A stochastic theory of non-ideal behaviour

Abstract

The stochastic theory developed in Parts I and II is applied here to a detailed study of the diffusion coefficients in binary and ternary systems. We start from an equation of Part I which permits us to describe with great ease the dependence of the mutual diffusion coefficient in a binary system on the composition and on the pair interaction parameter ω. That dependence is given by a product of a phenomenological coefficient Γ and an activity factor γ. The results show that for repulsions (ω > 0) both Γ and γ are smaller than the ideal value of one. At the critical point γ →0 and hence the mutual diffusion coefficient, proportional to Γ_γ, falls to zero ; Γ, hewever, remains finite. For attractions (ω < 0), Γ is smaller than one (as for repulsions), while γ is greater than one ; the mutual diffusion coefficient attains a maximum near the critical point. Subsequently, we derive expressions for the four diffusion coefficients in a ternary system [A, B, C]. The expressions are in terms of thermodynamic quantities of the ternary system at equilibrium, which can be easily evaluated as functions of the three pair interaction parameters ω _AB , ω _AC and ω _BC . We then deal with self diffusion in binary systems, notably with a quasi-ternary system in which the third component (an isotope) closely resembles the second and is present in trace quantities.

Having presented the theoretical framework, we turn to an application to real non-ideal binary and ternary systems, with short range interactions. The experimental data for the activity factor of binary systems at equilibrium permit us to evaluate the values of ω for these systems and hence to compute diffusion coefficients with the help of our theory. The results agree reasonably well with the experimental values, supporting the basic assumptions of our theory, but are not significantly better than those obtained with certain other equations employed in the literature. Still these equations do not explain diffusion data with the help of interaction parameters (specific for the system, but independent of the composition) as we do, but require the knowledge of auxiliary experimental data over the whole range of composition.