A solution model has been developed for coexisting magnetite–ulvöspinel and hematite–ilmenite solid solutions and applied to the Buddington–Lindsley (1964) geothermometer and oxygen barometer. The model is based on results from the hydrothermal experiments of Lindsley (550–1000°C), gas-mixing experiments of Katsura et al. (1976) and Webster and Bright (1961) (1000–1200°C), and new hydrothermal experiments performed by Spencer and Lindsley (1978) using the Co–CoO buffer. The model assumes (1) ilmenitess behaves as a binary asymmetric Margules solution; (2) titanomagnetite behaves as a binary asymmetric Margules solution below 800°C and as an ideal binary solution above 800°C; (3) configurational entropy terms can be approximated by a molecular mixing model for magnetites, and by Rumble’s (1977) model B (disorder of Fe3+) for (R3) ilmenites; (4) only ordered (R3) ilmenite solutions are present.
The free energy of the exchange reaction Fe3O4 + FeTiO3 = Fe2O3 + Fe2TiO4 and the excess parameters for each solution were solved by least-squares fit of the experimental data. The model has successfully reproduced experimental data in the temperature-fO2 range 600–1300°C, bounded (approximately) by the nickel–nickel oxide and wüstite–magnetite buffer curves. The model predicts a consolute point for Mt–Usp of ~550°C at ~Usp 32 Mt 68. No attempt was made to estimate mathematically the Hem–Ilm two-phase field. Uncertainties in T and fO2 are approximately 40–80°C and 0.5–1.0 log units fO2 (2σ) assuming ±1% uncertainties in Uspss and Ilmss compositions.