DEVELOPING A METHOD TO CALCULATE OXYGEN FUGACITY BASED ON OLIVINE-MELT EQUILIBRIUM USING EXPERIMENTAL DATA

In order to connect volcanic rocks to their mantle sources, it is essential to consider redox equilibria and their dependence on temperature, pressure, chemical composition, and oxygen fugacity. Oxygen fugacity (fO₂) is an intensive variable that strongly affects the behavior of those elements in magmas that are sensitive to changes in redox state, such as Fe, and therefore Fe-Mg silicates, such as olivine. Since fO₂ plays an important role in fractional crystallization, in principle it is possible to estimate fO₂ from analyses of olivine in equilibrium with the melt. This research describes a new method based on this principle called the Olivine-Melt Equilibrium Method. This method requires a model that describes the relationship between Fe³⁺/Fe²⁺, T, P, melt composition, and fO₂. To determine the Fe³⁺/Fe²⁺ of melt in equilibrium with olivine, an olivine-melt distribution coefficient (K_D) is utilized. Therefore, this method can be used even if the Fe³⁺/Fe²⁺ ratio of the melt is unknown.

This research includes application of the Olivine-Melt Equilibrium Method to datasets from various published experimental runs under anhydrous conditions at 1 bar. Since there are several different K_D equations and empirical relationships between Fe³⁺/Fe²⁺ and fO₂, this research involves using these experimental datasets in order to constrain which equation best reproduces the fO₂ measured during these experiments. First, published experimental data with analyzed Fe₂O₃ and FeO contents were used to calculate fO₂ using different Fe³⁺/Fe²⁺ models. The model that best reproduces the fO₂ imposed on the experiments was selected after filtering the runs to the range of fO₂ expected for natural samples (FMQ ± 3). Next, to select the appropriate K_D equation, the Olivine-Melt Equilibrium Method was applied to experimental data in which the Fe₂O₃ and FeO contents are unknown, with total Fe reported as FeO_T. These datasets were filtered to ensure the olivine-melt pairs represent equilibrium conditions. The Fe³⁺/Fe²⁺ model of Kress and Carmichael (1991), and the K_D of Gee and Sack (1988) were found to best reproduce experimental results (± 0.3 log units fO₂).