# Nitrogen sequestration in the core at megabar pressure and implications for terrestrial accretion

Dongyang Huang, Julien Siebert, Paolo Sossi, Edith Kubik, Guillaume Avice, Motohiko Murakami

► To cite this version:

Dongyang Huang, Julien Siebert, Paolo Sossi, Edith Kubik, Guillaume Avice, et al., Nitrogen sequestration in the core at megabar pressure and implications for terrestrial accretion. Geochimica et Cosmochimica Acta, 2024, 376, pp.100-112. 10.1016/j.gca.2024.05.010. insu-05081575

HAL Id: insu-05081575

https://insu.hal.science/insu-05081575v1

Submitted on 23 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Nitrogen sequestration in the core at megabar pressure and implications for terrestrial accretion

Dongyang Huang<sup>a,b,*</sup>, Julien Siebert<sup>a,c</sup>, Paolo Sossi<sup>b</sup>, Edith Kubik<sup>a</sup>, Guillaume Avice<sup>a</sup>, Motohiko Murakami<sup>b</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

Associate editor: Fabrice Gaillard

Dataset link: https://doi.org/10.17632/tcy7x24vbx.1

**Keywords:**

Core formation

Atmospheric loss

Nitrogen

Metal-silicate partitioning

Volatile depletion

High pressure

## ABSTRACT

Nitrogen (N) is the most abundant element in Earth's atmosphere, but is extremely depleted in the silicate Earth. However, it is not clear whether core sequestration or early atmospheric loss was responsible for this depletion. Here we study the effect of core formation on the inventory of nitrogen using laser-heated diamond anvil cells. We find that, due to the simultaneous dissolution of oxygen in the metal, N becomes much less siderophile (iron-loving) at pressures and temperatures up to 104 GPa and 5000 K, a thermodynamic condition relevant to the bottom of the magma ocean in the aftermath of the moon-forming giant impact. Using a core-mantle-atmosphere coevolution model, we show that the impact-induced processes (core formation and/or atmospheric loss) are unlikely to account for the observed N anomaly, which is instead best explained by the accretion of mainly N-poor impactors. The terrestrial volatile pattern requires severe N depletion on precursor bodies, prior to their accretion to the proto-Earth.

## 1. Introduction

Nitrogen (N) is an essential volatile element for both life and the atmosphere on Earth. Knowledge of how the Earth acquired its nitrogen and other volatiles is of great importance for understanding our planet's habitability. It is widely recognized that the Earth is strongly depleted in volatiles (e.g. Marty, 2012; Halliday, 2013), such as carbon (C), hydrogen (H) and noble gases, when compared to the solar composition as represented by CI carbonaceous chondrite; intriguingly, N is even more depleted, by about one order of magnitude, than the above volatiles (Marty, 2012). This yields the C/N ratio of the measurable bulk silicate Earth (BSE), i.e. atmosphere, crust and mantle (Hirschmann, 2018), about five times higher than those of CI chondrites, but within the range of CV-CO chondrites (Marty et al., 2020) (Fig. 1) or parent bodies of some volatile-rich iron meteorites (e.g. Grewal and Asimow, 2023). However, this similarity with CV-CO chondrites does not imply directly that Earth's volatile budget is inherited from this type of bodies, because one has to consider the role of planetary accretion/differentiation in shaping Earth's nitrogen deficit.

The initial distribution of N between terrestrial reservoirs is determined by its behaviour in a magma ocean (e.g. Huang et al., 2022a).

Depending on nitrogen's affinity for either iron-rich metal or silicate liquids, N can be stored in the core or mantle; as found by earlier studies (Kadik et al., 2011; Roskosz et al., 2013; Li et al., 2016; Dalou et al., 2017, 2019a; Speelmanns et al., 2019; Grewal et al., 2019a,b, 2021, 2022; Jackson et al., 2021; Shi et al., 2022; Li et al., 2023), the metal-silicate partition coefficient of N is determined by the interplay of pressure, temperature, oxygen fugacity ($fO_2$) and silicate/metal composition, and it varies over several orders of magnitude below the iron-wüstite (IW) buffer, with $fO_2$ and light elements dissolved in the liquid metal being the controlling factors (e.g. Dalou et al., 2017; Grewal et al., 2021). However, there is still uncertainty as to, under the supposed core-forming redox conditions, whether N behaves like a siderophile (iron-loving) or lithophile (rock-loving) element (e.g. Speelmanns et al., 2019; Li et al., 2023), which may be partly due to the limited P-T range explored in the above work (Jackson et al., 2021). While core formation has been modelled to occur at much greater depths up to ~70 GPa (e.g. Fischer et al., 2015; Huang et al., 2020), the above metal-silicate partitioning experiments on nitrogen were performed at relatively low pressures less than 7 GPa, with two exceptions up to 26 GPa (Roskosz et al., 2013; Jackson et al., 2021).

<footnote><sup>a</sup> Institut de Physique du Globe de Paris, 75005 Paris, France</footnote>

<footnote><sup>b</sup> Institute of Geochemistry and Petrology, ETH Zürich, 8092 Zürich, Switzerland</footnote>

<footnote><sup>c</sup> Institut Universitaire de France, 75005 Paris, France</footnote>

<footnote>* Corresponding author at: Institute of Geochemistry and Petrology, ETH Zürich, 8092 Zürich, Switzerland. E-mail address: dongyang.huang@erdw.ethz.ch (D. Huang).</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** C/N versus ³⁶Ar/N ratios in meteorites and the bulk silicate Earth. Chondrite (CI, CM, CR, CV, CO and EC) data are taken from Marty et al. (2020) and references therein. Note that Pearson et al. (2006) and Alexander et al. (2012), indicating CI-like C/N ratios for CO and CV chondrites, are not shown because the relevant ³⁶Ar data are unavailable; as the reason for the discrepancies remains unclear (Hirschmann, 2016), We emphasize that the C/N ratios in carbonaceous chondrites are used here as an indicator reflecting accretion processes, not to imply that chondrites are Earth's building blocks pe se. Volatile budget for the bulk silicate Earth, viz. atmosphere, crust and mantle, is estimated to range from 140 to 506 ppm (parts per million by mass) for C (Hirschmann, 2018; Marty et al., 2020) and 2.8 ± 0.6 ppm for N (Hirschmann, 2018), which yields a C/N ratio of 50–181 for the observable Earth (red star). Note that due to the debatable estimates for BSE's C/N ratio (Hirschmann, 2018; Marty et al., 2020), the red vertical line is not the uncertainty of BSE C/N per se, rather, it represents the above two end-member C/N ratios which also encompass recent estimations in the literature (Bergin et al., 2015; Johnson and Goldblatt, 2015).</figcaption></figure>

Apart from core formation, magma ocean may outgas the majority of its N into an early formed atmosphere (e.g. Sossi et al., 2020; Huang et al., 2022a) under oxidized conditions (Libourel et al., 2003); subsequent atmospheric loss introduced by impact erosion (Genda and Abe, 2005) can then provide an alternative solution to the observed N deficit. Previous attempts have been made to quantitatively evaluate the influence of atmospheric loss on Earth's C/N ratio (Dalou et al., 2017; Speelmanns et al., 2019; Grewal et al., 2021; Jackson et al., 2021; Shi et al., 2022; Chen and Jacobson, 2022; Li et al., 2023), most of which nevertheless lack sufficient temporal and/or chemical complexity (details in Discussion) necessary to capture the heterogeneous nature of Earth's accretion (e.g. Schönbächler et al., 2010; Lichtenberg et al., 2021; Huang et al., 2021). Particularly, none of the earlier models include the potential effect of oxygen dissolved in the core at extreme P-T conditions (c.f. Badro et al., 2016; Huang et al., 2020), given that the peak pressure for core formation can readily reach megabar regime (~100 GPa) during events such as the moon-forming giant impact (e.g. Nakajima and Stevenson, 2015). Here, in order to understand its behaviour in a deeper magma ocean relevant to the Earth, we investigate the distribution of N between molten metal and silicate in a laser-heated diamond anvil cell.

