The Fate of Carbon during Earth’s Core–Mantle Differentiation

I. Blanchard1*, E. S. Jennings2, I. A. Franchi3, X. Zhao3, S. Petitgirard1, N. Miyajima1, S. A. Jacobson4, D.C. Rubie1 1 Bayerisches Geoinstitut, Universität Bayreuth, 95440 Bayreuth, Germany 2 Department of Earth and Planetary Sciences, Birkbeck, University of London, Malet Street, London WC1E 7HX, UK 3 School of Physical Sciences, Open University, Milton Keynes MK7 6AA, UK 4 Department of Earth and Environmental Sciences, Michigan State University, East Lansing, MI 48824, USA *Corresponding author: ingrid.blanchard@uni-bayreuth.de


Earth's accretion and, depending on the concentration of carbon in accreting bodies, can
easily reach or exceed estimated BSE values. In contrast, simple models of "continuous core formation" [11][12][13] require all BSE carbon to be accreted after core formation ended, but this is not consistent with astrophysical models of accretion.
The extents to which the volatile contents of terrestrial planets were determined by the processes of accretion and core formation, impact-driven volatile loss, and addition of a late veneer subsequent to core formation are highly controversial 9,14-17 . The Earth is considered to have formed from bodies of chondritic composition, although it is unlikely that any particular chondrite group constituted the sole building blocks of the planet 18 . Different classes of chondrites have varying carbon concentrations, but importantly, such concentrations are all high, at the weight percent level 19 . This is far in excess of the concentration of carbon present in the Bulk Silicate Earth (BSE) today, which is currently estimated to be 80-120 ppm 4,5 or possibly as high as 765 ± 300 ppm 20 . Additionally, the metal-silicate partition coefficient of carbon at low pressures and temperatures (≤ 13 GPa and ≤ 2000 K) is very high (D > 1000; see D defined in Eq. 2 and ref. [1][2][3]21 ). Consequently, almost all carbon should have partitioned into the core during its formation, leaving the mantle almost completely depleted in this element. core-mantle differentiation 9,10 , and so we show that the present BSE carbon concentration is the direct consequence of core formation.
We performed laser-heated diamond anvil cell (LH-DAC) experiments to reproduce the pressures and temperatures of the putative conditions of Earth's core-mantle differentiation in the laboratory. We performed experiments at 49-71 GPa and 3600-4000 K for a few tens of seconds using a double-sided laser-heated system (see Methods section for details). After melting and quenching at high pressure, our recovered samples consisted of a central metallic sphere surrounded by quenched silicate glass, as observed in previous similar studies [24][25][26] (Fig.   1a). Samples were prepared for analysis using a Focused Ion Beam system and analysed for major elements using Electron Probe Microanalysis (EPMA see Methods section). To measure the concentrations of carbon in the quenched silicate melt, we used NanoSIMS, for which we synthesized appropriate standards (the carbon contents of which were analysed by FTIR; see the Methods section).
We calculated the oxygen fugacities of our experiments relative to the iron-wüstite redox buffer (1) Oxygen fugacities of our experiments lie between -0.9 and -1.5 log units relative to the IW buffer ( Table 1) (Table 1) and are 1-2 orders of magnitude lower than those determined in previous low-pressure studies.
In order to understand the metallic phase better, we obtained images with SEM and TEM of the sample BAS C 39 (Fig. 1), and we performed electron diffraction analyses that show the presence of stoichiometric Fe7C3 inclusions in the quenched metal (Fig. 1b). To further investigate the quench textures (Fig. 1c), we performed scanning TEM-energy dispersive spectroscopy (EDS) mapping to identify Si-O-rich exsolved inclusions in the metal phase ( Fig.   1d) along with a C-rich domain that could be an exsolved diamond, as also observed in previous similar experiments 27 .
