiffusion experiment including the concentration profiles, the Kirkendall shift and interdiffusion fluxes of the components as a function of position and time. In addition, the intrinsic and vacancy fluxes, and the lattice shifts and lattice velocity profiles are also obtained at all positions within the diffusion zone. Since the simulation can handle variations in molar volume, information regarding fluxes and mean velocities in various reference frames are also provided. The internal consistency of the simulation is tested with the aid of an analytical model for a binary system where the interdiffusion coefficient and the ratio of the intrinsic diffusion coefficients are constant.