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Many important diffusion problems in the earth sciences and other disciplines involve multicomponent materials. Nevertheless, it is common practice to apply the binary diffusion formalism, which goes back more than 140 years (1), to these problems. The pseudo-binary approximation cannot explain all features of diffusion in multicomponent systems, such as nonmonotonic composition profiles in isothermal diffusion couples, and may introduce sizable errors in the prediction of mass transfer rates. The quality of the pseudo-binary approximation is difficult to evaluate because it depends on the composition of the diffusion couple and the particular component being considered. Furthermore, it is not theoretically justified. The classic studies of Onsager, beginning in the 1930s (2), gave multicomponent diffusion a coherent phenomenological basis, including cross terms (3).
The presence of cross-coupling and the symmetry of the phenomenological coefficient matrix had been anticipated earlier for a few transport processes (4), but it was the statistical mechanical approach of Onsager, based on the principle of microscopic reversibility, that enabled formulation of a generalized approach to the thermodynamics of irreversible phenomena (5). A key element of the theory of irreversible processes, or nonequilibrium thermodynamics, is the set of relations known as the Onsager reciprocal relations (ORR)--when the thermodynamic forces and fluxes are chosen appropriately, the phenomenological coefficient matrix is symmetric. Similar to the fundamental laws of equilibrium thermodynamics, the ORR can only be verified experimentally.
A large impediment to experimental tests is the prerequisite of obtaining experimental data for both diffusion coefficients and activity coefficients in the same range of composition so that the experimental D sub ik matrix can be transformed to the Onsager phenomenological L sub ik matrix. Because of the lack of thermodynamic data, the validity of the ORR for isothermal, multicomponent chemical diffusion has been confirmed for a relatively small number of aqueous and metallic systems (6). Indeed, the ORR have not been verified for molten silicate solutions, although accurate D sub ik are known for several ternary systems (7, 8). In this report, we summarize the results of calculations that enable an accurate test of Onsager's reciprocity hypothesis for the molten ternary system consisting of 40% CaO, 20% Al sub 2 O sub 3 , and 40% SiO sub 2 by weight. We have performed the tedious, but...