An experimental study of Fe-Mg partitioning between garnet and olivine and its calibration as a geothermometer

The partitioning of Fe and Mg between coexisting garnet and olivine has been studied at 30 kb pressure and temperatures of 900 ° to 1,400 °C. The results of both synthesis and reversal experiments demonstrate that K_D (= (Fe/Mg)_gt/(Fe/Mg)_OI) is strongly dependent on Fe/Mg ratio and on the calcium content of the garnet. For example, at 1,000 °C/30 kb, K_D varies from about 1.2 in very iron-rich compositions to 1.9 at the magnesium end of the series. Increasing the mole fraction of calcium in the garnet from 0 to 0.3 at 1,000 ° C increases K_D in magnesian compositions from 1.9 to about 2.5. The observed temperature and composition dependence of K_D has been formulated into an equation suitable for geothermometry by considering the solid solution properties of the olivine and garnet phases. It was found that, within experimental error, the simplest kind of nonideal solution model (Regular Solution) fits the experimental data adequately. The use of more complex models did not markedly improve the fit to the data, so the model with the least number of variables was adopted. Multiple linear regression of the experimental data (72 points) yielded, for the exchange reaction: 3Fe₂SiO₄+2Mg₃Al₂Si₃O₁₂ olivine garnet ⇌ 2Fe₂Al₂Si₃O₁₂+3Mg₂SiO₄ garnet olivine ΔH ° (30kb) of -10,750 cal and ΔS ° of -4.26 cal deg^-1 mol^-1. Absolute magnitudes of interaction parameters (W_ij) derived from the regression are subject to considerable uncertainty. The partition coefficient is, however, strongly dependent on the following differences between solution parameters and these differences are fairly well constrained: W_FeMg ^ol-W_FeMg ^gt≃ 800 cal W_CaMg ^gt-W_CaFe ^gt≃ 2,670 cal. The geothermometer is most sensitive in the temperature and composition regions where K_Dis substantially greater than 1. Thus, for example, peridotitic compositions at temperatures less than about 1,300 ° C should yield calculated temperatures within 60 °C of the true value. Iron rich compositions (at any temperature) and magnesian compositions at temperatures well above 1,300 °C could not be expected to yield accurate calculated temperatures. For a fixed K_Dthe influence of pressure is to raise the calculated temperature by between 3 and 6 °C per kbar.