## 2. Methods

### 2.1. Starting materials

The starting silicate was glass synthesized in an aerodynamic levitation furnace. The glass was modelled after a silicate Earth-like composition of pyrolite (Huang et al., 2022b) (Table 1), by mixing high

purity (≥99%) oxides (FeO, MgO, Al₂O₃, SiO₂ and sometimes Cr₂O₃ and V₂O₃) and carbonate (CaCO₃), without trace elements below 1 wt% (i.e., Ti, Mn, Ni, Na, K, and P) (McDonough and Sun, 1995). The formation of osbornite (TiN) in metal-silicate partitioning experiments was reported to increase the siderophility of N (Speelmanns et al., 2019), which however does not represent terrestrial core formation because it occurs exclusively in Ti-rich (~2 wt%) materials, but not in the peridotitic system (~0.2 wt% TiO₂). The powder mixture was decarbonated at 950 °C for 12 h before fused into a glass bead using the levitation furnace coupled with a 75 W CO₂ laser. The fO₂ for making the glass beads were imposed at ΔIW-1.2 by controlling the ratio of CO₂ to H₂ (diluted in an Ar carrier gas) in the overflowing gas mixture (details in Huang et al. (2022b)). The glass was then polished to ~20 µm thick and machined into round disks suitable for DAC loading using a picosecond laser machining system. The starting iron-rich material was commercially purchased iron nitride Fe₃N (x=2-4, Alfa Aesar). Chemical composition of the silicate glass and metal was confirmed to be homogeneous by energy-dispersive X-ray spectroscopy (EDS) results (Table S1).

### 2.2. Laser-heated diamond anvil cell experiments

A symmetric diamond anvil cell (DAC) was used to simulate high pressure conditions in deep Earth. The iron nitride was sandwiched between two plates of pyrolite glass, of which the whole assemblage was loaded into a drilled Re gasket. Pyrolite glass also served as thermal and chemical insulators during laser heating. Sample was compressed to a pressure of interest and subsequently heated from both sides using a 200 W fibre laser (λ = 1070 nm) with a focused beam size of ~20 µm in diameter. Laser power was firstly ramped and held for 30 to 90 s at a temperature higher than the pyrolitic liquidus (e.g. 4980 K at 104 GPa) (Fiquet et al., 2010; Andrault et al., 2011), then switched off to quench the sample to an amorphous state. It has been argued that, based on arguments such as diffusivity and thermodynamics, these heating durations should be sufficient to allow for the attainment of equilibrium between the metal and silicate liquids at these extreme temperatures (Huang et al., 2021).

Temperature was monitored every one or two seconds from both sides of the heated area by fitting the thermally emitted visible light (500–750 nm) to the Planck black-body function and using the Wien fitting (Benedetti and Loubeyre, 2004). During heating, temperature measurements were actively aligned with the centre of the brightest regions from both sides. The temperature for each experiment (Table 1) was then obtained by averaging the temperatures (i) fitted by the above two methods, (ii) from both sides of the hot spot, and (iii) over the entire heating duration after the target temperature was attained and before quench. A typical temperature profile (T vs. time) recorded from both sides of the sample during Exp. No. X6 is shown in Fig. 2. As can be seen, upon reaching a temperature plateau at ~20 s, despite that the measured temperatures on side A are mostly higher than those on side B by 10 to 200 K, they remain reasonably stable for ~70 s prior to quench. In general, when a heating spot is insufficiently insulated from the anvils, temperature is expected to be unsteady for long durations; the observed temperature stability over 30 to 90 s therefore indicates a sufficient thermal insulation in our experiments. The global uncertainties in temperature were estimated to be ±250 K (upper limit, see Table 1) by combining uncertainties in individual temperature fitting, standard deviations from averaging temperatures and systematic errors (e.g. the aforementioned axial temperature gradient). Pressure was obtained by measuring Raman shifts of diamond anvils before and after each experiment (Akahama and Kawamura, 2004), and corrected by adding thermal pressure (ΔP = 2.7 MPa/K) estimated from in situ X-ray diffraction measurements (Siebert et al., 2012). Uncertainties in pressure, including those originated from the thermal pressure estimates, are assessed to be ~10% of the total pressure (Table 1).
<table><caption>**Table 1**
Summary table for experimental conditions in laser-heated diamond anvil cells.</caption><thead><tr><th>Exp. No.</th><th>X1-1</th><th>X1-2</th><th>X9</th><th>X4-2</th><th>X4-1</th><th>X3</th><th>X6</th></tr></thead><tbody><tr><td>P (GPa)</td><td>36 ± 4</td><td>46 ± 5</td><td>57 ± 6</td><td>64 ± 6</td><td>76 ± 8</td><td>87 ± 9</td><td>104 ± 10</td></tr><tr><td>T (K)</td><td>3310 ± 170</td><td>3670 ± 180</td><td>4040 ± 200</td><td>4020 ± 200</td><td>4200 ± 210</td><td>4480 ± 220</td><td>4980 ± 250</td></tr><tr><td>Starting metal</td><td>FexN</td><td>FexN</td><td>FexN</td><td>FexN</td><td>FexN</td><td>FexN</td><td>FexN</td></tr><tr><td>Starting silicate</td><td>PYR2-1</td><td>PYR2-1</td><td>PYR4-2</td><td>PYR2-1</td><td>PYR2-1</td><td>PYR2-1</td><td>PYR2-1</td></tr><tr><td>fO<sub>2</sub>(ΔIW)<sup>*</sup></td><td>-1.1</td><td>-1.1</td><td>-0.9</td><td>-1.9</td><td>-1.2</td><td>-1.2</td><td>-1.0</td></tr><tr><td>D<sub>N</sub>(molar base)</td><td>4.0</td><td>2.4</td><td>2.8</td><td>4.1</td><td>1.8</td><td>2.4</td><td>1.9</td></tr></tbody></table>

Note: Oxygen fugacity relative to the iron-wüstite buffer is approximated as fO₂(ΔIW) = log₁₀(xFe/xFeO), assuming ideal mixing.

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Temperature variations recorded from both sides of the sample at 104 GPa during experiment No. X6. Temperatures from side A are shown in red, and side B in green; dots and triangles denote temperatures obtained from the Planck fitting and Wien fitting, respectively. Error bars correspond to an estimate of the uncertainty of the fitted temperature based on Benedetti and Loubeyre (2004). The quoted temperature (4890 K) corresponds to the average of the monitored temperature from both sides using different fitting methods after reaching the target temperature (from ~20 to 90 s).</figcaption></figure>

## 2.3. Sample morphology

Focused ion beam (FIB) equipped with a field emission gun (Zeiss Auriga 40) was used to extract thin sections from the laser-heated area after quench and decompression. Samples were sectioned to 3–4 µm in thickness with the same metal-silicate geometry on both sides, in order to avoid potential fluorescence from adjacent phases in EPMA analysis (Huang and Badro, 2018). A backscattered electron image of a thin section recovered from 57 GPa and 4040 K is shown in Fig. 3 as an example, where the typical morphology is comprised of a metallic blob surrounded by a layer of silicate melt. As observed by previous partitioning experiments using diamond anvil cells (e.g. Siebert et al., 2012; Fischer et al., 2015; Huang and Badro, 2018; Huang et al., 2020, 2021), quench texture was ubiquitous in all of our experiments.

### 2.3.1. Metal texture

Here we differentiate between two types of textures in the metal, originated from two different experimental pressure regimes, by comparing with lower-pressure experiments. Type A is large ‘vesicles’ (typically 5 to 15 µm) found in piston-cylinder or multi-anvil press experiments (e.g. Speelmanns et al., 2018; Grewal et al., 2022), which are essentially gas bubbles, considered to be either in equilibrium with the melt (Speelmanns et al., 2018) or formed during quench (Grewal et al., 2022), that suggest N loss through polishing during sample recovery.

Type B is the small ‘blobs’ in the metal (typically less than 200 nm in diameter, see close-ups in Fig. 3) observed in diamond anvil cell experiments, which is Si-O-rich in nature (Jennings, 2020) and was likely formed during rapid cooling (c.f. Siebert et al., 2012; Fischer et al., 2015; Huang and Badro, 2018; Huang et al., 2020, 2021). Note that the size of type A ‘vesicles’ is larger than type B ‘blobs’ in our samples by about two orders of magnitude, and is comparable to the size of our whole sample (metal + silicate, Fig. 3). Given the absence of such ‘vesicles’ in our FIB-polished samples, we find no evidence for nitrogen loss during sample preparation in our experiments.

### 2.3.2. Silicate texture

Similar to the texture found in the metallic phase, the majority of the Fe-rich blobs in the silicate matrix are <200 nm in diameter and are evenly distributed within the silicate, suggesting a quench origin. In contrast, a few large (>200 nm) Fe-rich droplets, besides the main central Fe blob, are present in much lower numbers, suggesting that they formed in equilibrium with the silicate and were trapped thereof upon quench before merging with the central metal piece. The latter (large Fe-rich droplets) was avoided during chemical analysis.

