Experimental metal–silicate partitioning data for Ni, Co, V, Cr, Nb, Mn, Si and W were used to investigate the geochemical consequences of a range of models for accretion and core formation on Earth. The starting assumptions were chondritic ratios of refractory elements in the Earth and the segregation of metal at the bottom of a magma ocean, which deepened as the planet grew and which had, at its base, a temperature close to the liquidus of the silicate. The models examined were as follows. (i) Continuous segregation from a mantle which is chemically homogeneous and which has a fixed oxidation state, corresponding to 6.26 per cent oxidized Fe. Although Ni, Co and W partitioning is consistent with chondritic ratios, the current V content of the silicate Earth cannot be reconciled with core segregation under these conditions of fixed oxidation state. (ii) Continuous segregation from a mantle which is chemically homogeneous but in which the Earth became more oxidized as it grew. In this case, the Ni, Co, W, V, Cr and Nb contents of core and mantle are easily matched to those calculated from the chondritic ratios of refractory elements. The magma ocean is calculated to maintain a thickness approximately 35 per cent of the depth to the core–mantle boundary in the accreting Earth, yielding a maximum pressure of 44 GPa. This model yields a Si content of the core of 5.7 per cent, in good agreement with cosmochemical estimates and with recent isotopic data. (iii) Continuous segregation from a mantle which is not homogeneous and in which the core equilibrates with a restricted volume of mantle at the base of the magma ocean. This is found to increase depth of the magma ocean by approximately 50 per cent. All of the other elements (except Mn) have partitioning consistent with chondritic abundances in the Earth, provided the Earth became, as before, progressively oxidized during accretion. (iv) Continuous segregation of metal from a crystal-melt mush. In this case, pressures decrease to a maximum of 31 GPa and it is extremely difficult to match the calculated mantle contents of the highly incompatible elements Nb and W to those observed. Progressive oxidation is required to fit the observed mantle contents of vanadium. All of the scenarios discussed above point to progressive oxidation having occurred as the Earth grew. The Earth appears to be depleted in Mn relative to the chondritic reference.
Accretion and core formation on the Earth took place within ca 30 Myr of the origin of the Solar System (Kleine et al. 2002; Yin et al. 2002), while the Moon appears to have been generated by a giant impact between 20 and 120 Myr later (Touboul et al. 2007). Information provided by these radiogenic isotope studies gives some idea of timing of these events, but few constraints on the actual physical conditions on the early Earth as the core formed. Although the latter are reflected in the composition of the accessible silicate mantle (Righter & Drake 1997; Li & Agee 2001; Wade & Wood 2005), using this composition to unravel the accretion and differentiation history of the Earth is a complex problem without, as yet, a unique solution. It is the purpose of this contribution to review and amplify recent progress made towards understanding the differentiation of the core from the mantle.
As the Earth accreted and the core segregated, all elements were distributed between the Fe-rich metallic phase and the silicate mantle according to their partition coefficients Di defined as follows:(1.1)where [i] is the concentration of element I in the phase of interest. Elements with high values of D (siderophile) were strongly depleted in the silicate mantle while those with low D values (lithophile) were concentrated in the mantle. In order to extend these qualitative ideas, one can use the observations which indicate that the Earth has strong chemical affinities with the chondritic meteorites (Allègre et al. 1995; McDonough & Sun 1995). If we define as ‘refractory’ all those elements (e.g. Ca, Ti, Ni, Fe and the rare earths) that would condense from a solar gas at higher temperature than Mg (Wasson 1985), then we observe that refractory lithophile elements are present in the mantle in approximately the same proportions to one another as in CI chondrites (Allègre et al. 1995; McDonough & Sun 1995). This implies that all refractory elements are present in the bulk Earth (core plus mantle) in roughly chondritic proportions. Table 1 presents estimated core–mantle partition coefficients for a number of elements, refractory and non-refractory, based on this chondritic model. The question now is how one uses these partition coefficients to deduce the physical conditions of temperature, pressure and oxygen fugacity which attended core formation.
