The role 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 version, the equation reads $D_A = D_A^* \Gamma$, with $\Gamma$ the thermodynamic factor. The question addressed in this paper is how $D_A$ and $D_A^*$ depend separately on $\Gamma$. 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), it is shown that the intrinsic diffusivity does not depend on $\Gamma$. This approach simplifies a previous theoretical analysis that reaches the same result. Experimental results of diffusion in a Ni-Pd and Fe-Pd alloys (M. J. H. van Dal et al., Acta mater. 48, 385, 2000) are used to check the theory.