Furthermore, a fine feature in the silicate melt, namely the varying concentrations of the small metal blobs within the silicate (Fig. 3), has been observed repeatedly in our experiments (Huang and Badro, 2018; Huang et al., 2020, 2021). The electron probe micro-analysis (EPMA) is however insensitive to this sub-micron heterogeneity, because the latter would be well integrated over the typical interaction volume with a diameter of ~1 to 2 µm (depending on beam voltage and sample composition). The EPMA analyses over these distinct regions (details see below) report limited compositional variations, particularly for N, as evidenced by the small standard deviations obtained from multiple measurements (Table S2). Similar chemical homogeneity at the scale of EPMA analyses has also been observed in our previous metal-silicate partitioning experiments using diamond anvil cells (Huang and Badro, 2018; Huang et al., 2020, 2021).

## 2.4. Quench texture and EPMA analysis

Compositions of both metal and silicate phases were determined by wavelength dispersive X-ray spectroscopy (WDS) using EPMA on a Cameca SX-five at Camparis. An accelerating voltage of 15 kV and a beam current of 40 nA were used in all cases. Peak counting times were 30 s for N and O and 10 s for other elements, with a background counting time of 15 s. Diopside (Ca, Si and Mg), orthoclase (Al), hematite (Fe and O), vanadinite (V), Cr₂O₃ (Cr) and BN (N) were employed as internal standards. The LPCO crystal was utilized for measuring N. The background was collected before and after the peak and was used to interpolate background intensity at the interested wavelength. The particularity of the multi-layer crystals is to have broad peaks and therefore to be less sensitive to the potential difference in peak position between the sample and the standard. All elements were analysed using Kα₁ lines. For each phase, at least 5 spots/windows were collected by microprobe to obtain the mean. The interaction volume increases with higher beam voltage and lower sample density; the maximum interaction depth for a 15 kV beam was estimated to be 2 µm for the silicate and less than 1 µm for the metal. Therefore, the thickness of
<figure><img src="image_6.png" /><figcaption>Fig. 3. An exemplary backscattered electron image of a thin section recovered using focused ion beam. Prior to the sample extraction, the metal (bright sphere) and the silicate (dark blob encapsulating the central metal piece) were melted and equilibrated at 57 GPa and 4040 K in a laser-heated diamond anvil cell. Detailed discussions on the quench texture are in the main text.</figcaption></figure>

3–4 µm of the FIB thin sections avoids low totals that are commonly observed when the sample is thinner than the interaction volume. Contamination through beam interaction from adjacent phases was avoided during analysis by analysing areas sufficiently far from the metal-silicate phase boundary (details can be found in Huang et al. (2020, 2021)).

There are possibilities of C contamination through sample preparation or C diffusion from diamond anvils at high temperatures during heating. However, our previous experiments using the same approach (Siebert et al., 2012, 2013) found C content below detection limit (~1 wt%), notwithstanding carbon might be introduced during analysis by carbon coating or carbon tape (c.f. Huang et al., 2021). Nevertheless, despite carbon likely being below the detection limit, its potential presence in the metal could still affect the partitioning of nitrogen, necessitating further investigation. Assuming that the carbon content in the metal is 1 wt%, the maximum estimated amount according to the above discussion and a reasonable concentration in Earth's core (e.g. Hirose et al., 2021), we refitted Eq. (1) and found the parameters with and without C in the metal (Table S3) to be equivalent to each other within uncertainties, in agreement with a recent study that found relatively small effect of low C content on D<sub>N</sub> (Jackson et al., 2021).

Note that the EPMA measurements suffer from the deviation of totals from 100% (Table S2); in fact, high or low total is a known feature in partitioning experiments using LHDAC (Fischer et al., 2020; Huang et al., 2021). This is due to the aforementioned submicron-scale heterogeneity formed during quenching. However, the accuracy of the measured partition coefficients is corroborated by (i) the agreement between available EDS and EPMA results (Table S4), (ii) the fact that the adjustments in absolute concentrations due to non-unity totals are offset, at least partly, by dividing the absolute concentrations (i.e. partition coefficient), and (iii) the consistency within the same thermodynamic model between high- and low-P data obtained from DAC, piston-cylinder or multi-anvil press (Section 3.1).

## 3. Results

Apart from the non-unity totals, our EPMA data (Table S2) show several features as follows. (i) With the measured N content ranging from ~3 to 7 wt% in the metal and ~1 to 2 wt% in the silicate, under these extreme P-T conditions, N retains its siderophile character, albeit less prominently than extrapolated from previous results obtained at lower pressures (Figs. 4–5). (ii) While the starting metal in our experiments contained no oxygen (Table S1), we found high solubility of

O in the quenched metal (6 to 17 wt%, Table S2). This is attributed to the increasing pressure and temperature (c.f. Badro et al., 2015; Huang et al., 2020), the effects of which on D<sub>N</sub> are discussed later in Section 3.3. (iii) Redox conditions in our experiments end up similarly oxidized (1 to 2 log units below the IW buffer, Fig. 4). This can be explained by the partitioning of Si into the metal at increasing pressure and temperature where metallic Fe is oxidized to FeO, which is a common feature under extreme P-T conditions in DACs (e.g. Fischer et al., 2015; Huang et al., 2020, 2021).

### 3.1. Thermodynamics of N partitioning between metal and silicate liquids

The partitioning of nitrogen is controlled by P, T, fO<sub>2</sub> and metal/silicate compositions in a magma ocean. Here, we adopt an empirical thermodynamic model to predict the partitioning of N between metal and silicate, by parameterizing the above parameters using

$$ \begin{aligned} \log_{10} D_N = & a + \frac{b}{T} + c \cdot \frac{P}{T} \\ & + d \cdot \log_{10}(1 - x_C) + e \cdot \log_{10}(1 - x_S) \\ & + f \cdot \log_{10}(1 - x_{Si}) + g \cdot \log_{10}(1 - x_O) \\ & + h \cdot nbo/t + i \cdot \Delta IW. \end{aligned} \quad (1) $$

D<sub>N</sub> is the partition coefficient of N, which is the ratio of its molar fractions (x<sub>N metal</sub>/x<sub>N silicate</sub>) in relevant phases. P is pressure in gigapascal and T is temperature in kelvin. x<sub>C</sub>, x<sub>S</sub>, x<sub>Si</sub>, x<sub>O</sub> are respectively the molar fractions of C, S, Si and O in the metallic phase. nbo/t denotes the molar ratio of non-bridging oxygens (nbo) per tetrahedrally coordinated cations (t). Note that nbo/t is a highly empirical parameter as melt structure changes with pressure (Huang et al., 2022b). Finally, ΔIW is the oxygen fugacity (fO<sub>2</sub>) relative to the iron-wüstite (IW) buffer, which is calculated by ΔIW = 2log<sub>10</sub>(x<sub>FeO</sub>/x<sub>Fe metal</sub>), assuming ideal behaviour.

To obtain better statistics for the parameterization, we combine our data with N partitioning data from the literature (Kadik et al., 2011; Roskosz et al., 2013; Li et al., 2016; Dalou et al., 2017, 2019a; Speelmanns et al., 2019; Grewal et al., 2019a,b, 2021, 2022; Jackson et al., 2021; Shi et al., 2022; Li et al., 2023), and recompute the above parameters for each experiment (Table S5). With our data collected at megabar pressures (Table 1), the updated dataset contains 288 experiments, covering probable pressures (1–104 GPa), temperatures (1523–4980 K) and fO<sub>2</sub> (IW-8–IW-0.8) at magma ocean conditions relevant to Earth-sized planets. They are shown as D<sub>N</sub> vs. ΔIW in Figs. 4 and S1. Note that two experiments (N17, N27) from Speelmanns et al. (2019) were not included, because the formation of osbornite
<table><caption>**Table 2**
Coefficients of the thermodynamic model Eq. (1) for the metal-silicate partitioning of N.</caption><thead><tr><th>Coefficient</th><th>Value</th><th>1σ</th></tr></thead><tbody><tr><td>a</td><td>0</td><td>–</td></tr><tr><td>b (K)</td><td>2732</td><td>156</td></tr><tr><td>c (K/GPa)</td><td>0</td><td>–</td></tr><tr><td>d</td><td>4.04</td><td>0.60</td></tr><tr><td>e</td><td>2.00</td><td>0.46</td></tr><tr><td>f</td><td>5.57</td><td>0.87</td></tr><tr><td>g</td><td>6.28</td><td>1.07</td></tr><tr><td>h</td><td>0.49</td><td>0.03</td></tr><tr><td>i</td><td>0.40</td><td>0.02</td></tr></tbody></table>

makes N anomalously siderophile in those experiments. Due to the strong influences of C and Si on N partitioning (Table 2), simultaneous high concentration of Si in the metal under C-saturated conditions leads to significant deviations from the model predictions (the model fails to converge). We therefore excluded 7 experiments from Grewal et al. (2019a), 1 experiment (PC_N_EXP3) from Jackson et al. (2021), and 1 experiment (N-4) from Shi et al. (2022), where the metals are concentrated with both C and Si.

