In Fe-rich metamorphic and highly evolved igneous rocks, quartz can coexist with Fe2SiO4-rich olivine. The relationships between these phases and the Fe-Ti oxides are governed by the equilibrium
abbreviated QUI1F. For pure fayalite the QUI1F assemblage in equilibrium with metallic Fe is isobarically invariant, falling at 1058 ± 3 °C and log fO2 = −14.7 ± 0.1 at 1-bar pressure. With increasing fO2, metallic Fe is lost, and the assemblage becomes isobarically univariant, the ulvospinel and ilmenite gaining Fe3O4 and Fe2O3, respectively. The QUI1F assemblage is stable at 942 ± 10 °C and 10−14 bars fO2 (WM buffer, 1 bar); at lower temperatures it becomes asymptotic to the FMQ buffer curve. The univariant equilibrium can be expressed by the relation In KQuI1F = 3827/T − 2.868 + 0.0280(P − 1 )/T (T in kelvins, P in bars; ). Above QUI1F, fayalite and ilmenite are not both stable with titanomagnetite and quartz; below QUI1F, quartz and titanomagnetite are not both stable with fayalite and ilmenite. Because QUI1F contains the subassemblage titanomagnetite and ilmenite, it provides redundant information on the temperature and fO2 of formation if the presssure can be estimated to within 1-2 kbar.
If the olivine is not pure Fe2SiO4, displacement of QUI1F can be calculated by use of a solution model for olivine. Furthermore, if either fayalitic olivine or quartz is absent from the assemblage, QUI1F can be used to calculate the activity of the corresponding component−provided that pressure is known and that the primary compositions of the oxides can be determined. Likewise, if titanomagnetite or ilmenite is missing, QUI1F provides an estimate of aFe3O4 or aFe2O3.
The crystallization of a number of volcanic and plutonic rocks appears to have been controlled by the QUI1F equilibrium, with the oxide assemblages broadly reflecting the silica activity. Those fayalite-bearing rocks that contain ilmenite as the sole oxide are invariably silica-saturated; those with ilmenite and titanomagnetite may be either saturated or undersaturated with respect to silica; and most of those with only titanomagnetite are strongly undersaturated and commonly contain nepheline. The QUI1F equilibrium also adds important constraints to geothermometry. It decreases by an order of magnitude the uncertainty in the two-oxide thermometer that results from precision of analysis; it allows one to estimate oxygen fugacity in rocks where the oxides have re-equilibrated; and even in cases for which no textural evidence remains, it can show the extent to which Fe-Ti oxides have re-equilibrated and indicates what the original compositions must have been.