Interdiffusion in Cr-Fe-Co-Ni medium-entropy alloys

Diffusion in multi-component alloys is attracting renewed attention because of the worldwide interest in high-and medium-entropy alloys (HEAs/MEAs). In the present work, we used diffusion multiples made from MEAs of the quaternary Cr-Fe-Co-Ni system arranged as six distinct pseudo-binary diffusion couples (Cr29Fe13CO29Ni29-Cr29Fe29CO29Ni13, Cr29Fe29Co13Ni29-Cr29Fe29CO29Ni13, and so on, where the interdiffusing elements are italicized for clarity). In the two halves of each couple, the starting concentrations of the interdiffusing elements (Fe,Ni and Co,Ni in the above examples) were different while those of the background elements (Cr,Co and Cr,Fe in the above examples) were the same. The diffusion multiples were annealed at temperatures between 1153 and 1355 K at times from 100 to 900 h, after which the concentrations of the different elements were measured as a function of distance across each couple. Interdiffusion coefficients were derived from such concentration profiles using the standard Sauer-Freise method and compared with literature data as well as with published tracer diffusion coefficients. Although the background elements were homogeneously distributed initially, some of them developed distinct sine-wave shaped concentration gradients near the interfaces after annealing, implying that uphill diffusion of these elements had occurred. We show using a kinetic model for substitutional diffusion via vacancy hopping that such uphill diffusion can occur even in the absence of thermodynamic interactions, i.e. in ideal solid solutions in which the thermodynamic factor Phi of each element is equal to one (Phi(i) = 1 + partial derivative ln f(i)/partial derivative ln c(i) where f(i) and c(i) are the activity coefficient and mole fraction of element i, respectively). The model accounts for all elemental fluxes and also rationalizes the diffusion profiles of the major interdiffusing elements.