Thermodynamic analyses of equilibria involving olivine, orthopyroxene and garnet

Abstract

Experiments were made on the orthopyroxene-garnet relationships in the system FeSiO 3-MgSiO 3-Al 2O 3 at 50 kbar and 1100–1500°C. Combining new and previously published data, thermodynamic analysis was carried out on the following equilibria: 1. (1) Mg 2Si 2O 6 + MgAl 2SiO 6 = Mg 3Al 2Si 3O 12 opx solid solution garnet 2. (2) Fe 2Si 2O 6 + FeAl 2SiO 6 = Fe 3Al 2Si 3O 12 opx solid solution garnet 3. (3) 1 2 Fe 2Si 2O 6 + 1 3 Mg 3Al 2Si 3O 12 = 1 2 Mg 2Si 2O 6 + 1 3 Fe 3Al 2Si 3O 12 opx garnet opx garnet 4. (4) 1 2 Fe 2SiO 4 + 1 3 Mg 3Al 2Si 3O 12 = 1 2 Mg 2SiO 4 + 1 3 Fe 3Al 2Si 3O 12. olivine garnet olivine garnet The free energy changes of reactions (1), (2), (3) and (4) were obtained as a function of temperature (kcal/mol) for 50 kbar: ΔG 0 1 = (−16.54 ± 0.72) − (−2.02 ± 0.25) × 10 −3 T( K) ΔG 0 2 = (−27.52 ± 2.10) − (−7.17 ± 1.31) × 10 −3 T( K) ΔG 0 3 = (−4.74 ± 0.24) − (−2.16 ± 1.53) × 10 −3 T( K) ΔG 0 4 = (−1.96 ± 0.15) − (−0.82 ± 0.10) × 10 −3 T( K). The intracrystalline exchange of Fe 2+ and Mg 2+ between M1 and M2 sites of the Al 2O 3-free orthopyroxene is given by RT In X M2 MgX M1 Fe X M2 FeX M1 Mg = 1240 − 3.58T+ (11700 − 6.16T)X M1 Fe −(10400 − 6.616T)X M2 Fe . A multisite regular solution for orthopyroxene and regular solutions for both olivine and garnet are sufficient to describe equilibria between these phases. The microscopic model shows that the ferrosilite-enstatite solid solution system is macroscopically an asymmetric mixture with an excess free energy that is practically temperature-independent above 1100°C.