The simplest approach to estimating the conditions of core formation is to assume an oxygen fugacity consistent with the current Fe contents of mantle and core and to use experimental data to calculate pressure and temperature at which the core and mantle would, at equilibrium, generate the partition coefficients of table 1. The result, at the current composition of the mantle, is a pressure of ca 40 GPa and temperature of approximately 3800 K (Gessmann & Rubie 2000; Chabot & Agee 2003; Wade & Wood 2005). The observation that high pressures are needed to explain the Ni and Co concentrations in the mantle led to the ‘deep magma ocean’ hypothesis that, at its simplest, is interpreted as core–mantle equilibration at a single pressure, temperature and mantle composition (Li & Agee 1996; Righter & Drake 1997). Wade & Wood (2005) took this model a step further by considering that it was likely that core formation was a continuous process, starting when the Earth was 10 per cent of its current size or less and that pressures and temperatures must have increased as the planet grew. The purpose of this paper is to build on the ‘continuous growth’ model using newer metal–silicate partitioning data and considering alternative hypotheses for the conditions of metal segregation.
2. Metal–silicate partitioning data
I follow Wade & Wood (2005) in considering elements M and Fe to be exchanged between oxidized (silicate) and reduced (metal) phases according to the following equilibrium:(2.1)The partition coefficient Kd is the ratio of mole fractions of the two elements in the two phases, and it is this which is needed to calculate core–mantle partitioning. The partition coefficient is defined as follows:(2.2)The dependence of Kd on pressure, temperature and composition describes an equation of form(2.3)which with rearrangement becomes(2.4)In equation (2.4), the metal–silicate partition coefficients Di are strictly molar rather than weight values, but due to the similarities of molecular weights of metal and silicate phases they can generally be used as weight values. The factor m is 0.5 n. The development of equation (2.4) and the relationship between the parameters and standard thermodynamic properties are presented in appendix A. Parameters of equation (2.3) for the elements considered here are given in table 2.
3. Application to models of core formation
As discussed earlier, the estimated core–mantle partition coefficients of table 1 are consistent with equilibration of core and mantle at ca 40 GPa and temperature of approximately 3800 K with the FeO content of the mantle fixed at its current value. In the ‘deep magma ocean’ model of core formation, these conditions are interpreted as those at the base of the magma ocean. In this view, droplets of metallic liquid would have descended through an approximately 1200 km deep magma ocean, equilibrating with the silicate as they fell (Rubie et al. 2003). The liquid metal ponded at the base of the magma ocean and subsequently descended in large diapirs to the growing core without further equilibration with the surrounding silicate (figure 1).
Wade & Wood (2005) extended the deep magma ocean model by taking account of the fact that, since small asteroids and planets such as Mars have cores (Kleine et al. 2002), the Earth almost certainly had a core when it was a Mars-sized body. The core must therefore have segregated continuously during accretion with concomitant increases in pressure and temperature as the planet grew. The same kind of model is used to calculate the apparent mean life of Earth accretion from W-isotope data (Yin et al. 2002; Kleine et al. 2004). A physically realistic model of a magma ocean on the growing Earth requires that its base must have remained at a temperature close to the liquidus of the mantle silicate (figure 1). This fixed point allows for the strong viscosity contrast between the liquid upper part of the mantle and the solid lower mantle above which the metal would have ponded. If temperature were above the liquidus or below the solidus of the silicate, there would be no physical reason for separation of the metal layer at the relevant depth.
