Diffusion in silicate melts: III. Empirical models for multicomponent diffusion

Abstract

Empirical models for multicomponent diffusion in an isotropic fluid were derived by splitting the component's dispersion velocity into two parts: (a) an intrinsic velocity which is proportional to each component's electrochemical potential gradient and independent of reference frame and (b) a net interaction velocity which is both model and reference frame dependent. Simple molecules (e.g., M pO q) were chosen as endmember components. The interaction velocity is assumed to be either the same for each component (leading to a common relaxation velocity U) or proportional to a common interaction force (F). U or F is constrained by requiring no local buildup in either volume or charge. The most general form of the model-derived diffusion matrix [D] can be written as a product of a model-dependent kinetic matrix [L] and a model independent thermodynamic matrix [ G], [D] = [L] · [ G]. The elements of [ G] are functions of derivatives of chemical potential with respect to concentration. The elements of [L] are functions of concentration and partial molar volume of the endmember components, C io and V io, and self diffusivity D i, and charge number z i of individual diffusing species. When component n is taken as the dependent variable they can be written in a common form L ij = D jδ ij + C io[V noD n − V joD j)A i + (p nz nD n − p jz jD j)B i] where the functional forms of the scaling factors A i and B i depend on the model considered. The off-diagonal elementL ij (i ≠ j) is directly proportional to the concentration of component i, and thus negligible when i is a dilute component. The salient feature of kinetic interaction or relaxation is to slow down larger (volume or charge) and faster diffusing components and to speed up smaller (volume or charge) and slower moving species, in order to prevent local volume or charge buildup.Empirical models for multicomponent diffusion were tested in the ternary system CaOAl 2O 3SiO 2 at 1500°C and 1 GPa over a large range of melt compositions. Model-derived diffusion matrices calculated using measured self diffusivities (Ca, Al, Si, and O), partial molar volumes, and activities were compared with experimentally derived diffusion matrices at two melt compositions. Chemical diffusion profiles computed using the model-derived diffusion matrices, accounting for the compositional dependency of self diffusivities and activity coefficients, were also compared with the experimentally measured ones. Good agreement was found between the ionic common-force model derived diffusion profiles and the experimentally measured ones. Secondary misfits could result from either inadequacies of the model or inaccuracies in activity-composition relationship. The results show that both kinetic interactions and thermodynamic nonideality contribute significantly to the observed diffusive coupling in the molten CaOAl 2O 3SiO 2.