Diffusion Paths in Ternary Systems – Comparison of Onsager and Darken Models

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.