Following Wade & Wood (2005), I constructed a model in which the Earth was grown in 1 per cent steps and the core segregated at the base of a magma ocean. The depth to the base of the magma ocean was assumed to increase in fixed proportion to the radius of the growing planet, which was assumed to grow from 0 to 100 per cent without any removal of material. In the initial approach, I assumed that the mantle was stirred rapidly enough to remain homogeneous as the Earth grew, the only changes in its composition coming through gradual changes in partitioning the base of the magma ocean. At each increment, the added metal was equilibrated with the total mass of the mantle and then separated to the core without undergoing further re-equilibration. The peridotite liquidus temperature was taken from Wade & Wood (2005) and assumed to be a linear function of pressure (in GPa)I fixed the oxidized Fe content of the mantle at the current value of 6.26 per cent (McDonough & Sun 1995) and grew the Earth as described above, with the depth of the magma ocean being controlled by the required partitioning for the most pressure-sensitive element Ni. As can be seen in figure 2, a good fit to the Ni partitioning data can be achieved if the pressure at the base of the magma ocean increases to ca 41 GPa. Under these conditions, the partitioning of Ni, Co, W, Cr and Mn are all within the range of ‘target’ values of table 1. There would be almost no Si or Nb in the core (figure 2) and the core–mantle partition coefficient of V, a refractory element, would be well below the expected range. The overall value of DV shown in figure 2, 0.3, could be achieved only by increasing the uncertainties in the equation for V partitioning (Wood et al. 2008; table 2) by 1 standard error in both intercept and pressure (c) terms. The best-fit values for V give DV of 0.2, while increase of a and c terms by 2 standard errors only raises DV to 0.73. For this reason, since the target is 1.5–2.2 (table 1), Wade & Wood (2005) concluded that the segregation of the core at fixed oxidation state of the Earth could not satisfy the constraints provided by partitioning of vanadium. Increase of temperature to approximately 1200° above the liquidus would enable V, Ni and Co partitioning to be simultaneously matched, but the temperatures become so high that the core should contain implausibly high contents of Si (approx. 15 wt%) and Nb (approx. 60% of Earth's budget). Furthermore, temperatures well above the liquidus are physically incompatible with metal segregation at the base of a magma ocean (figure 1).
The next approach is to allow the oxidation state of Fe in the Earth to change during accretion. It was assumed (figure 3) that the Earth was more reduced (low Fe content of mantle) during the early stages of accretion and approached the current FeO content in steps, the final step corresponding to the approximately 10 per cent of Earth mass added by the Moon-forming impact (Halliday 2004). The oxidation path shown in figure 3 is one of many which satisfy the vanadium partitioning constraints and, as can be seen, all of the elements of interest fit within the anticipated range of table 1. The maximum pressure at the base of the magma ocean is constrained by Ni and Co partitioning and this is little affected by the reducing conditions, increasing from 41 to 44 GPa. New Ni and Co partitioning data (Kegler et al. 2008) are in good agreement with this maximum pressure of equilibration. In contrast to Ni and Co, the reduced accretion path has a considerable effect on the elements of high oxidation state Nb and Si which partition much more strongly into the core in this scenario. Thus, we find, for example, DSi of 0.27, which would lead to 5.7 per cent Si in the core, in good agreement with cosmochemical estimates (Allègre et al. 1995; McDonough 2003) and with recent isotopic data on Si in the silicate Earth (Georg et al. 2007). Therefore, the partitioning and isotopic data point to the Earth becoming more oxidized during accretion, a suggestion made previously on the basis of more limited data (Wänke & Dreibus 1988; O'Neill 1991a,b).
