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

Abstract

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 $D_A = D_A^* Gamma$, 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 extbf{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 extit{et al.}, Acta mater. extbf{48}, 385, 2000) 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.