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doi: 10.7185/geochemlet.1737 The long term thermal and dynamic evolution of Earth’s core depends on its energy budget, and models have shown that radioactive decay due to K and U disintegration can contribute significantly to core dynamics and thermal evolution if substantial amounts of heat-producing elements are dissolved in the core during differentiation. Here we performed laser-heated diamond anvil cell experiments and measured K and U solubility in molten iron alloy at core formation conditions. Pyrolitic and basaltic silicate melts were equilibrated with metallic S–Si–O-bearing iron alloys at pressures of 49 to 81 GPa and temperatures of 3500 to 4100 K. We found that the metal-silicate partitioning of K is independent of silicate or metal composition and increases with pressure. Conversely, U partitioning is independent of pressure and silicate composition but it strongly increases with temperature and oxygen concentration in the metal. We subsequently modelled U and K concentration in the core during core formation, and found a maximum of 26 ppm K and 3.5 ppb U dissolved in the core, producing up to 7.5 TW of heat 4.5 Gyr ago. While higher than previous estimates, this is insufficient to power an early geodynamo, appreciably reduce initial core temperature, or significantly alter its thermal evolution and the (apparently young) age of the inner core. Received 1 August 2017 | Accepted 7 September 2017 | Published 4 October 2017 1. Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS, F-75005 Paris, France # Now at Bayerisches Geoinstitut, Universität Bayreuth, 95440 Bayreuth, Germany * Corresponding author (email: Ingrid.Blanchard@uni-bayreuth.de) 2. Institut Universitaire de France, Paris, France 3. Earth and Planetary Science Laboratory, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland Introduction The long term thermal evolution of the core plays a fundamental role in the potential of a terrestrial planet to sustain life. Indeed, the existence of a magnetic field is one of the tenets of planetary habitability, which is generated by a geodynamo operating in the planet’s convective liquid core. The present day geodynamo is mainly driven by compositional buoyancy, due to light element release by the crystallisation of the inner core. A core with large thermal conductivity (e.g., Pozzo et al., 2012; Ohta et al., 2016) yields a young age (less than 1 Gyr) for the inner core (Labrosse, 2015; Nimmo, 2015a), which is in apparent contradiction with palaeomagnetic evidence for an old geodynamo dating back to at least 3.5 Ga (Tarduno et al., 2010). Even with a low core thermal conductivity (Konôpková et al., 2016), the problem is partially mitigated, in that a dynamo can be sustained for 3.5 Gyr (e.g., Labrosse, 2003; Nimmo, 2015a), but initial core temperatures are very high, above 7000 K, which implies a fully molten Earth for extended periods of time. Recently, MgO exsolution (Badro et al., 2016) and SiO2 crystallisation (Hirose et al., 2017) have been proposed as an alternative source of chemical buoyancy to drive a dynamo prior to inner core growth. These are potent sources of energy and dissipation, and while they both eradicate the need for a hot initial core, their effect is not predicted to kick in until 1 to 2 Gyr after Earth’s formation for MgO, and even later for SiO2, leaving the Earth devoid of a geodynamo, assuming a young inner core age. One possible mechanism to drive a very early dynamo, in the first billion years of Earth’s history, is the dissolution of radioactive heat-producing elements in the core during formation (Gubbins et al., 2003). Because radionuclide abundance decreases with time, the process is dominant very early in Earth’s history and vanishes with time. Potassium and uranium are the main sources of heat in the Earth, and their incorporation in the core has been thoroughly examined through the years (e.g., Buffett, 2002; Gubbins et al., 2003; Labrosse, 2003, 2015; Nimmo et al., 2004), and it was shown that the incorporation of ~100s of ppm K in the core would mitigate the young inner core/early geodynamo/hot initial core conundrum. Both K and U are nominally lithophile elements, with no predisposition to fractionate in the metallic phase during metal-silicate equilibration. Bukowinski (1976) proposed that potassium might become a transition metal at high pressure, with the ability to dissolve easily in core-forming metal, later confirmed experimentally by Parker et