Experimental calibration of the partitioning of Fe and Mg between biotite and garnet

The cation exchange reaction Fe₃Al₂Si₃O₁₂ +KMg₃AlSi₃O₁₀(OH)₂ = Mg₃Al₂Si₃O₁₂+KFe₃-AlSi₃ O₁₀(OH)₂ has been investigated by determining the partitioning of Fe and Mg between synthetic garnet, (Fe, Mg)₃Al₂Si₃O₁₂, and synthetic biotite, K(Fe, Mg)₃AlSi₃O₁₀(OH)₂. Experimental results at 2.07 kbar and 550 °–800 ° C are consistent with In (Mg/Fe) garnet/(Mg/Fe) biotite] = -2109/T(°K) +0.782. The preferred estimates for ¯H and ¯S of the exchange reaction are 12,454 cal and 4.662 e.u., respectively. Mixtures of garnet and biotite in which the ratio garnet/biotite=49/1 were used in the cation exchange experiments. Consequently the composition of garnet-biotite pairs could approach equilibrium values in the experiments with minimal change in garnet composition (few tenths of a mole percent). Equilibrium was demonstrated at each temperature by reversal of the exchange reaction. Numerical analysis of the experimental data yields a geothermometer for rocks containing biotite and garnet that are close to binary Fe-Mg compounds.