Interdiffusion under the chemical potential gradient; Comparison of Onsager and Darken models

The generalized Darken method of interdiffusion in multicomponent systems (GDM) enables obtaining an exact expression for the evolution of component distributions for arbitrary initial distributions and time dependent boundary conditions. In this, work we studied the consequences of the more general formulae for the diffusional flux (Planck's equation) which permits to take into account thermodynamical driving forces. This paper is based on our studies of diffusion couples in the Cu-Fe-Ni system at 1273 K. The Cu-Fe-Ni system was chosen because it is a single phase in a wide range of compositions and because its thermodynamic properties are fairly well known. However, the solid solutions in this system are not ideal and consequently the diffusivities depend on composition. The driving force for the diffusion in such ternary system is the gradient of the chemical potential which can be calculated from the concentration profiles and using the known thermodynamic data of the system. Consequently the diffusional flux can be expressed as a function of the concentration gradients of all elements in the system, of the thermodynamic terms and of the mobilities. The diffusion paths are discussed in the light of the ternary interdiffusion coefficients and the self diffusivities with the use of generalized Darken method. A comparison of the Onsager and Darken models is presented. The results show the prospect for the future application of the GDM in the modelling of stress affected diffusion in ternary and higher solid solutions.