To understand the effects of pressure and temperature on the metal-silicate partitioning of carbon, we assembled a dataset for our model from previous studies to supplement our new results (Fig. 2). However, only some published experiments are relevant to core formation because prior studies were often focussed on the effects of silicate melt composition 2 , fO2 28,29 , and the interaction of carbon with elements in the metal 7 . The partitioning of carbon is affected by the ratio of non-bridging oxygens to tetrahedral cations 2 (NBO/T), so we only included data from the literature for which NBO/T lies in a narrow range (0.5-1.5); the range for our samples is 0.56-1.34. We also only included data from previous low P-T studies with low concentrations (< 1 wt.%) of light elements (S, N, O, Si) in the metal because the interaction between carbon and other light elements may be significant 6 but is poorly constrained. As a consequence, we also excluded very low fO2 data (ΔIW < -3), as they are often associated with high concentrations of Si in the metal. On the other hand, our high P-T samples contain significant concentrations of oxygen and silicon in the metallic phase, as is typical for high temperature experiments 24,25 . By combining these two datasets, we thereby empirically include the interaction effects of these light elements in the regression presented below, because the concentrations of O and Si in metal are generally low during core formation at low P-T conditions 11,31 consistent with the data 1-3,8 selected from previous studies, whereas at high P-T conditions such concentrations become high 30,31 , which is consistent with the present study.
Interactions of carbon with oxygen and silicon in the metal of our experiments might be at least partly responsible for the scatter of our data (Fig. 2). Finally, we did not use literature data for which the silicate phase did not quench to a glass, because the quality of SIMS analyses may be compromised 1 . In Fig. 2, we present a comparison of our data together with the selected data from the literature as a function of temperature and pressure.
The metal-silicate partition coefficient of carbon (DC) is calculated as: where X is the mole fraction of the element in the phase of interest. D is a function of several parameters, including pressure (P), temperature (T), and oxygen fugacity.
To remove the effect of oxygen fugacity on D values, we use the distribution coefficient KD: where n is the valence of C when dissolved in silicate liquid, which is 4 for carbon in this case 32 .
Based on the aforementioned data selection, we fitted previously-published data 1-3,8 along with our new results to derive the following expression: distributed over a heliocentric distance of 0.7 to ~ 9.5 AU. In the accretion simulations, planets typically grow from the starting embryos through accretional collisions with other embryos and planetesimals. Each collision potentially involves a core formation event during which accreted metal equilibrates with silicate liquid in a magma ocean and then segregates to the proto-core.
By modelling metal-silicate equilibration using a mass balance approach, the evolving Here we use the "Grand Tack" 35,36 accretion simulation "4:1-0.5-8" 9 with the same model parameters as in our previous study 10 . We first assume that carbon is accreted to Earth only in bodies that originate beyond 4.5 AU and that their average C concentration is 1.6 wt.% (an approximately mean carbonaceous chondrite (CI, CM, CO and CV) value). The mantle C abundance increases throughout accretion from a very early stage and finally reaches the BSE value of 80-120 ppm (Fig. 3). However, in this model the final concentration of C in the core is 47 ppm which means that the carbon concentration of the bulk Earth is only 83 ppm, i.e. far below the lowest estimate of 520 ppm 20 . We have therefore developed a scenario that results in a bulk concentration of ~520 ppm. We assume that bodies from beyond 4.5 AU contain on average 1.6 wt.% carbon and that C concentrations in bodies originating at < 4.5 AU decrease along a linear gradient to reach a value of zero at a heliocentric distance of 1.88 AU. This is based on the condensation of volatile elements such C increasing with heliocentric distance as temperatures decrease and is analogous to a concentration gradient derived for sulfur 10 . The model then predicts a final mantle C concentration of 314 ppm (Fig. 3) and resulting in 0.14 wt.% C in the core.
There are two critical features of the accretion/differentiation model that explain why the BSE carbon concentration is not efficiently extracted during core formation in spite of its siderophile behaviour. First, bodies originating from the outer solar system are water ice-bearing and so fully oxidize and contain no metal. Thus, there is no core formation event when they are accreted and the delivered C remains in the magma ocean/mantle. Second, when differentiated metal-bearing bodies are accreted, the metal of the impactor only equilibrates with a fraction of the target's mantle, of which the value depends on the size of the impactor's core and the depth of the magma ocean 9,34 . The fractions of the mantle that equilibrate with metal in the present simulation are 0.16 to 2.5% for planetesimal impacts and 2.6 to 9.9% for embryo impacts.
