Experimental determination of cation diffusivities in aluminosilicate garnets - II. Multicomponent simulation and tracer diffusion coefficients

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, compositionally-dependent 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/Hartley-Crank or Manning-Lasaga models relating D^* and interdiffusion coefficients, and both models yielded D_Mg^*consistent with the direct measurement of D_Mg^*in by Cygan and Lasaga (1985) at lower temperatures (750-900° C). The results (equations 4.1-4.3 and Table 1) indicate that D_Fe^*≅D_Mg^*<D_Mn^*and Q_Fe≅Q_Mg>Q_Mn, where Q is the activation energy. In contrast, the asymmetry of pyrope-almandine profiles is too great to fit with either tracer model assuming constant D^* and indicates that D_Mg^*is similar to its value in spessartine-almandine couples but D_Fe^*is an order of magnitude less. The fit also suggests that D_Ca^*< D_Fe^*<D_Mg^*in pyrope-almandine couples. Synthesis of data from the two types of diffusion couples suggests that D_Mg^*is insensitive to compositional changes, whereas D_Fe^*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.