4.1. Fe-O System
 Using the high-temperature oxygen solubility data of Fischer and Schumacher  and Distin et al. , Kowalski and Spencer  derived a thermodynamic model that describes liquid immiscibility in the Fe-O system at ambient pressure. The associated solution model employs Fe, FeO, and FeO1.5 liquid species and predicts closure of the miscibility gap between Fe-rich metallic and FeO-rich ionic liquids at approximately 3000 K. The species have strong nonideal interactions in the liquid, but above 2000 K the proportion of FeO1.5 species in the ionic liquid predicted by the model is small (<5 mol%), and a very minor shift in liquid compositions results if FeO1.5 species are ignored. This makes the model computationally much simpler as the two liquids at equilibrium are then described using two chemical potentials, one for each component:
Taking the standard state as the pure phases at the pressure and temperature of interest, the expressions for the chemical potentials of FeO in the metallic and ionic phases are
where μFeo,P,T○ is the standard state chemical potential, R is the gas constant and γFeOmetal is, for example, the activity coefficient of FeO in the metallic phase. Similar equations can be written for the Fe components in the two liquid phases. When component chemical potentials are equated, as in equation (3), the standard state terms cancel out and can therefore be ignored for the present. The nonideal mixing terms for FeO and Fe in both metallic and ionic liquids are described using asymmetric Margules equations
where WFeO-Fe and WFe-FeO are interaction parameters. At ambient pressure, these terms are a function of temperature but in order to fit the high-pressure data a pressure-dependent term, i.e., an excess volume, is also included. Using a least-squares fitting routine, we derive two excess volume terms from the high-pressure experimental data to give
where the pressure P is in bars. The first two terms in each expression are derived from the ambient pressure Redlich-Kister expressions given by Kowalski and Spencer , and the final term, related to the excess volume, is derived from the high-pressure data. The uncertainties in the excess volume terms are derived from the standard deviation of individual fits to the miscibility gap at each pressure. The uncertainty in the WFe-FeO excess volume is quite large mainly as a result of the data at 12 GPa. As will be seen, however, the effect of this uncertainty on the calculations described in section 5 is relatively small. The fit of this model to the high-pressure data is shown in Figure 10. Although the model was refined using only the data from this study, its predictions are also in good agreement with the coexisting liquid compositions reported by Tsuno et al. .
4.2. Mg-Fe-O System
 In order to calculate the oxygen content of liquid iron metal in equilibrium with magnesiowüstite of a given FeO content, we need to consider the equilibrium between the FeO components, i.e.,
The chemical potentials for each phase are given by equations (4) and (5), where magnesiowüstite now takes the place of the ionic liquid. Although samples of magnesiowüstite are generally nonstoichiometric to some extent as a result of the presence of FeO1.5 defects, experiments have shown that samples synthesized under high pressures have significantly lower FeO1.5 contents than at ambient pressures [McCammon, 1993]. In the development of the following model, we, therefore, assume magnesiowüstite to be stoichiometric. Activity-composition relations for FeO in the metallic phase are given by equations (6)–(9) and for magnesiowüstite a symmetric solution model is employed from the literature [O'Neill et al., 2003; Frost, 2003]:
As opposed to the Fe-O system, the standard state chemical potentials of FeO in liquid Fe and magnesiowüstite no longer cancel out across equilibrium (10) but can be determined using thermodynamic data extracted from the melting curve of FeO. The chemical potential of solid FeO was determined from room pressure free energy data [Kowalski and Spencer, 1995] and using P-V-T equation of state data from high-pressure measurements [Seagle et al., 2008]. The chemical potential of liquid FeO was then determined at high pressure and temperature by refining a P-V-T equation of state for the liquid using data on the melting curve of FeO. Data from Lindsley , Tsuno et al. , and Seagle et al.  were employed to fit the melting curve. The high-pressure results of Seagle et al.  were preferred over other studies because they bracket the melting temperature of a composition that is close to stoichiometric FeO. In the refinement of the equation of state properties of liquid FeO, the experimental melting data were weighted using the temperature uncertainties. The refined melting curve is shown in Figure 11. The thermodynamic parameters for the fit are reported in Table 3. It may not be possible to use the FeO melting curve to determine the chemical potential of FeO liquid relative to the cubic FeO end member at pressures above 70 GPa because cubic FeO goes through a phase transformation to the NiAs-type B8 structure [Fei and Mao, 1994], which may appear on the solidus above 70 GPa.
Figure 11. Experimental determinations of the melting curve of FexO. The model (solid black curve) has been derived by fitting the P-V-T properties of liquid FeO using the experimental data of Lindsley  up to 3 GPa, Tsuno et al.  up to 20 GPa and Seagle et al.  at 50 GPa, (with the experimental brackets provided by the latter two studies indicated by filled and shaded large opposed triangles). The standard state chemical potential of liquid FeO is obtained at high pressure and temperature using the fitted melting curve and thermodynamic properties of solid FexO.