Consequently, core formation events are extremely inefficient at removing carbon from the bulk of the mantle and transferring it to the core. These two critical features are absent in the models of "continuous core formation" that are currently applied in many studies of Earth's differentiation 12,13 ; the result of a continuous core formation model for carbon is presented in the supplementary information for comparison. In such models all accreted material is assumed to contain metal and it is assumed (unrealistically) that all accreted metal equilibrates chemically with the entire Earth's mantle. Consequently, such models predict that essentially the entire BSE carbon budget has to be delivered during late accretion, i.e. after core formation has ended (see supplementary Information and Extended Data Fig. S3). We know of no astrophysical accretion simulations that would support this scenario which requires the accretion of carbon-poor material during core formation and carbon-rich material afterwards during late accretion.    proportions, decarbonated over night at 900°C, then added FeO. Powders were ground under 4 acetone for some time to ensure a homogeneous composition. We created pellets that were 5 subsequently fused in argon flux for several seconds at about 1400°C using a levitation furnace 6 device in Orléans, France 39 . Chemical composition of the glass was checked using EPMA 7 ("Basalt" in table S1) and we could verify that no compositional variation was detectable. The 8 glass sphere was subsequently polished down to a thickness of 20 µm and machined in IPGP, 9 France, to obtain small disks of 80 microns diameter 25 . 10 The goal of this study is to understand the effect of core formation on the partitioning of carbon 11 between Earth's most important reservoirs: the silicate mantle and the metallic core. Carbon is 12 a prominent contaminant in the laboratory, with multiple sources of contamination, from the 13 use of ethanol and acetone, various type of glue or ambient contamination. It has also been 14 suggested that diamonds used as pressure transmitting tool can also diffuse carbon to the 15 samples 40 . To better understand the origin of carbon, we used 13 C as the source of carbon in our 16 experiments. We synthesized the metallic phase using piston-cylinder apparatus. In order to 17 assess the extent of carbon contamination during LH-DAC experiments, we only used 13 C. We 18 mixed 5 wt.% of 13 C powder (97% pure from Cambridge Isotope Laboratories, Inc.) with 95 19 wt.% of Fe. We melted this alloy at 2 GPa and 1873 K in MgO capsule for 10 minutes using a 20 ½" piston-cylinder assembly at BGI. This 13 C-doped carbide was then crushed to be used for 21 the metallic part of the for laser-heated diamond anvil cell experiments. The composition was 22 checked by EPMA (see table S1, "Metal") using an Fe3C standard (see sections d) and e)). 23 We used diamonds with 250 µm culets and rhenium gaskets. Gaskets were pre-indented to 26 obtain a thickness of about 40 to 50 µm, and subsequently laser-drilled to have an experimental 27 chamber of about 90 µm in diameter. We then loaded two silicates discs encapsulating a flake 28 of carbide 25 . Samples were compressed to the target pressure, and then laser-heated at the 29 desired temperature using a doubled sided laser heating system at BGI. Temperature was 30 generated by two fiber continuous-wave (CW) YAG lasers (SPi©) with wavelength of 1064 31 nm and delivering 100 watts each. The laser beam was focused onto the sample using two NIR-32 Mitutoyo objectives lenses with x20 magnification. Temperature was measured simultaneously 33 and continuously on both sides of the diamond cell using a spectro-radiometric technique 41 34 using a 2500i spectrometer and pixis 400 CCD camera from Princeton-Instrument© from the 35 light collected through both objective lenses. The peak temperature, above the liquidus 36 temperature of the material, was maintained for few tens of seconds, before switching off the In the samples, we observed two quenched phases that had been molten at high pressure and 46 high temperature: a silicate and metallic one (see Fig. 1-a in the main text).

