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The solid-state diffusion in binary and ternary systems is overall treated and modeled using the bi-velocity method. The mathematical formulation is given, and the boundary conditions discussed. The model allows the calculation of concentration profiles, spatial distribution of the entropy production rate, and diffusion path. The last two can be used to identify the phases present in the diffusion zone of the ternary system, and determine the thicknesses of the respective layers. The model is applied for the first time to simulate diffusion during aluminization of nickel and its super-alloys, MAR-M200+Hf and CMSX-4, and the predictions are compared with the results of the experiments performed by the authors. The results give a new quantitative explanation of the high-active and low-active regimes of aluminization. It is, in particular, confirmed that the high-active and low-active regimes of nickel aluminization can be carried out by a variation of the HCl/H2 flow ratio. The most important, and a brand new, result concerns the entropy production rate. It is shown that its maxima coincidence with the two-phase zone boundaries in real space, which gives new insight into the modeling of the diffusion in ternary systems. [ABSTRACT FROM AUTHOR]