A stepwise ordinary least-squares (OLS) regression to the above dataset firstly (step 1) found that a (intercept) and c (pressure) terms are insignificant ($p$-value=0.50 and 0.25, respectively). Therefore, a and c were kept at zero, and the remaining coefficients (b, d, e, f, g, h, i) were regressed again (step 2). The fitting results obtained in the two steps are consistent with one another, while the uncertainties from the last regression are statistically more relevant. Covariances of the fitted regression are provided in Table S6. Residuals of the fit for Eq. (1) are plotted in Fig. S2.

Eq. (1) and the fitted results (Table 2) allow one to evaluate the individual effect of the thermodynamic parameters on N partitioning as follows. (i) Previous experiments conducted between 1500 K and 3437 K revealed a negative temperature effect, indicating that increasing temperature leads to a decrease in $D_N$. Our data, which extends the temperature range to 5000 K, confirm this trend, as evidenced by the positive coefficient b for reciprocal temperature in our thermodynamic model (Eq. (1) and Table 2, as illustrated in Fig. 5). Note, however, that direct comparison of the absolute values of the coefficients with those of previous models would not offer quantitative insight. This is because the addition and/or omission of any term in the model (e.g. the absence of the pressure term in our case) would alter the absolute values due to the correlation and interplay of fitted coefficients. For robustness, it is necessary to evaluate the entire set of coefficients simultaneously. (ii) Among other light elements in the Fe-rich alloy, S exerts the least influence on N, because its coefficient e is nearly half of those of C, Si and O. This is consistent with (Grewal et al., 2019b), where the solubility of S hardly changes the behaviour of N. Furthermore, this is in agreement with (Jackson et al., 2021), where an expanded concentration expression, associated a fitted S-N interaction parameter, yields a minor effect of S relative to other parameters. (iii) The presence of C and Si distinctly expels N from the metal (decreasing $D_N$) as d and f are relatively large and positive. This is in line with (a) previous experiments (c.f. Grewal et al., 2021), where C-saturated samples have lower $D_N$ at similar oxygen fugacity, which are illustrated in Fig. 4, and (b) a negative effect of C on $D_N$, based on their interaction parameter determined with a metallurgical interaction model (Jackson et al., 2021). (iv) The incorporation of oxygen in the alloy (parameter $x_O$ and coefficient g) greatly reduces the siderophily of N, which is a new feature revealed by our N partitioning experiments under higher P-T conditions (Fig. 5). Fig. 5 is obtained by correcting for the effects of oxygen fugacity, silicate ($nbo/t$) and metal ($x_C, x_S, x_{Si}$) compositions against their own values at each individual experimental condition, i.e. $log_{10}D_N^* = log_{10}D_N - d \cdot log_{10}(1 - x_C) - e \cdot log_{10}(1 - x_S) - f \cdot log_{10}(1 - x_{Si}) - h \cdot nbo/t - i \cdot \Delta I W$ (Eq. (1)), in order to

separately show those of temperature and oxygen concentration in the metal. (v) In agreement with previous results (Grewal et al., 2019a, 2021), higher degree of polymerization in silicate melts, i.e. lower $nbo/t$, makes N more lithophile ($h > 0$). (vi) As expected, $fO_2$ ($\Delta I W$) plays an important role in controlling N distribution, where oxidizing conditions promote the incorporation of N in the metal (Figs. 4 and S1). In light of the above parameterization, one can assess the influences of limited number of parameters on N partitioning, by correcting for other parameters (e.g. Figs. 5 and S1).

## 3.2. The effect of Ni

The effect of Ni has been shown to be negligible on the partitioning of Ni, Cr and V (Huang and Badro, 2018), likely due to the similarities between Fe and Ni regarding atomic mass and radius (c.f. Huang et al., 2023); apart from this general trend, however, two studies suggested a resolvable effect of Ni on the partitioning of N (Roskosz et al., 2013; Jackson et al., 2021). The former study observed a negative correlation between N and Ni contents in the metal (Fig. 4 thereof); this however does not mean that Ni makes N less siderophile because no correlation can be found if one plots their $D_N$ versus Ni content in the metal, which in turn confirms the observed Fe-Ni ideality (Huang and Badro, 2018). The reasons for the effect of Ni resolved in the latter work might be (i) the different dataset used for regression and (ii) the different choice of the significance threshold from ours. Substantiated by the rapid data accumulation for N partitioning in recent years (compiled and reported in Table S5), our statistical significance threshold for model parameters is set to 0.01, because, except for the Ni term ($p$-value = 0.03) and the pressure term ($p$-value = 0.25), the remaining parameters being regressed individually yield a maximum $p$-value of $10^{-6}$, significantly lower than the above values. Accordingly, the Ni and pressure terms are determined to be statistically insignificant.

## 3.3. The effects of oxygen and pressure

The most remarkable result obtained under these extended P-T conditions (up to 104 GPa and 5000 K) is the pronounced influence of dissolved oxygen in the metal (Figs. 4–5) on the N partition coefficient between metal and silicate, $D_N$. Our experiments show that this value approaches unity (i.e., subequal distribution of N between silicate and metal) as temperature approaches 5000 K. The presence of light elements in Earth's core is required by its density deficit relative to pure iron (Birch, 1964), and these light elements are known to exert a considerable influence on the partitioning behaviour of N, as recently resolved for C and Si (Grewal et al., 2019b, 2021). Using laser-heated diamond anvil cells, we are able to quantify the effect of increasing solubility of oxygen in the metal, as a consequence of increasing P-T conditions (in other words, deepening magma oceans) (e.g. Badro et al., 2015; Huang et al., 2020). We find that N in our experiments with O-rich metals, performed at deep magma ocean conditions, becomes much less siderophile (Fig. 5), compared to previous C-undersaturated (by two orders of magnitude) and C-saturated (by one order of magnitude) samples at moderate P-T conditions (Fig. 4) (Kadik et al., 2011; Roskosz et al., 2013; Li et al., 2016; Dalou et al., 2017, 2019a; Speelmanns et al., 2019; Grewal et al., 2019a,b, 2022; Jackson et al., 2021; Shi et al., 2022; Li et al., 2023).

Based on the limited pressure range (1–26 GPa) under which the experiments were conducted in earlier studies, the impact of pressure on $D_N$ has been proposed to be negative (Roskosz et al., 2013; Dalou et al., 2017), positive (Grewal et al., 2019a, 2021; Jackson et al., 2021) or unresolvable (Speelmanns et al., 2019). Here, with the benefit of an expanded pressure (1–104 GPa) and temperature range (up to 5000 K), pressure effect on $D_N$ is determined to be statistically negligible with the current thermodynamic model (Table 2). However, this does not mean pressure has no effect on N partitioning, rather, it is because P and T are strongly correlated variables, making it
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Metal-silicate partition coefficient of nitrogen ($D_N$) as a function of oxygen fugacity (relative to the iron-wüstite buffer, ΔIW). Top south west arrow represents the trend (vs. ΔIW) of $D_N$ in carbon-undersaturated conditions (Grewal et al., 2021), which is about one order of magnitude higher than that of carbon-saturated samples (Kadik et al., 2011; Roskosz et al., 2013; Li et al., 2016; Dalou et al., 2017, 2019a; Speelmanns et al., 2019; Grewal et al., 2019a,b, 2022; Jackson et al., 2021; Shi et al., 2022; Li et al., 2023) (middle south west arrow), and is two orders of magnitude higher than our experiments (yellow squares) at higher P-T conditions with high solubility of O in the metal. These are consistent with our modelling (Eq. (1) and Table 2), where the coefficient for O (g) is larger than that for C (f) and both are positive (g > f > 0), meaning that both O and C make N less siderophile with the former having a stronger effect. The apparent ‘exception’ to the O-rich trend at ΔIW-1.9 (Exp. No. X4-2) is due to its low oxygen content in the metal, which relatively increases its $D_N$ and in turn validates the resolved negative effect of O on N partitioning. Note that the above experiments were performed in a wide P-T-composition space, the aforementioned observations are thus only qualitative. The impact of oxygen solubility on N partitioning is quantitatively illustrated in Fig. 5.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Metal-silicate partition coefficient of nitrogen ($D_N$) as a function of reciprocal temperature (10,000/T) and oxygen concentration in the metal ($x_O^{metal}$, in molar fraction, colour bar). The same dataset as in Fig. 4 are used. The dashed line denotes the temperature dependence of N partitioning obtained from a least-squares regression of the above data. $D_N$ is calculated by dividing N concentration in the metal by that in the silicate, and is corrected for oxygen fugacity and melt composition ($D_N^*$, see main text), to isolate the effects of temperature and oxygen solubility. As can be seen, increasing temperature makes N less siderophile (dashed line); at relevant core-forming temperatures (vertical shaded area), the addition of oxygen in the metal (colour bar), further decreases the siderophily of nitrogen.</figcaption></figure>

challenging to rigorously separate their effects. Moreover, this implies that the pressure-induced volume change of the N partitioning reaction is minimal at depth, and agrees with the insignificant dependence of N speciation with pressure in silicate melts (Huang et al., 2022a). While

