(1) Diffusion Paths in Ternary Systems - Comparison of Onsager and Darken Models M. Danielewski 1 , R. Bachorczyk 1 , B. Bo¿ ek 2 , A. Milewska 1 and Y. Ugaste 3 1 University of Mining and Metallurgy, Faculty of Materials Science and Ceramics, 30-059 Cracow, al. Mickiewicza 30, Poland 2 University of Mining and Metallurgy, Faculty of Applied Mathematics, 30-059 Cracow, al. Mickiewicza 30, Poland 3 Pedagogical University of Tallinn, 25 Narva Road, Tallinn 10120, Estonia Keywords: diffusion paths, ternary alloys, Fe-Ni-Cu alloys Abstract. The generalized Darken method for multicomponent interdiffusion is presented. Its solution enables one to obtain an exact expresion for the evolution of component distributions, for arbitrary initial distributions and time dependent boundary conditions. The paper is based on our studies of diffusion couples in the Fe-Ni-Cu system at 1273 K. The Fe-Ni-Cu system was chosen because it allows a wide range of compositions to be used as starting materials in the diffusion couples and because its thermodynamic properties are fairly well known. However, the solid solutions in this system are not ideal and consequently the intrinsic diffusivities depend on the composition. The driving force for diffusion in such a ternary system is the gradient of the chemical potential, which can be calculated from the concentration profiles and using the known thermodynamical data of the system. Consequently the diffusional flux can be expressed as a function of the concentration gradient, the thermodynamical term and of the mobility. The diffusion paths are discussed in the light of the ternary interdiffusion coefficients and the intrinsic diffusivities with the use of generalized Darken method. A comparison of the Onsager and Darken models is presented. Theory A key problem in multicomponent diffusion is the prediction of the diffusion path between the two terminal alloys. For reliable diffusion analyses as well as for the predictive calculations, the data for the interdiffusion, intrinsic diffusivities and/or self diffusion coefficients and their concentration dependence have to be known. Moreover the thermodynamic data for the system have to be known in order to calculate the chemical potentials for each component. Using the Matano-Boltzmann analysis for the multicomponent system [1-4 ], the interdiffusion fluxes can be calculated from the experimental diffusion profile: where are the terminal concentrations of the alloys employed for the couple and x 0 refers to the location of the Matano plane. Onsager’s formula for the interdiffusion flux of i-th component