Fig. 6: Comparisons of oxygen fugacities (fO₂s) of natural samples to geochemical indices of fractionation, and spreading rates.

Simple models for mantle melting and crystal fractionation are also shown. Oxygen fugacities of the natural samples were determined using measured Eu distributions and Eqs. 7–19, and are plotted relative to the fayalite-magnetite-quartz buffer³⁴ (Δ FMQ) at 0.4 GPa at their REE temperatures. In (a), Δ FMQ is plotted against plagioclase An# (100 × Ca/(Ca + Na + K), in moles), in (b), against glass Mg# (100 × Mg/(Mg + Fe²⁺+ Fe³⁺), in moles), in (c), against Nd in glass, in parts per million (ppm), in (d), against half spreading rate, in millimeters per year (mm/y). Symbol colors and types are as defined in Fig. 1; larger symbols are melt inclusion data and smaller symbols are phenocryst-host glass pairs. Note the systematic inverse correlation of fO₂ with An# (a), Mg# (b), and spreading rate (d) and positive correlation with Nd (c). The trend for other REEs is similar to Nd, with samples exhibiting higher REE concentrations having higher fO₂s. Fractional and batch melting and fractional crystallization models (solid red, blue and black lines respectively) assume fO₂ is modulated by magmatic fractionation of divalent from trivalent iron. Bulk Fe³⁺ partition coefficients assumed in the melting models are indicated. Unless otherwise noted, small dots on the melting and fractional crystallization models are 5% increments (F indicates extent of melting, Eqs. 21–23). Dash-dotted red line in (a) shows fO₂s of an instantaneous fractional mantle melt cooled to the point of plagioclase saturation (the melting model assumes bulk a \({D}_{{{Fe}}^{3+}}\) of 0.1). All melting models assume adiabatic decompression of a DMM source³² at a potential temperature of 1300°C. Iron species proportions are calculated using the model of Kress and Carmichael⁴⁷ using fO₂s determined from Eu distributions and Eqs. 7–15 at the REE temperatures. Error bars are estimated 1σ uncertainties recovered from Monte Carlo simulations (see Methods and Supplementary Figs. S10–S12 for details).