<table><caption>**Table 3**
Bulk Earth’s (BE) volatile building blocks compared with CI chondrite composition.</caption><thead><tr><th>Volatile content (ppm)</th><th>C</th><th>N</th><th>S</th><th>C/N</th><th>C/S</th></tr></thead><tbody><tr><td>CI<sup>1</sup></td><td>35 357</td><td>1485</td><td>51 000</td><td>24</td><td>0.69</td></tr><tr><td>BE<sup>2</sup></td><td>707</td><td>6</td><td>3000</td><td>118</td><td>0.24</td></tr><tr><td>Early vaporization<sup>3</sup></td><td>98.0%</td><td>99.6%</td><td>94.1%</td><td></td><td></td></tr></tbody></table>

¹ CI chondrite values are taken from Kerridge (1985) for C and N, and Braukmüller et al. (2019) for S.

² Bulk Earth composition comprises/is (a) 2% CI material regarding carbon content, and (b) CV-CO-like in terms of volatile ratios, where C/N is 118(41) (Marty et al., 2020) and C/S equals 0.24(1) (Wasson and Kallemeyn, 1988).

³ Early vaporization means early volatile loss (%) in Earth’s building blocks compared to CI-chondrite, namely (1-BE/CI)×100.

pressure increases the coordination number of cation-oxygen bonds in silicate melts, except that of the oxygen-oxygen bond (Huang et al., 2022b), species of multivalent nitrogen is more complex in silicate melts than in liquid metal (Bajgain et al., 2019) and is most sensitive to redox conditions (Huang et al., 2022a).

# 4. Discussion

## 4.1. Earth’s core as the largest terrestrial reservoir for nitrogen

Having characterized the behaviour of N under these extreme P-T conditions, our thermodynamic model (Eq. (1)) that considers the effects of pressure, temperature, oxygen fugacity and melt composition to quantify N partitioning, allows us to predict the distribution of N between Earth’s metallic core and silicate mantle. Fig. 6 showcases the negative effect of temperature and oxygen content of the metal on nitrogen’s siderophile character in a Si-poor core (Badro et al., 2014) during a single-stage core formation event, where the composition of the accreting components is kept constant (i.e., CI-like, Table 3). The oxygen content in the core (x-axis, Fig. 6) is a free parameter; although
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Distribution of N as a function of oxygen content in the core (wt%) during Earth's core–mantle equilibrium segregation in the canonical CI-like Earth model. Three end-member core-forming pressure–temperature conditions are tested (solid lines, full mapping of the T-xymetal O space can be found in Fig. S3). The dissolution of oxygen in Earth's liquid metallic core as well as the high temperatures reduce the amount of nitrogen entering the core (b–d), as both parameters decrease its partition coefficient D<sub>N</sub> in (a). Nevertheless, and as shown in (d), the core remains the largest reservoir for the total N delivered to the Earth, its mantle abundance (N<sub>BSE</sub> in c) is constantly overestimated compared to the observed value of 2.8(6) ppm (horizontal shaded area), if the CI-like Earth model is assumed.</figcaption></figure>

high O concentrations (up to 6 wt%) can be expected if the Earth accreted from oxidizing conditions (e.g. Siebert et al., 2013), it clearly does not contribute to lowering the overabundant N in the BSE. As can be seen, under a range of potential core-forming P-T conditions, despite that O expels N to the mantle, N remains mildly siderophile (3<�D<sub>N</sub><12, Fig. 6a), by preferentially entering the core (Fig. 6b). Consequently, Earth's core becomes the largest reservoir by taking up more than 50 wt% of all accreted nitrogen, regardless of the P-T (Fig. 6d). However, the only observable in this case, i.e. 2.8 ± 0.6 ppm of N in the bulk silicate Earth (Hirschmann, 2018), is violated by having a mantle that is too rich in N (8–20 ppm, Fig. 6c).

An Si-rich core, as may be expected for heterogeneous accretion of the Earth in which the nascent stages of its growth are typified by accretion of reduced bodies (Rubie et al., 2015), is shown in Fig. S4. An Si-rich core exacerbates the mismatch between the observed N abundance in the BSE and the model, which yields N in the range 12–27 ppm. This arises because Si expels N from the core and it becomes increasingly soluble in the silicate melt as the nitride (N<sup>3−</sup>) moiety (Huang et al., 2022a; Dalou et al., 2019b), in line with Grewal et al. (2021) and our thermodynamic model.

To resolve the common issue (i.e. overly abundant N in the BSE), earlier studies propose (i) N loss (through outgassing) on either planetary embryos or the proto-Earth (e.g. Grewal et al., 2021; Speelmanns et al., 2019), or (ii) stronger siderophile behaviour of N under more

oxidizing or higher pressure conditions (Grewal et al., 2019a; Jackson et al., 2021; Roskosz et al., 2013). Nonetheless, because (i) preferential loss of N is improbable as both N and C are similarly volatile during nebular condensation (Lodders, 2003) and during planetary magma ocean-related outgassing, depending on fO<sub>2</sub> (Sossi et al., 2020; Gaillard et al., 2022; Huang et al., 2022a), and (ii) in the previously investigated moderate pressure range, C is invariably more siderophile than N (e.g. Dalou et al., 2017; Grewal et al., 2019b), the above propositions are somewhat undermined by not incorporating the behaviour of C.

This poses a major challenge, namely models should be able to simultaneously reproduce the C/N, and C and N abundances in the BSE, by the integration of processes occurring on the precursor bodies and on the proto-Earth (Hirschmann, 2016). Two earlier studies tackle the problem by resorting to late accretion (Dalou et al., 2017) or proposing a wide spectrum of impactor compositions in which the giant impact, ostensibly rich in S, leads to core formation under which C becomes less siderophile than N (Grewal et al., 2019b). However, the former considers only the C/N ratio in the BSE constrained by low pressure (<3 GPa) partitioning data, which, as discussed below, are likely insufficient as a test of the model. On the other hand, the inverse model (Grewal et al., 2019b), employed to back-constrain impactor compositions using BSE's C-N-S pattern, requires extreme scenarios in which metal-silicate equilibrium (k) values are < 0.2, a condition not supported by observed elemental/isotopic fractionation of the Hf/W system (e.g. Rudge et al.,
2010; Bourdon et al., 2018). Focusing simultaneously on C and N abundances in the BSE, recent work aiming to reproduce Earth's N isotopic composition concludes that the majority of the Earth accreted from enstatite chondrite-like material (Shi et al., 2022), while another maintains the nature of Earth's superchondritic C/N ratio remains to be an open question (Li et al., 2023). Chen and Jacobson (2022) study the delivery of major terrestrial volatiles by investigating dynamical aspects of accretion simulations, which, however do not account for N sequestration into the core, and thereby provide only a partial picture.

The common feature of all previous work is that their discussions are based on the extrapolation of relatively low pressure data (up to 26 GPa) for N metal-silicate partitioning, which are applicable to a shallow magma ocean and do not account for the aftermath of giant impacts (e.g. nearly wholesale mantle melting (Nakajima and Stevenson, 2015)). Shi et al. (2022) makes the effort and advances their discussions by (i) exploring broader parameter space (e.g. degrees of core-mantle disequilibrium and atmospheric loss), and (ii) incorporating partitioning data of other volatiles (H and C) obtained at higher pressures ranging from 30 to 71 GPa. This wider parameter search notwithstanding, the accuracy of their model is limited by the use of N metal-silicate partitioning data at lower pressures (up to 26 GPa) than thought to prevail during core formation on Earth.