Figure 4 shows the instantaneous Ni and Co metal–silicate partition coefficients for each of the first two accretion scenarios. These are both elements with strongly pressure-dependent partitioning and I used their overall partitioning as the constraint on the maximum pressure of the magma ocean (41 and 44 GPa for figures 2 and 3, respectively). The important point is that, although the two accretion paths begin with dramatic differences in Ni and Co partitioning, there is strong convergence in the last 10–20 per cent of accretion. This is because moderately siderophile elements such as Ni and Co have their overall partitioning fixed in the later stages of accretion and the early stages are largely irrelevant. The overall partitioning of weakly siderophile elements such as V on the other hand is strongly affected throughout the accretion path. Hence, vanadium partitioning provides information on the path taken while Ni (and to a lesser extent Co) partitioning reflect the highest pressures achieved in the later stages of planetary growth. One final point is that the final instantaneous DNi and DCo values at the end of accretion are approximately 20. This value is in good agreement with an experimental point for Ni partitioning at 42 GPa and 2680 K (Bouhifd & Jephcoat 2003). It should be noted that, although the giant impact that is considered to have formed the Moon would have melted virtually the entire mantle (Canup 2004), metal–silicate partitioning does not appear to have been established at core–mantle boundary pressures. Rather the latest stages of metal segregation were at approximately one-third of the depth to the core–mantle boundary. The robustness of this conclusion depends of course on the quality of the high-pressure partitioning data and further experimental data at pressures above 25 GPa are essential to test it.
The accretion models discussed above are based on the assumption of continuous segregation of metal from a convecting homogeneous mantle. Dynamical simulations indicate, however, that metal droplets should sink more rapidly than the silicate mantle homogenizes (Rubie et al. 2003; Höink et al. 2006). Thus, the final equilibration of a metal droplet is with a very restricted volume of silicate mantle at the base of the magma ocean. The effect is to increase the overall metal–silicate partition coefficient of elements such as Ni for which D decreases strongly with depth (Li & Agee 2001; Rubie et al. 2003; Höink et al. 2006). The net result is that the final pressure of equilibration of metal and silicate increases substantially. In the context of this paper, the questions to be asked are whether the inhomogeneity of the magma ocean has the potential to alter the conclusion that the Earth became oxidized during accretion and what the potential effects are on the partition coefficients of weakly siderophile elements such as V and Nb. I made an end-member model of an inhomogeneous magma ocean by assuming that, at its base, the segregating metal equilibrates with twice its mass of silicate and that the overall volume of material has chondritic element ratios. This allows the effects of the restricted silicate volume of equilibration to be investigated without explicit introduction of any dynamics. The Earth was grown as before in 1 per cent increments and the metal equilibrated with a restricted volume of silicate at the base of the magma ocean. As before, the magma ocean was assumed to have a depth corresponding to a fixed fraction of the depth to the core–mantle boundary. Figure 5 shows that the magma ocean would have to be, as previously concluded (Rubie et al. 2003), substantially deeper than in the case of a homogeneous mantle, the maximum pressure reached being approximately 62 GPa rather than 44 GPa. I find that oxidation during accretion is still required to explain the V content of the mantle even if the A and C parameters are (as shown in the figure) increased by 1 standard error from the best-fit values. So this conclusion appears robust. Both Si and Nb are partitioned more strongly into the metal in this accretion scenario than in the case of a homogeneous mantle, so the A and C parameters for these two elements were reduced slightly (by less than 1 standard error) to keep partitioning within the limits defined in table 1. Since this accretion model requires even longer extrapolation beyond the experimental pressure range (0–25 GPa) than the homogeneous mantle models, however, it is difficult to assess the uncertainties realistically. All one can state is that core segregation from an inhomogeneous mantle is consistent with oxidation during accretion and an increased depth to the base of the magma ocean.
