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The Fe–Mg exchange coefficient between olivine (ol) and melt (m), defined as    $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$    Kd     Fe   T   -  Mg       = (Fe ol /Fe m )·(Mg m /Mg ol ), with all Fe T  expressed as Fe 2+ , 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 H 2 O (≤ 7 wt%) over a wide range of  f O 2  (iron-wüstite buffer to air), pressure (≤ 1.7 GPa), temperature (1025–1425 °C) and melt composition. The ratio of Fe 3+  to total Fe (Fe 3+ /∑Fe), as determined by Fe K-edge µXANES and/or Synchrotron Mössbauer Source (SMS) spectroscopy, lies in the range 0–0.84. Measured Fe 3+ /∑Fe is consistent (± 0.05) with published algorithms and appears insensitive to dissolved H 2 O. Combining our new data with published experimental data having measured glass Fe 3+ /∑Fe, we show that for Fo 65–98  olivine in equilibrium with basaltic and basaltic andesite melts,    $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$    Kd     Fe   T   -  Mg       decreases linearly with Fe 3+ /∑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 Fo 50  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 Fe 3+ /∑Fe in olivine-bearing experimental melts, from which  f O 2  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– f O 2  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 Fe 3+ /∑Fe to a precision of ≤ 0.04.

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