## 4.2. Core–mantle–atmosphere coevolution model

To utilize the newly quantified effect of oxygen at higher pressures and temperatures pertinent to giant impact-induced deep magma oceans, we design a multi-stage core–mantle–atmosphere coevolution model that tracks simultaneous distributions of C and N in the three reservoirs.

### 4.2.1. Core–mantle differentiation

To model the complexity during Earth's accretion, we form and differentiate the early Earth in a discrete fashion by accreting 100 impactors (each possesses 1% Earth's mass) (c.f. Huang et al., 2021). Each impactor has an identical bulk composition, that is, 2% of CI-chondrite budget of C and N (hence CI-like C/N ratio, Table 3). Rather than being arbitrary, the 2% assumption for Earth's volatiles is constrained by the comparison of terrestrial water, carbon and noble gases budgets with those of CI-CM chondrites (Marty, 2012). At each individual impact, the impactor's core equilibrates with silicate melt in the magma ocean, before the latter being transported through convection to the surface to form an atmosphere by outgassing. Note that for simplicity we consider metal-silicate equilibration taking place prior to the MO outgassing, which is based on the assumptions and/or observations that (i) the impactors are differentiated small bodies, with their metal cores highly concentrated in N due to low-pressure core–mantle equilibration (Fig. 5), and (ii) the majority of N that is stored in impactors' cores, after the latter breaks up and emulsifies in the MO (e.g. Rubie et al., 2003), would most likely partitions into the silicate melt first, and subsequently becomes available for outgassing.

The metal-silicate equilibration is modelled to take place at (i) 40% of the core–mantle boundary pressure (with a final pressure of 54 GPa in the last step to match Ni and Co mantle abundances), and (ii) mantle liquidus temperature of the average of Ref. Fiquet et al. (2010) and Andrault et al. (2011), in a pyrolitic magma ocean (nbo/t = 2.7). Along the accretion path, the fO₂ linearly increases from IW-3 to IW-2. For a first-order approximation, the redox condition at the surface of the MO is considered to be identical to that of the core–mantle equilibration in our model; future models that take account of vertical variations of fO₂ in the MO are needed, in order to investigate the effect of pressure-dependent difference in molar volume between Fe²⁺ and Fe³⁺ (e.g. Armstrong et al., 2019; Deng et al., 2020). We also model the concurrent partitioning of C (Fischer et al., 2020), S (Suer et al., 2017), Si and O (Siebert et al., 2013), in order to quantify interactions among light elements and their influences on N partitioning (Eq. (1)).

The partitioning behaviour of N in this study and recently that of C (Fischer et al., 2020; Blanchard et al., 2022) measured under extended P-T conditions allow direct predictions of their core–mantle fractionation in a deep magma ocean, without extrapolation.

### 4.2.2. MO outgassing

To quantify the amounts of C and N degassed into the atmosphere and therefore available for atmospheric loss, we use existing solubility laws between gas and silicate melt (Dixon et al., 1995; Yoshioka et al., 2019; Libourel et al., 2003) and a mass balance approach (e.g. Sossi et al., 2020; Bower et al., 2022) detailed as follows. To simulate the genesis of an atmosphere produced via outgassing of a putative terrestrial magma ocean, we consider a fiducial scenario in which the magma ocean is assumed to encompass the entire mass of the mantle at each accretion step (i.e. impact). The partial pressure of any gaseous species is proportional to its mass in the atmosphere, which is given by

$$p_v = \frac{g M_v}{4\pi r^2}, \qquad (2)$$

where g is the acceleration due to gravity, r is the radius of the body and M_v is the mass of species v in the atmosphere at an accretion step. M_v is finite because it depends on the total amount of the element in the growing Earth, and its solubility in the magma ocean. This relationship can be described by mass balance

$$(MX_v)_0 = (MX_v)_{\text{atm}} + (MX_v)_{\text{MO}}, \qquad (3)$$

where the subscripts 0, atm and MO refer to the total, atmospheric and magma ocean reservoirs. We substitute Eq. (2) into Eq. (3), and solve it for p_v. The partial pressures (and hence fugacities in a real gas) of the individual gas species (CO, CO₂ and N₂) are solved by mass balance according to their equilibrium distribution between melt and atmosphere, as dictated by their solubilities using existing parameterizations (cf. Sossi et al. (2020)). In addition, the composition of the atmosphere depends on the fO₂ (set by the metal-silicate equilibrium) and temperature at the atmosphere-magma ocean interface. We opt for a temperature of 2073 K to approximate the peridotite liquidus temperature at 1 bar (Takahashi, 1986). Note that the outgassing of S is not considered, because under redox conditions relevant to Earth's accretion (IW-3 to IW-2), S almost entirely (>99.9%) resides in the magma ocean (Gaillard et al., 2022).

### 4.2.3. Model output: no solution for a CI-like earth model

Two key parameters are explored for their roles in establishing Earth's high C/N ratio (Fig. 7): (i) the degree of metal-silicate equilibration k ∈ [0, 1], where k = 0 or 1 represents zero or full equilibrium achieved between the impactor's core and the magma ocean; and (ii) the fraction l of the atmosphere blown away to space by impact.

We find that, if the Earth accretes from materials with bulk CI-like C/N value (~24), no solution is found for the BSE's superchondritic (relative to CI chondrite) C/N ratio; in fact, the resultant C/N ratios in the BSE are constantly lower than that of its building blocks (Fig. S5). The reason, as demonstrated in Fig. 8a, is that core formation invariably sequesters more C than N into the core, leaving behind a silicate Earth with a lower C/N ratio. Neither disequilibrium nor atmospheric loss could mitigate this issue, because the former further reduces the silicate C/N value by fractionating more C (relative to N) into the core, and the latter barely alters C/N ratio by impartially losing both volatiles to space (Fig. 7a–c). Although the relative volatilities of C and N depend on fO₂, only outgassing at fO₂ much higher than those relevant to the Earth's magma ocean (e.g. ~IW+0.5 (Sossi et al., 2020; Huang et al., 2022a)), equating the fO₂ at the MO surface with that of the core–mantle equilibration at depth for a first-order approximation (cf. model details in Section 4.2.1), is able to induce preferential loss of N relative to C. This results from the existence of C as CO₂ species in the gaseous phase, which is moderately soluble in silicate melts (Dixon et al., 1995), while N is stable as N₂ (Huang et al., 2022a) and remains almost entirely in the gaseous phase (Libourel et al., 2003; Boulliung et al., 2020).
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Disequilibrium (k) during core formation with atmospheric loss (l) in the CV–CO-like Earth model. Results are shown, as a function of fractions of metal-silicate equilibration k and atmospheric loss l, for a C/N ratio, b–c C and N concentrations in the BSE (i.e. mantle + atmosphere), and e–f C and N concentrations in the core. Solution space that simultaneously satisfies the four observables in a–c and e is marked in red in **d**. In **a**, BSE's C/N ratio falls into the required range (50–181), which, however does not necessarily reproduce the observed mantle abundances in b–c. The C/N ratio alone therefore may not be a robust constraint on Earth's accretion history as suggested by earlier results (Dalou et al., 2017); rather, it is the absolute elemental abundance that provides a more definitive answer. Simultaneous reproduction of C and N mantle contents further constrains the degrees of metal-silicate disequilibrium (k) and atmospheric loss (l) in **d**. For example, if the core and mantle are in full equilibrium (k = 1), 2 to 4% of the atmosphere needs to be lost to space in order to decrease C and N in the BSE to the observed levels (b–c). In general, higher fractions of equilibration k require larger portions, albeit limited, of atmospheric loss l. For a 2D representation of this figure, readers are referred to Fig. 8.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** (a) Evolutions of N and C partition coefficients between the core and mantle and (b) the resultant C/N ratio in the BSE. The low C/N ratios in **b** at the start of accretion are due to the high D~C~/D~N~ ratios in **a** at low pressures. This is consistent with lower pressure results (e.g. Dalou et al., 2017; Li et al., 2023), which showed that D~C~ is about two orders of magnitude higher than D~N~ in a shallow magma ocean; however, the difference rapidly diminishes as N becomes equally, or slightly more, siderophile as C (D~N~≥D~C~, inset in **a**) in the final accretion steps with a deepening magma ocean where the effect of oxygen becomes pronounced. The grey shaded area in **b** denotes the estimated C/N ratio (50–181) in the BSE, which requires impactors at least twice more depleted in N than CI chondrites.</figcaption></figure>