d) Fabrication of analytical standards 49
For EPMA analysis of the carbon contents of metals, we synthesized a Fe3C (cementite) carbide 50 standard at BGI 42 , by inserting a 1 mm diameter, 10 mm long, 99.99 % purity Fe wire in a thick 51 graphite sleeve and heating it to 1423 K at 15 kbar in a piston cylinder for one week. The 52 reaction product was confirmed to have the Fe3C cementite structure by XRD and was assumed 53 to be stoichiometric. 54 For the nanoSIMS analysis of quenched glasses, we synthesized 13 C-doped glass standards 43 . 55 We first mixed oxides in basaltic proportions and made a glass at 1600°C in a furnace for two 56 hours. This glass was analyzed by EPMA for major elements, and by FTIR to confirm that it 57 was carbon-free ("B1" in table S1). Subsequently, we performed piston-cylinder experiments 58 to incorporate 13 C into the basaltic glass. The source of 13 C was chosen as oxalic acid enriched 59 in 13 C (Cambridge Isotope Laboratories, Inc.), that was loaded along with the basaltic glass in 60 a Pt capsule and pressurized to 2 GPa and heated to 1600°C for 10 minutes 43 . We created two 61 glass standards (B1145 and B1147) containing 785 ppm and 1263 ppm of carbon respectively, 62 as measured by FTIR at BGI. For the FTIR measurements, we used an extinction coefficient 44 63 of 69500 L.mol -1 .cm -1 . We report the FTIR measurements along with EPMA analyses on table 64 S1 for the carbon-free (B1) and the two carbon-doped glasses. 65 66 e) EPMA analysis 67 background, and 20 seconds on the peak for all elements, and the samples and Fe3C standard 74 were not carbon coated. 75 Analyzing carbon using the microprobe requires special consideration 45 . In order to quantify 76 the carbon content of both the experimental metals and the metal starting material, we 77 synthesized a Fe3C carbide primary standard (see section d)). During C analysis, we took 78 particular care in repeating the measurements on the metallic standards to quantify background 79 levels (contamination) inside the EPMA. We measured the count rate from the C kα peak on a 80 pure Fe standard continuously for ten minutes, and found no statistically-significant change in 81 peak height over that timescale 42  Oxygen and silicon are also present in the metallic phase, from 2.8 to 7.5 wt.% oxygen and 0.3 93 to 5.6 wt.% silicon. We report on tables S2 and S3 the full analyses of our recovered runs for 94 silicate and metal respectively. Whilst some analytical totals are low, these low totals are not

f) nanoSIMS analysis 99
The abundance of carbon in the silicate phase was expected to be extremely small, due to its 100 high siderophility 1 . Laser heated diamond anvil cell experiments produce very small samples, 101 with silicates phases that are only few micrometers wide. Therefore, NanoSIMS was used in 102 this study to achieve required analytical precision and spatial resolution and quantitatively 103 analyze the low carbon contents in the silicate phase. 104 NanoSIMS measurements are sensitive to matrix effects, so we took particular care in 105 synthesizing and using relevant standard glasses (see section d)). Along with those two 106 standards, we used two standards of natural rocks containing natural and known amounts of After spot analyses, selected sample areas were also measured in imaging mode. A 50 pA Cs + 123 beam was also used in imaging mode, with five secondary ions ( 12 C -, 13 C -, 30 Si -, 56 Fe 13 Cand 124 56 Fe 16 O -) monitored simultaneously. Each imaging analysis consisted of 10 frames. A frame 125 size of 256×256 pixels was used for all images with an integration time of 500 ms per pixel, 126 leading to total analysis time of 5-6 minutes for each image. 127 The mass resolving power (m/Δm) for both spot and imaging mode was set to 9000 (CAMECA 128 definition), sufficient to resolve all interferences from neighbouring mass peaks, such as 13 C 129 from 12 CH. We could extract from the region of interest (ROIs) the ratios of 13 C/ 30 Si and 130 12 C/ 30 Si. We derived a precise calibration line using those standards, which was used to infer 131 the amount of carbon (both 12 C and 13 C, see figures S1-a and S1-b) present in each of our 132 samples. During analyses, we carefully avoided metal blebs that are sometimes present in the 133 silicate phase in this style of experiments, interpreting them to be entrained rather than exsolved 134 on quench. We present in Fig. S2 NanoSIMS ion images of the metallic phase of sample BAS-135 C-39, to highlight the level of detail that can be reached with NanoSIMS. 