Effect of redox on Fe–Mg–Mn exchange between olivine and melt and an oxybarometer for basalts

The Fe–Mg exchange coefficient between olivine (ol) and melt (m), defined as $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg = (Feol/Fem)·(Mgm/Mgol), with all FeT expressed as Fe2+, is one of the most widely used parameters in petrology. We explore the effect of redox conditions on $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg using experimental, olivine-saturated basaltic glasses with variable H2O (≤ 7 wt%) over a wide range of fO2 (iron-wüstite buffer to air), pressure (≤ 1.7 GPa), temperature (1025–1425 °C) and melt composition. The ratio of Fe3+ to total Fe (Fe3+/∑Fe), as determined by Fe K-edge µXANES and/or Synchrotron Mössbauer Source (SMS) spectroscopy, lies in the range 0–0.84. Measured Fe3+/∑Fe is consistent (± 0.05) with published algorithms and appears insensitive to dissolved H2O. Combining our new data with published experimental data having measured glass Fe3+/∑Fe, we show that for Fo65–98 olivine in equilibrium with basaltic and basaltic andesite melts, $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg decreases linearly with Fe3+/∑Fe with a slope and intercept of 0.3135 ± 0.0011. After accounting for non-ideal mixing of forsterite and fayalite in olivine, using a symmetrical regular solution model, the slope and intercept become 0.3642 ± 0.0011. This is the value at Fo50 olivine; at higher and lower Fo the value will be reduced by an amount related to olivine non-ideality. Our approach provides a straightforward means to determine Fe3+/∑Fe in olivine-bearing experimental melts, from which fO2 can be calculated. In contrast to $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg , the Mn–Mg exchange coefficient, $${\text{Kd}}_{{{\text{Mn}} {-} {\text{Mg}}}}$$ Kd Mn - Mg , is relatively constant over a wide range of P–T–fO2 conditions. We present an expression for $${\text{Kd}}_{{{\text{Mn}} {-} {\text{Mg}}}}$$ Kd Mn - Mg that incorporates the effects of temperature and olivine composition using the lattice strain model. By applying our experimentally-calibrated expressions for $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg and $${\text{Kd}}_{{{\text{Mn}} {-} {\text{Mg}}}}$$ Kd Mn - Mg to olivine-hosted melt inclusions analysed by electron microprobe it is possible to correct simultaneously for post-entrapment crystallisation (or dissolution) and calculate melt Fe3+/∑Fe to a precision of ≤ 0.04.