DIFFUSION IN MULTICOMPONENT METALLIC SYSTEMS: VIII. A KINETIC CALCULATION OF THE ONSAGER L COEFFICIENTS IN SUBSTITUTIONAL SOLID SOLUTIONS

Abstract

Diffusion in multicomponent close-packed solutions is described by means of two transition-state models—a pure interchange model and a pure vacancy model. In the first, the fluxes are given directly in the number-fixed frame of reference, which in dilute solutions may be identified with the volume-fixed frame of reference. In the second, the fluxes are calculated directly in the lattice-fixed (Kirkendall) frame of reference. The fluxes and the kinetically determined L matrix for the second model are transformed to the number-fixed frame for comparison with the first model. In both cases the L coefficients appear in a form to which Onsager's theorem of reciprocal relations is applicable, and all other thermodynamic requirements are satisfied. For dilute solutions the L coefficients are found to vary with composition as where the K's are slowly varying coefficients. The K's are always positive for the exchange model, but in exceptional circumstances the K_ij may be negative in the vacancy model. The predictions of both models are found to be consistent with some experimental results for diffusion in an almost ideal nonaqueous ternary liquid mixture.Nonzero off-diagonal coefficients in the L matrix of an n component system necessarily arise as a consequence of the dependence between the n fluxes and the applicability of the Gibbs–Duhem relation to the thermodynamic forces. In rich substitutional solutions, these off-diagonal coefficients are nearly always expected to give measurable contributions to the fluxes.