Effect of the thermodynamic factor on the intrinsic and tracer diffusivities in binary mixtures

One of the Darken equations gives a relationship between the intrinsic and the tracer diffusion coefficients, D_{A} and D_{A}^{*}, of species A in a solid binary mixture. In its original formulation, the equation reads D_{A}=D_{A}^{*}Γ, with Γ the thermodynamic factor. The question addressed in this paper is how D_{A} and D_{A}^{*} depend separately on Γ. Using a recent result for transition probabilities in terms of the excess chemical potential [M. Di Muro and M. Hoyuelos, Phys. Rev. E 104, 044104 (2021)2470-004510.1103/PhysRevE.104.044104], it is shown that the intrinsic diffusivity does not depend on Γ. This approach simplifies a previous theoretical analysis that reaches the same result. Experimental results of diffusion in Ni-Pd and Fe-Pd alloys [M. J. H. van Dal et al., Acta Mater. 48, 385 (2000)1359-645410.1016/S1359-6454(99)00375-4] are used to check the theory. Numerical simulations of Ni-Pd were performed to show that the migration energy is the main factor responsible for the increase in diffusivity at intermediate concentrations.