A final possibility is that, instead of segregating from liquid silicate, the metallic core separated from a crystal–liquid mush. This is a plausible consequence of the fact that, in the case of a magma ocean extending to the core–mantle boundary, numerical simulations suggest that the lower mantle would crystallize in a few thousand years (Abe 1997). One can readily envisage, therefore, that metal would separate from a mixture of crystals and silicate melt rather than a completely molten mantle. In order to simulate the effect of a crystal–liquid mixture, I grew the Earth as before in 1 per cent increments and allowed the metal to segregate from a homogeneous mantle containing 90 per cent crystals and 10 per cent melt (figure 6). Of the elements of interest, Ni and Co are moderately compatible in most mantle phases, while V, Mn and Cr are slightly incompatible with, for olivine at low oxygen fugacity, crystal liquid partition coefficients of DV≃DCr≃DMn≃0.5 (Taura et al. 1998; Canil 2002). These values were all, therefore, fixed at 0.5. Partition coefficients for Ni and Co are strongly dependent on melt composition and I have conservatively estimated values of 3 for Ni and 2 for Co, which would correspond to equilibrium with a high-pressure komatiitic-type melt (Canil & Fedortchouk 2001). In contrast to these, Nb and W are almost completely incompatible in major mantle phases so crystal–melt D values of 0 are appropriate for these elements. Finally, DSi is approximately 0.9 for olivine coexisting with komatiitic melt. Figure 6 shows an accretion path that yields the ‘correct’ overall partitioning of Ni, Co and V between core and mantle. Since Ni and Co are compatible in mantle silicates, they are more easily retained in the mantle if a high proportion of crystals is present, so pressures do not have to reach such high values as in the cases of equilibrium between liquid metal and liquid silicate. For this accretion scenario, a maximum pressure of 31 GPa at a subliquidus temperature of 2680 K is indicated. This means that virtually the entire accretion is within the P–T regime of the experimental partitioning data, therefore increasing the accuracy of the results. As shown in figure 6, substantial oxidation is required to match the required partition coefficients for vanadium. The elements W and Nb should, owing to their exclusion from the silicates, partition more strongly into the core in this case, and both have overall partition coefficients much higher than the expected range, despite the use of A and C parameters for Nb, which are 1 standard error below the best-fit values. Silicon, on the other hand, is almost completely excluded from the core in this model, a result that conflicts with recent Si isotopic data.
In summary, growth of the core in equilibrium with a homogeneous mantle of current Fe content cannot yield agreement with the current Ni, Co and V contents of the mantle if the metal segregates under conditions close to the silicate liquidus. Ni and Co can be readily matched, but temperatures approximately 1200°C in excess of the liquidus would be required to match vanadium contents of the mantle (Wade & Wood 2005). Under mid-mantle conditions, these are physically implausible and lead to Si and Nb contents of the core, which are geochemically unreasonable. If, instead, we assume that the base of the deepening magma ocean remains at temperatures of the peridotite liquidus, then the only possible solution requires the oxidation state of the Earth to have increased during accretion. This applies for all three cases considered here, equilibrium of metal with a homogeneous silicate mantle, equilibrium with a small volume of mantle and equilibrium with a crystal liquid mixture. A final point is that all three accretion scenarios lead to Mn contents of the core well below those required if the Earth were to contain its full chondritic complement of this element as shown in table 1 (Allègre et al. 1995). The overall values of DMn obtained in this study are consistent with the mantle containing 60–75 per cent of the Earth's budget of Mn, which implies that most of the Mn ‘deficit’ is due to volatility rather than partitioning into the core (O'Neill & Palme 1998).
Oxidation of the Earth during accretion may have been the result of addition of progressively more oxidized materials as the young Earth grew. There are, however, mechanisms of ‘self-oxidation’ of the Earth, which could have operated during accretion (Frost et al. 2004; Wade & Wood 2005). The Earth's lower mantle is currently approximately 80 per cent by volume magnesium silicate perovskite (Mg,Fe)SiO3 (Wood 2000). This phase accommodates the 5 per cent Al2O3 which it contains in peridotite compositions by a coupled substitution with Fe3+ (Wood & Rubie 1996; McCammon 1997) as follows:This substitution mechanism is so stable that it forces disproportionation of ferrous iron into ferric iron plus metal (Frost et al. 2004; Auzende et al. 2008) by reactions such asThis means that, as perovskite began to crystallize from the magma ocean, it dissolved ferric iron as FeAlO3 component and produced Fe metal. This process would have begun when perovskite was stabilized in the mantle corresponding to a growing Earth of approximately 11 per cent of its current size. Downward segregation of metal during growth of the core would inevitably have carried with it some of the metal produced by disproportionation. When combined with episodic release of Fe3+ from the perovskite layer by dissolution caused by impact heating, the result would have been to increase the oxidized Fe content of the mantle. In practice, one may readily imagine the released Fe3+ reacting with the next input of metal from accreting planetesimals and thereby increasing the Fe2+ content of the magma ocean and the oxygen fugacity of core separation. A second mechanism of mantle self-oxidation is through Si dissolution in the core. Unlike most of the other elements considered here, Si is a major element so its extraction from silicate into metal at high pressures and temperatures involves the liberation of significant amounts of oxygen. This means, for example, that producing a core concentration of 5 wt% Si would, if this element had all been initially added to the Earth as oxidized SiO2, be capable of raising the oxidized Fe content of the mantle by 10 wt%.
