Fe-Ti oxide geothermometry: thermodynamic formulation and the estimation of intensive variables in silicic magmas

A new thermodynamic formulation of the Fe–Ti oxide geothermometer/oxygen barometer is developed. The method is based upon recently calibrated models for spinel solid solutions in the quinary system (Fe²⁺, Mg)(Al,Fe³⁺,Cr)₂O₄–(Fe²⁺, Mg)₂TiO₄ by Sack and Ghiorso, and rhombohedral oxides in the quaternary system (Fe²⁺,Mg,Mn)TiO₃–Fe₂O₃ (this paper). The formulation is internally consistent with thermodynamic models for (Fe²⁺,Mg)-olivine and -orthopyroxene solid solutions and end-member thermodynamic properties tabulated by Berman. The constituent expressions account for compositional and temperature dependent cation ordering and reproduce miscibility gap features in all of the component binaries. The calibration does not account for the excess Gibbs energy resulting from compositional and temperature dependent magnetic ordering in either phase. This limits application of the method to assemblages that equilibrated at temperatures above 600° C. Practical implementation of the proposed geothermometer/oxygen barometer requires minimal use of projection algorthms in accommodating compositions of naturally occurring phases. The new formulation is applied to the estimation of temperature and oxygen fugacity in a wide variety of intermediate to silicic volcanic rocks. In combination with previous work on olivine and orthopyroxene thermodynamics, equilibration pressures are computed for a subset of these volcanics that contain the assemblage quartz, oxides and either ferromagnesian silicate. The calculated log₁₀ f _{O 2}-T relations are reflected in coexisting ferromagnesian mineral assemblages. Volcanics with the lowest relative oxygen fugacity (log₁₀ f _{O 2}) are characterized by the assemblage olivine-quartz, those with slightly higher log₁₀ f _{O 2} s, by the assemblage orthopyroxene-quartz. The sequence proceeds with the necessary phases biotite-feldspar, then hornblende-quartz-clinopyroxene, and finally at the highest log₁₀ f _{O 2} s, sphene-quartz-clinopyroxene. Quantitative analysis of these trends, utilizing thermodynamic data for the constituent phases, establishes that, in most cases, the T-log₁₀ f _{O 2}value computed from the oxides is consistent with the compositions of coexisting silicate phases, indicating that phenocryst equilibrium was achieved prior to eruption. There is, however, considerable evidence of oxide-silicate disequilibrium in samples collected from more slowly cooled domes and obsidians. In addition, T-log₁₀ f _{O 2}trends from volcanic rocks that contain biotite and orthopyroxene are interpreted to imply a condition of Fe²⁺–Mg exchange disequilibrium between orthopyroxene and coexisting ferromagnesian silicates and melt. It is suspected that many biotite-feldspar-quartz-orthopyroxene bearing low temperature volcanic rocks inherit orthopyroxene xenocrysts which crystallized earlier in the cooling history of the magma body.The problem is probably at least as complex as that of the feldspars... A.F. Buddington (1956)