### 4.3. Volatile depletion on precursors and limited atmospheric loss on early earth

Since our simulations over the investigated parameter space (Fig. S5) show that planetary formation processes (i.e. core formation and atmospheric loss) are unlikely to raise BSE's C/N from a CI-like value (~24) to the observed value (>50, Fig. 1), mechanisms responsible for the elevated C/N ratio are likely to occur on precursor bodies prior to their accretion to the proto-Earth, such as the volatile depletion

experienced by inward-drifting pebbles (e.g. Lichtenberg et al., 2021) or early differentiated planetesimals (c.f. Grewal and Asimow, 2023). Given that the majority of chondrites, viz. CI, CM, CR and EC, has C/N ratios lower than 40 (Fig. 1), except for CV–CO group with a mean C/N of 118 (Marty et al., 2020), Earth’s volatile budget may be more genetically represented by the latter; in other words, terrestrial building blocks might have experienced degrees of volatile depletion similar to those preserved in CV–CO chondrites’ C/N values. This is tested in Fig. 7, where the accreted volatiles are CV–CO-like and the
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** The effect of the degree of N depletion in precursor bodies on the *k*−*l* solution space matching the three observables (C/N ratio, C and N contents) in Earth's mantle. Model parameters are identical to those used for Fig. 7, with varying building block compositions for volatiles (cf. Fig. 8b, details in the main text).</figcaption></figure>

mantle observables can be reproduced simultaneously with low degrees of atmospheric loss (Fig. 7d).

Based on the Hf-W systematics, it is generally constrained that ~40% of Earth's core formed in equilibrium with the mantle (Rudge et al., 2010; Fischer and Nimmo, 2018). This corresponds to *k* = 0.4 and *l* = 0.01 in the solution space that satisfies the observed C/N ratio, C and N concentrations in the silicate Earth (Fig. 7d). For a bulk silicate Earth containing 140–506 ppm C (Hirschmann, 2018; Marty et al., 2020), the model predicts C content of the core to be 0.05–0.20 wt%, in agreement with recent estimations of at most 0.09(4) to 0.20(10) wt% (Fischer et al., 2020) and 0.13(3) wt% (Blanchard et al., 2022). Similarly, for a BSE with 2.8(6) ppm N (Hirschmann, 2018), our model predicts that Earth's core would contain 3–15 ppm N.

In Fig. 8b, using the same model parameters as in Fig. 7, with *k* and *l* fixed at one of the best-fit values (i.e. *k* = 0.4 and *l* = 0.01, see Fig. 7), we show that Earth's building blocks need to be depleted in N relative to the CI chondrite, in order to reproduce the observed N deficit in the BSE. Furthermore, should Earth's precursor bodies be more depleted in N, it increasingly lessens the need for invoking higher degrees of core–mantle disequilibrium and atmospheric loss. This is evident in Fig. 9, as the *k*−*l* solution space, for reproducing the C/N ratio, C and N contents in the BSE, shifts upward (i.e. higher levels of core–mantle equilibrium) and leftward (i.e. lower degrees of atmospheric loss) with increasing degrees of N depletion in the accreted materials. The lost mass fraction of the atmosphere *l* estimated here ranges from 0 to ~10%, which appears to be consistent with a scaling law from recent impact simulations (e.g. Kegerreis et al., 2020); however, while the scaling law has been shown to hold for impactor masses down to 5% of Earth's mass (*M*⊕), its validity for smaller bodies, e.g. 1% *M*⊕ in our case, remains unclear.

### 4.4. Constrains from mantle C/S ratio and isotope systematics

The C/S ratio is another useful indicator of early fractionation processes affecting the Earth's volatile element budget (e.g. Hirschmann, 2016). It is noteworthy that our model successfully reproduces not only the C/N, but also C/S ratios of the observable Earth (the BSE), if accreting CV–CO-like building blocks (Fig. S6). Early (~1 Myr) vapour loss/volatile depletion on planetesimals/pebbles has been proposed based on emerging evidence, in order to establish Earth's volatile inventory (e.g. Hin et al., 2017; Sossi et al., 2019; Lichtenberg et al., 2021). Still considering a fiducial CI-chondrite model for the Earth, our results allow one to estimate the degree of volatile depletion that affected its precursor bodies, in order to reproduce the observed C, N and S budgets in the bulk Earth (Table 3). A bulk Earth containing 707 ppm C is consistent with earlier and recent estimates of 730 ppm (Mcdonough, 2003) and 370–740 ppm (Fischer et al., 2020), based on cosmochemical and mineral physics arguments, respectively. This corresponds to, at

most, ~2% CI-chondrite contribution to the bulk Earth, as established by carbon, water and noble gases contents in the BSE (Marty, 2012); or equivalently, in the current context, substantial (98%) C loss/depletion on Earth's precursors, as suggested by an early inward migration of the soot line (i.e. carbon sublimation front) (Li et al., 2021) and the dehydration of inward-drifting pebbles (Lichtenberg et al., 2021). On the other hand, a bulk Earth with 3000 ppm S (i.e. CV–CO-like, Table 3) agrees with its partitioning behaviour under Earth's core-forming conditions (Suer et al., 2017), and indicates increasing degrees of devolatilization of S relative to C and N. The greater extent of C loss relative to S on planetesimals, inferred from reconstruction of iron meteorites' parent bodies (Hirschmann et al., 2021), corroborates early vaporization processes that led to the low C/S ratio in CV–CO chondrites (Marty et al., 2020).

The preferential depletion processes occurring on precursor bodies is further substantiated by terrestrial isotopic signatures. For instance, Earth's sulphur isotope values may be explained by our deduced 94% S loss on Earth's precursors, if sulphur evaporates mainly as H₂S (Wang et al., 2021). Although hydrogen isotopic compositions in mantle-derived samples suggest volatile contribution from both protosolar nebular and enstatite-like components (Hallis et al., 2015; Piani et al., 2020), both H and N isotopes measured in CV–CO chondrites lie between Earth's surface and mantle endmembers and are consistent with enstatite chondrites (Piani et al., 2020). As shown by recent N fractionation experiments (Shi et al., 2022), Earth's N isotopic compositions can be chiefly described by the accretion of enstatite- and thus CV–CO-like materials, owing to their above-mentioned isotopic similarity. The *ad hoc* assumption of a late veneer delivery with ~0.5% Earth mass' chondritic material (e.g. Wang and Becker, 2013) is not required by the early vaporization scenario, but is mutually compatible, if the late accreted material experienced similar degrees of volatile loss as recorded by the C-N-S patterns of CV–CO chondrites.

### 5. Conclusions

Superliquidus metal–silicate partitioning experiments have been performed on nitrogen in laser-heated diamond anvil cells under high P-T conditions up to 104 GPa and 5000 K. When combined with available literature data, the extended dataset covers pressures (1–104 GPa), temperatures (1523–4980 K) and *f*O₂ (IW-8–IW-0.8) pertinent to core formation in a magma ocean on Earth-sized planets. Under these extreme conditions in deep magma oceans envisaged to follow giant impacts, we find that O solubility in the metal, favoured at high temperatures, markedly reduces the siderophile character of N. Among the five most favoured light-element candidates in Earth's core (viz. Si, O, C, S and H), the amounts of the former four elements dissolved in the metal have been revealed to invariably make N less siderophile, with their effects follow the sequence of O>Si>C>S on
a molar basis. Apart from the well-defined positive effect of fO₂ on Dₙ, increasing temperature reduces the siderophily of N, whereas the effect of pressure is determined to be statistically insignificant, potentially due to the strong correlation with temperature and the minimal dependence of N speciation on pressure (Huang et al., 2022a).

Applying our results to a single-stage core formation model, we find that N remains siderophile, making the core its largest reservoir, notwithstanding that the simultaneous dissolution of oxygen in the core lowers that of nitrogen. However, this does not reproduce the observed N abundance in the mantle. Further combining the high-pressure partitioning behaviour of N with the simultaneous outgassing of magma oceans, our multi-stage core–mantle–atmosphere coevolution model shows that neither core formation nor atmospheric loss is capable of reproducing the N deficit observed in the BSE. This implies that Earth’s building blocks may have experienced the loss of N relative to CI chondrites. If terrestrial precursor bodies experienced volatile depletion akin to that observed in CV–CO chondrites, the vast majority of N (>99%) would have been lost on the precursors before their arrival to the proto-Earth, making N the most depleted among C, N and S (Table 3). Early vaporization/depletion processes that fractionate N from C, and further from S, together with core formation and the limited atmospheric loss on the Earth, set the terrestrial C-N-S budget, from which our planet eventually develops into a habitable world.