136 Some uncertainty of the NanoSIMS measurements may derive from the difference between the 137 composition of the samples and the one of the standards. We calculated the amount of carbon 138 in each of our samples using the C/Si ratio of the standards and the experimental runs for both 139 12 C and 13 C. The standards we used contained between 40 and 50 wt.% of SiO2 whereas the 140 runs contained between 35 and 40 wt.% SiO2. To encompass the range of potential sources of 141 uncertainty, we have assigned an uncertainty of ± 15% to the nanoSIMS measurements. 142 Analysing our samples and standards with the NanoSIMS revealed that the carbon present in 143 both cases was not only 13 C but also 12 C, with a lower 13 C/ 12 C ratio in experimental silicates 144 than in the metal (values from 2.8 to 6.9 for metal versus 0.37 to 1.7 for silicate, see Fig. S1-c). 145 The presence of significant concentrations of 12 C was unexpected, since we carefully prepared 146 the samples using only 13 C, but demonstrates that carbon contamination is probably ubiquitous 147 in high-temperature DAC experiments. The silicate starting powders were heated overnight at 148 900 °C and then converted to glass using an aerodynamic levitation system at temperatures of 149 about 1400 °C. Thus, despite several hours at elevated temperatures, it is extremely hard to 150 eliminate the presence of environmental carbon. 12 C could originate from the diamond anvils, 151 the carbonate powders being not fully decarbonated, by sorption of carbon from the atmosphere 152 or from residues of organic carbon contamination during sample preparation. 153 The 13 C/ 12 C measured in the experimental silicates was lower than in the corresponding metals 154 (Fig. S1-c). This indicates that experiments did not reach isotopic equilibrium, and implies that 155 the most significant source of carbon contamination was the silicate starting material rather than 156 the diamond anvils. This observation is contrary to what has been proposed in previous LH-157 DAC studies 26,40 . We also measured silicate in unmelted regions in DAC samples BAS C 39 158 and BAS C 42 at the NanoSIMS, that contained 386 and 347 ppm of carbon ( 12 C + 13 C) 159 respectively, highlighting the presence of carbon in the starting material. We demonstrate here, 160 for the first time with support of NanoSIMS measurements, that carbon contamination in our 161 DAC experiments is not due to carbon diffusion from the diamond anvils to the samples, but is 162 from the samples themselves. 163 164 h) TEM analysis 165 We performed transmission electron microscope (TEM) analyses on a FEI Titan G2 80-200 166 S/TEM equipped with X-ray energy dispersive spectrometer (EDS) and electron energy-loss 167 spectrometer (EELS) in Bayerisches Geoinstitut in order to observe and further analyze the 168 experimental metals. To do so, we further thinned down one of our samples to a thickness of 169 60-80 nm using FIB. The FIB lamella was plasma cleaned prior to TEM analysis in order to 170 remove surface contamination. We determined Fe/C ratios in our sample and also perform EDS 171 mapping in the metallic phase. The quantification of the EELS analyses followed the procedure previously described 40,51 , using experimentally-determined ratios of partial cross sections of C 173 K and O K edges against the Fe L edge versus sample thickness, which were calibrated with 174 synthetic Fe0.94O and Fe3C samples. Note that due to the inhomogeneity of the metallic phase 175 of the sample (see Fig. 1-a,-b,-c)    suggestions, based on first principles molecular dynamics 12 and experiments 13 , that carbon is 321 not a dominant element in Earth's core. As discussed in the main text, this simple scenario is 322 not coherent with astrophysical accretion scenarios. This model assumes that the bulk Earth C-323 content is known a priori, and the assumption that all accreted metal equilibrate with all the 324 mantle is also unrealistic. 325 326 Bibliography 327