al. (1996), which motivated a suite of metal-silicate experiments (performed below Geochemical Perspectives Letters Letter Geochem. Persp. Let. (2017) 5, 1-5 | doi: 10.7185/geochemlet.1737 2 25 GPa in large-volume presses LVP) to address and quantify the partitioning of potassium between metal and silicate during Earth’s differentiation (Gessmann and Wood, 2002; Murthy et al., 2003; Bouhifd et al., 2007; Corgne et al., 2007). Similarly, uranium partitioning studies (LVP) have shown a limited solubility in the metal, recently confirmed by a study of U partitioning in the laser-heated diamond anvil cell (LH-DAC). U was shown to become more siderophile with: (i) increasing sulphur content in the metal (Wheeler et al., 2006; Malavergne et al., 2007; Bouhifd et al., 2013; Chidester et al., 2017), (ii) high temperatures (Chidester et al., 2017), and (iii) low SiO2 concentration in the silicate (Chidester et al., 2017). However, even in the most favourable conditions, including an unrealistically high sulphur content of the core (8 wt. %), no more than 3.5 ppb U could be dissolved in the core (Chidester et al., 2017), providing no more than 2.4 TW as early as 4.5 Gyr ago, which is insufficient to have any effect on an early geodynamo. The solubility of thorium, the other major radioactive element in the Earth, in metal was not addressed in the present work as LH-DAC experiments from Chidester et al. (2017) showed no measurable Th in the metallic phases. Experiments and Results Here we investigated the metal-silicate partitioning of both U and K at the relevant P-T conditions of core formation, through LH-DAC experiments. Two silicate compositions were used (pyrolitic and basaltic) to examine the effect of silicate composition on partitioning; similarly, several metal compositions (with various amount of S, Si and O dissolved) were used to examine the effect of metal composition on that same partitioning (see Supplementary Information and Table S-1). The samples were compressed to 41 to 81 GPa and laser-heated to 3600 to 4100 K (Table S-2), achieving conditions above the liquidus of both metal and silicate and efficiently melting the sample. Thin sections were recovered from the centre of the laser-heated area using a focused ion beam (Fig. S-1) and analysed using an electron probe (Tables S-3 and S-5). K and U partitioning between metal and silicate are driven by an exchange reaction involving Fe in the metal and FeO in the silicate, and are written as: 1⁄2 Fe + 1⁄2 K2O ↔ K + 1⁄2 FeO (Eq. 1) Fe + UO ↔ U + FeO (Eq. 2) The equilibrium constants K of reactions (1) and (2) are a function of P, T, and can be expressed as a function of the reaction’s exchange coefficient (D) and activity coefficients (g): log KK = log DK DFe 0.5 + log γ K metal γ Fe metal = a + b T + c P T (Eq. 3) log KU = log DU DFe + log γU metal γ Fe metal = a + b T + c P T (Eq. 4) where a, b and c are related to change in entropy, enthalpy and volume, respectively; g the activity coefficients of K, U, and Fe in the metal, which are a function of the interaction parameters ei , e s i and ei Si for K and U. We used a valence of +1 for potassium, and +2 for uranium (as proposed by Chidester et al., 2017) and combined our data with values from the literature (see Table S-6) to perform a least squares linear fit (details of the fitting procedure are in the Supplementary Information) for all the parameters of the equilibrium constant (Eq. 3 and Eq. 4). The data and the fitted regressions are plotted in Figure 1, and the parameters resulting from the fit are listed in Table 1. We find that potassium has no measurable interaction with O, Si, or S in the metal. Its partitioning in the metal shows a strong pressure dependence (c = 65 ± 2.5 K/GPa) but no intrinsic temperature dependence (b = 0 K), as can be seen from the excellent linear fit to the data (R2 = 0.94). Uranium, on the other hand, has a very strong interaction parameter with oxygen in the metal, as illustrated from our fitted value of eU =-31, which signals that oxygen dissolved in the metal enhances the siderophile behaviour of uranium. No measurable effect of Si and S on U partitioning was found. Lastly, a strong temperature dependence (b = -10133 ± 642 K) and no pressure dependence (c = 0 K/GPa) were found, as can be seen once again by the excellent linear fit (R2 = 0.91). A detailed discussion and comparison of these results with previous estimates is provided in Supplementary Information.

The solubility of heat-producing elements in Earth’s core