I have examined the geochemical consequences of continuous segregation of the core at the base of a magma ocean, which deepened as the Earth grew (Li & Agee 1996; Righter & Drake 1997; Righter 2003). The maximum pressure at the base of the magma ocean was constrained by the observed core–mantle partitioning of Ni and Co (table 1), which is very pressure sensitive. Assuming continuous segregation from a homogeneous mantle, the current V content of the silicate Earth cannot be reconciled with core segregation under conditions of fixed relative oxygen fugacity (corresponding to fixed FeO content of the mantle), even if 2 standard error uncertainties are applied to the fit parameters.
There are two simple ways of relaxing the model so that the V partitioning results become consistent with table 1. The first is to allow temperature to increase above the silicate liquidus. Although such a departure is physically unreasonable, it is possible to achieve the appropriate partitioning values for V if temperatures are raised to approximately 1200° above the liquidus. The result, however, would be a core containing approximately 15 per cent Si and greater than 60 per cent of the Earth's niobium, figures approximately four times the plausible amounts (Allègre et al. 1995; table 1). A more likely scenario is that the Earth became more oxidized as it accreted (Wänke 1981; Wänke & Dreibus 1988; O'Neill 1991b). In this case, I find that, with temperatures fixed on the silicate liquidus, the Ni, Co, W, V, Cr and Nb contents of core and mantle are easily matched to those calculated from the chondritic abundances of refractory elements in the Earth. The magma ocean is calculated to maintain a thickness approximately 35 per cent of the depth to the core–mantle boundary in the accreting Earth and yields a Si content of the core of 5.7 per cent, in good agreement with cosmochemical estimates.
Two further variations on this model were examined to test the robustness of the conclusion that the Earth became more oxidized as it grew. The first approach assumed that the mantle was not continuously homogenized during core segregation and that the metal equilibrated only with a small volume of metal at the base of the magma ocean. This is found to increase pressure (constrained by Ni and Co partitioning) by approximately 50 per cent. All of the other elements (except Mn) have partitioning (within uncertainty) consistent with chondritic abundances in the Earth provided the Earth became, as before, progressively oxidized during accretion. The final model assumed segregation of metal from a crystal-melt mush at a temperature approximately 200° below the liquidus. In this case, pressures constrained by Ni and Co decrease substantially and it is extremely difficult to match the calculated mantle contents of the highly incompatible elements Nb and W to those observed (figure 6). As before, however, oxidation is required to fit the observed mantle contents of vanadium. It appears therefore that oxidation of the mantle during accretion is the most likely explanation for the observed partitioning of this wide range of moderately and weakly siderophile elements.
None of the models is consistent with a chondritic abundance of Mn in the bulk Earth. The most likely explanation for this is that Mn is largely depleted in the silicate Earth due to volatility rather than due to partitioning into the core.
This work commenced at the University of Bristol with support from NERC grant GR3/11535 and continued at Macquarie University with support from ARC grants FF0456999 and DP0664537. Discussions with Jon Wade, Alex Corgne and Mike Walter helped clarify some of the ideas. The comments of two anonymous reviewers are acknowledged with thanks.
One contribution of 14 to a Discussion Meeting Issue ‘Origin and differentiation of the Earth: past to present’.
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