A practical solution for the diffusion equations in binary and multicomponent systems with constant intrinsic diffusion coefficients

A practical solution for the diffusion equations in binary and ternary systems is presented which leads to a prediction of the concentration-penetration curves, diffusion paths, and the values for the intrinsic and interdiffusion fluxes. The model is very simple and gives insight into a variety of diffusion phenomena and zero-flux planes. The model has been applied to systems in which the intrinsic diffusion coefficients are constant and which, as far as ternary systems are concerned, are thermodynamically ideal. Although not mathematically exact, the results agree within the expected experimental accuracy with exact solutions presented in the literature. Even if the intrinsic diffusion coefficients are not constant, or if the ternary system is not thermodynamically ideal, the results agree semi-quantitatively with experimental results found in the literature. With some adaptations the agreement will be still better.