Self-diffusion of magnesium in spinel and in equilibrium melts: Constraints on flash heating of silicates

We have measured Mg self-diffusion in spinel and coexisting melt at bulk chemical equilibrium using an isotopic tracer. The diffusion coefficients were calculated from the measured isotope profiles using a model that includes the complementary diffusion of ^(24)Mg, ^(25)Mg, and ^(26)Mg in both phases with the constraint that the Mg content of each phase is constant. This model also permits the calculation of the diffusion coefficient in one phase from the measured data in a coexisting phase. The activation energy and pre-exponential factor for Mg self-diffusion in spinel are, respectively, 384 ± 7kJ and 74.6 ± 1.1 cm^2/s. These data indicate Mg diffusion in spinel is much slower than previous estimates, probably because earlier measurements included grain boundary transport. The activation energy for Mg self-diffusion in coexisting melt is 343 ± 25 kJ and the pre-exponential factor is 7791.9 ± 1.3 cm^2/s. The results from this study were applied to evaluate cooling rates of Plagioclase-Olivine Inclusions (POI) in the Allende meteorite. Given a maximum melting temperature for POIs of ~ 1500°C, these results show that a 10 μ radius spinel would equilibrate isotopically with a melt within about 60 min. To preserve Mg isotopic heterogeneity, the POIs must have initially cooled faster than 15 to 250°C/h depending on the initial temperature of flash heating. The cooling rate must also be slow enough to generate the observed basaltic textures. The inferred cooling rate appears to be comparable or up to ten times greater than those inferred from experimental and textural studies of synthetic CAI systems. The nature of the heating process is thus required to be short with relatively rapid cooling, such as flash heating. However, the relatively rapid cooling cannot be due to radiation into a cold, ~400°K nebula but would require radiation into a rather stable hot environment