FE-MG EXCHANGE BETWEEN OLIVINE AND LIQUID AS A TEST OF EQUILIBRIUM: PROMISES AND PITFALLS

The Fe-Mg exchange equilibrium constant between olivine and liquid, K_D^ol-liq = [(FeO/MgO)^ol]/[(FeO/MgO)^liq] (molar), is perhaps one of the most powerful petrologic tools developed (Roeder and Emslie, 1970). While studies indicate that K_D can vary with composition (Toplis, 2005) or P (Herzberg and O’Hara, 1998; Putirka, 2005), analysis of 1,610 experimental data show that such variations are minor. Using Kress and Carmichael (1988) to calculate Fe3+/Fe2+ in experimental liquids: K_D = 0.41 – 0.006[TiO₂ wt.%] – 0.004[CaO wt.%] - 0.00813[Na₂O+K₂O wt.%], which describes ca. 15% of the variation in K_D, half of which is controlled by the last term. The K&C (1988) expression is preferred because it recovers a median value for experimental data compared to comparable models, and unlike more recent calibrations it does not use FeOt as input to predict Fe₂O₃/FeO. Encouragingly, residuals from the above expression are normally distributed and do not vary with experimental run duration or reported compositional error. Experimental error thus, on the whole, appears to be random. This supports an ever-present implicit assumption that equilibrium is the most probable of states obtained by experiment. The best petrologic models should thus reproduce as large a data set as possible.

An important caveat, though, is that K_D is sensitive to the model used to calculate Fe3+/Fe2+ in liquids. Fortunately, models that describe various oxygen buffers (e.g., NNO, QFM) induce <1% relative error. But models that relate Fe3+/Fe2+ to fO₂ (e.g., Kilinic et al.,1983; Kress and Carmichael, 1988; Kress and Carmichael, 1991; Eqns. 6, 7; Jayasuria et al., 2004; Eqn. 12; Borisov, 2010), yield quite different K_Ds. The Jayasuria et al. (2004; Eqn. 12) and K&C (1991; Eqn. 7) models are the extrema: for 1,076 experiments where fO₂ is reported, mean K_D = 0.350 ±0.057 and 0.336 ± 0.054 respectively. This 4% difference, while within 1σ error leads, for example, to 50-70^oC differences in olivine-liquid or mantle potential temperatures when a fractionation correction is applied to a picrite. Worse still, differences in calculated K_Ds range up to 20%. Simple solutions are few, except to average multiple estimates of Fe3+/Fe2+ to indicate error, avoid models that use Fe to predict Fe3+/Fe2+, or ignore Fe3+ altogether.