Data from experimentally-induced diffusion profiles at approximately 40 Kbar, 1,300-1,500 ~ C in spessartine-almandine couples and a pyrope-almandine couple at 40 Kbar, 1,440 ~ C, described in Part I, were used to derive tracer diffusion coefficients (D*) of Fe, Mn and Mg in garnet. The experimental data were fitted by numerical simulations that model multicomponent, compositionallydependent difussion, including the effects of nonideal thermodynamic mixing. The simulations use the formalism of irreversible thermodynamics and an eigenvector technique of solution.
We were able to fit the asymmetrical spessartine-almandine profiles using constant D* and either the Darken/Hart-Icy-Crank or Manning-Lasaga models relating D* and interdiffusion coefficients, and both models yielded D*g consistent with the direct measurement of D*g by Cygan and Lasaga (1985) at lower temperatures (75(~900 ~ C). The results (equations 4.1-4.3 and Table l) indicate that Dve= DMg < DMn and QFe ~ QMg > QMn, where Q is the activation energy. In contrast, the asymmetry ofpyrope-almandine profiles is too great to fit with either tracer model assuming constant D* and indicates that D~g is similar to its value in spessartine-almandine couples but D* e is an order of magnitude less. The fit also suggests that D~a < DFe < DMg in pyrope-almandine couples. Synthesis of data from the two types of diffusion couples suggests that D~g is insensitive to compositional changes, whereas D* e is affected by Mn/Mg and Fe/Mg ratios and probably by other factors. These compositional effects on tracer coefficients are compatible with those documented by Morioka (1983) for cation diffusion in olivine. and interfacial fracturing. These simulations enable us to constrain the intrinsic or tracer diffusivities of the divalent cations of Fe, Mg, and Mn in garnet. We define here the tracer coefficient, D*, in the sense of Darken (1948), as the diffusion coefficient of a species in response to its isotopic concentration gradient in an otherwise chemically homogeneous medium of diffusion. The tracer diffusion coefficients are, in principle, functions of the composition of the medium.
The interdiffusion of two or more mutually soluble species, such as those discussed in the Part I, can be described, at a fixed composition, by a single interdiffusion coefficient, D, which incorporates their tracer diffusivities in a medium of the same composition (Darken 1948). The interrelationships of D and D*, which are discussed later, show that D must vary as a function of composition except in the limiting case of equal tracer diffusivities of the mutually soluble species. Additional compositional effects on D could arise from the nonideal thermodynamic mixing of the diffusing species, and the compositional dependence of D*, as illustrated, for example, by Darken (1948), Johnson and Babb (1956), and Vignes and Badia (1971). We have demonstrated in Part I that the interdiffusion coefficients of divalent cations in natural aluminosilicate garnets vary as functions of composition. In the following treatment, we examine these observed compositional dependences of D in terms of the above effects through numerical simulations on the basis of irreversible thermodynamic formulation of the multicomponent diffusion phenomenon, the available models of mixing property in garnet and D-D* relations.