Download figure to PowerPoint
Table 3. Thermodynamic Model Parametersa
| μ°(Wüstite,1 bar,T) (kJ mol−1)||−279318 + 252.848T − 46.12826T ln(T) − 0.0057402984T2||1|
| V0,298K (J/bar)||1.225||2|
| α, thermal expansion (K−1)||3.481e−5 + 2.968e−9T − 0.0806T−2 − 0.0014437T−1||2|
| KT (bar)||1,500,000 − 2.64e2(T-298) + 0.01906(T-298)2||3|
| μ°(FeO,liquid,1 bar,T) (kJ mol−1)||μ°(Wüstite,T,1 bar,) + 34,008 − 20.969T||1|
| V0,298 K (J/bar)||1.3244||4|
| α, thermal expansion (K−1)||4.923e−5 + 2.968e−9T − 0.0806T−2 − 0.0014437T−1||4|
| KT (bar)||802,655 − 100(T-298)||4|
 The proportion of FeO in Fe liquid at a given P, T, and magnesiowüstite Fe/(Fe + Mg) can be calculated using equation (10) and employing equations (4)–(12) to calculate the chemical potential of FeO in each phase. The oxygen distribution coefficient (KD) can then be calculated using the determined FeO contents. In Figure 12, curves calculated for KD using this model are compared with the multianvil experimental data of Asahara et al. . The curves are calculated for a magnesiowüstite Fe/(Fe + Mg) ratio of 0.15, which is midway within the range of values displayed by the experimental data. The model curves are in excellent agreement with the experimental data, although the model was derived completely independently.
 In Figure 13a, the thermodynamic model is compared with the DAC results obtained in this study. The model curves are calculated for the magnesiowüstite compositions of the individual experiments. At pressures below 25 GPa, the model predicts that KD is independent of composition. However, above 25 GPa, KD becomes strongly dependent on the magnesiowüstite FeO content. As shown in Figure 13a, above 25 GPa the curve calculated at 3500 K for a magnesiowüstite Fe/(Fe + Mg) ratio of 0.19 flattens out and crosses beneath that calculated for a lower temperature and lower magnesiowüstite Fe content. This behavior is mirrored exactly by the experimental data, with which the model is in excellent agreement, even though it has been derived completely independently.
Figure 13. (a) Results of oxygen partitioning experiments from the diamond anvil cell between 28 and 70 GPa are compared with curves calculated from the thermodynamic model for the individual experimentally observed magnesiowüstite Fe/(Fe + Mg) values (XFe). At high pressure, the model predicts that KD becomes compositionally dependent, in good agreement with the experimental data. Data from the recent study of Ozawa et al.  are also shown. (b) The oxygen content of liquid Fe metal in the experimental samples is plotted as a function of the equilibrium magnesiowüstite Fe/(Fe + Mg) ratio. Curves calculated at the experimental pressures and temperatures are determined from the thermodynamic model. Symbols are the same as those in Figure 13a. At high pressure, the curves are no longer linear, indicating that KD is no longer constant with varying magnesiowüstite Fe/(Fe + Mg).
Download figure to PowerPoint
 Data from the recent study of Ozawa et al. , which was performed up to 134 GPa, are also shown up to 80 GPa in Figure 13a. Between 18 and 94 GPa, values of ln KD determined by Ozawa et al.  are consistently lower by up to 1 natural log unit compared with our model, although data at 134 and 124 GPa are within 0.3 natural log units of the model, which is close to the reported experimental uncertainty. The lower Fe metal oxygen contents and consequent low values of KD reported by Ozawa et al.  could have resulted from FeO loss from Fe-liquid during quenching, as observed in previous studies by O'Neill et al. . As the Fe liquid metal cools during quenching, FeO liquid exsolves and can migrate to the boundary with the surrounding magnesiowüstite. If samples quench too slowly or Fe liquid regions are relatively small, the time scale for this process can be short enough for the Fe to be strongly depleted in FeO. On the other hand, unless temperatures in our study were significantly overestimated, it is hard to envisage experimental mechanisms that could lead to erroneously high values of KD.
 In Figure 13b, the Fe metal oxygen concentration has been calculated as a function of the FeO content of magnesiowüstite at the conditions of our experiments using the thermodynamic model. The experimental data are also plotted. At low pressure, there is a linear relationship and KD, which is essentially the gradient, is constant with composition. A curvature develops at high pressures and temperature, however, causing KD, to become compositionally dependent. Models that assume a constant KD will therefore tend to overestimate oxygen concentrations at typical FeO concentrations and conditions of the present-day lower mantle.
 The predictions of the model, particularly when extrapolated to the core-mantle boundary, are sensitive to the melting curve of FeO employed. We use a melting curve constrained by the data of Seagle et al. ; however, previous experimental studies by Shen et al.  and Knittle and Jeanloz  have derived both lower and higher temperature melting curves, respectively (Figure 11). Some idea of the uncertainties in the model can also be gained by employing these two studies to calibrate the model. When using the data of Shen et al. , a relatively minor shift in the calculated ln KD occurs with values that are on average more positive by approximately 0.5 natural log units at 60 GPa. Although still generally consistent with our diamond cell results, a poorer fit is obtained. When employing a curve that is bracketed midway between the liquid and solid temperatures reported by Knittle and Jeanloz  values of ln KD are driven consistently lower with pressure and the minima apparent for low XFe compositions in Figure 13 disappears. At 60 GPa, the calculated ln KD is approximately 0.8 log units below the curve at 3100 K shown in Figure 13a and is, therefore, in poor agreement with our experimental data. This model is in much better agreement with the data of Ozawa et al.  up to pressures of 74 GPa, but because the model displays no minima it predicts values that are over 1 natural log unit lower than the experimental data of Ozawa et al.  at the highest reported pressure (134 GPa). There is, however, a large difference in temperature between conditions where the solid and liquid phases are observed in the study of Knittle and Jeanloz , and a melting curve passing closer to the minimum estimated temperature up to 70 GPa would be quite consistent with the results of Seagle et al. , and multianvil experiments [Tsuno et al., 2007] and result in an oxygen partitioning model that is very similar to that shown in Figure 13.