### CRediT authorship contribution statement

**Dongyang Huang:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Julien Siebert:** Writing – review & editing, Methodology, Investigation, Conceptualization. **Paolo Sossi:** Writing – review & editing, Methodology. **Edith Kubik:** Writing – review & editing, Investigation. **Guillaume Avice:** Investigation. **Motohiko Murakami:** Investigation.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data are available through Mendeley Data at https://doi.org/10.17632/tyc7x24vbx.1.

### Acknowledgements

We are grateful to James Badro for help with experiments; Nicolas Rividi for assistance with microprobe analysis. We thank Colin Jackson and two anonymous reviewers for their constructive comments and Fabrice Gaillard for handling this manuscript. J.S. and D.H. acknowledge support from the French National Research Agency (ANR project VolTerre, Grant ANR-14-CE33-0017-01). We also acknowledge funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (Grant 101019965–SEPtIM). P.S. was supported by the Swiss National Science Foundation (SNSF) through an Eccellenza Professorship (203668) and the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract No. MB22.00033, a SERI-funded ERC starting grant “2ATMO”. G.A. is supported by funding from the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation program (grant agreement no. 101041122).

## Appendix A. Supplementary material

Supplementary materials provide (i) a PDF file that contains information related to the valence of nitrogen in silicate melts resolved at mantle pressures over a broad range of redox conditions (Fig. S1), residuals of the OLS fit for Eq. 1 (Fig. S2), distribution of N as a function of oxygen solubility in the core and temperature in the canonical CI-like Earth model with an Si-poor or Si-rich core (Figs. S3–S4), disequilibrium model output during core formation with atmospheric loss, assuming a CI-like bulk Earth composition (Fig. S5), core–mantle–atmosphere coevolution model output reproducing mantle C and S concentrations (Fig. S6), and references therein; (ii) a spreadsheet that includes Energy-dispersive X-ray spectroscopy (EDS) results for starting materials (Table S1), Wavelength-dispersive X-ray spectroscopy (WDS) results (Table S2) for metal and silicate recovered from high pressures and temperatures, fitting parameters for Eq. 1 with or without 1 wt% carbon assumed in metal liquids (Table S3), EDS results for recovered metal and silicate (Table S4), N partitioning data employed for parameterization (Table S5), and covariances of the fitted regression using Eq. 1 (Table S6).

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.gca.2024.05.010.

### References

Akahama, Y., Kawamura, H., 2004. High-pressure Raman spectroscopy of diamond anvils to 250 GPa: Method for pressure determination in the multimegabar pressure range. J. Appl. Phys. 96 (7), 3748–3751. http://dx.doi.org/10.1063/1.1778482.

Alexander, C.M.O., Bowden, R., Fogel, M.L., Howard, K.T., Herd, C.D.K., Nitler, L.R., 2012. The provenances of asteroids, and their contributions to the volatile inventories of the terrestrial planets. Science 337 (6095), 721–723. http://dx.doi.org/10.1126/science.1223474, arXiv:https://www.science.org/doi/pdf/10.1126/science.1223474, URL https://www.science.org/doi/abs/10.1126/science.1223474.

Andrault, D., Bolfan-Casanova, N., Nigro, G.L., Bouhifd, M.A., Garbarino, G., Mezouar, M., 2011. Solidus and liquidus profiles of chondritic mantle: Implication for melting of the Earth across its history. Earth Planet. Sci. Lett. 304 (1–2), 251–259. http://dx.doi.org/10.1016/j.epsl.2011.02.006.

Armstrong, K., Frost, D.J., McCammon, C.A., Rubie, D.C., Boffa Ballaran, T., 2019. Deep magma ocean formation set the oxidation state of Earth’s mantle. Science 365 (6456), 903–906. http://dx.doi.org/10.1126/science.aax8376, arXiv:https://science.sciencemag.org/content/365/6456/903.full.pdf, URL https://science.sciencemag.org/content/365/6456/903.

Badro, J., Brodholt, J.P., Piet, H., Siebert, J., Ryerson, F.J., 2015. Core formation and core composition from coupled geochemical and geophysical constraints. Proc. Natl. Acad. Sci. USA 112 (40), 12310–12314. http://dx.doi.org/10.1073/pnas.1505672112, URL http://www.pnas.org/content/112/40/12310 abstract.

Badro, J., Cote, A.S., Brodholt, J.P., 2014. A seismologically consistent compositional model of Earth’s core. Proc. Natl. Acad. Sci. 111 (21), 7542–7545. http://dx.doi.org/10.1073/pnas.1316708111, URL http://www.pnas.org/cgi/doi/10.1073/pnas.1316708111.

Badro, J., Siebert, J., Nimmo, F., 2016. An early geodynamo driven by exsolution of mantle components from Earth’s core. Nature 536 (7616), 326–328. http://dx.doi.org/10.1017/CBO9781107415324.004.

Bajgain, S.K., Mookherjee, M., Dasgupta, R., Ghosh, D.B., Karki, B.B., 2019. Nitrogen content in the earth’s outer core. Geophys. Res. Lett. 46 (1), 89–98. http://dx.doi.org/10.1029/2018GL080555.

Benedetti, L.R., Loubeyre, P., 2004. Temperature gradients, wavelength-dependent emissivity, and accuracy of high and very-high temperatures measured in the laser-heated diamond cell. High Press. Res. 24 (4), 423–445. http://dx.doi.org/10.1080/0895795041233133718.

Bergin, E.A., Blake, G.A., Ciesla, F., Hirschmann, M.M., Li, J., 2015. Tracing the ingredients for a habitable earth from interstellar space through planet formation. Proc. Natl. Acad. Sci. 112 (29), 8965–8970. http://dx.doi.org/10.1073/pnas.1500954112, arXiv:https://www.pnas.org/doi/pdf/10.1073/pnas.1500954112, URL https://www.pnas.org/doi/abs/10.1073/pnas.1500954112.

Birch, F., 1964. Density and composition of mantle and core. J. Geophys. Res. 69 (20), 4377–4388. http://dx.doi.org/10.1029/JZ069i020p04377, URL http://doi.wiley.com/10.1029/JZ069i020p04377.

Blanchard, I., Rubie, D., Jennings, E., Franchi, I., Zhao, X., Petitgirard, S., Miyajima, N., Jacobson, S., Morbidelli, A., 2022. The metal–silicate partitioning of carbon during Earth’s accretion and its distribution in the early solar system. Earth Planet. Sci. Lett. 580, 117374. http://dx.doi.org/10.1016/j.epsl.2022.117374, URL https://www.sciencedirect.com/science/article/pii/S0012821X22000103.
Bouliung, J., Füri, E., Dalou, C., Tissandier, L., Zimmermann, L., Marrocchi, Y., 2020. Oxygen fugacity and melt composition controls on nitrogen solubility in silicate melts. Geochim. Cosmochim. Acta 284, 120–133. http://dx.doi.org/10.1016/j.gca.2020.06.020.

Bourdon, B., Roskosz, M., Hin, R.C., 2018. Isotope tracers of core formation. Earth-Sci. Rev. 181 (November 2017), 61–81. http://dx.doi.org/10.1016/j.earscirev.2018.04.006.

Bower, D.J., Hakim, K., Sossi, P.A., Sanan, P., 2022. Retention of water in terrestrial magma oceans and carbon-rich early atmospheres. Planet. Sci. J. 3 (4), 93.

Braukmüller, N., Wombacher, F., Funk, C., Münker, C., 2019. Earth's volatile element depletion pattern inherited from a carbonaceous chondrite-like source. Nat. Geosci. 12 (7), 564–568. http://dx.doi.org/10.1038/s41561-019-0375-x.

Chen, H., Jacobson, S.A., 2022. Impact induced atmosphere-mantle exchange sets the volatile elemental ratios on primitive Earths. Earth Planet. Sci. Lett. 594, 117741. http://dx.doi.org/10.1016/j.epsl.2022.117741, arXiv:2207.13087, https://linkinghub.elsevier.com/retrieve/pii/S0012821X22003776.

Dalou, C., Füri, E., Deligny, C., Piani, L., Caumon, M.-C., Laumonier, M., Bouliung, J., Edén, M., 2019a. Redox control on nitrogen isotope fractionation during planetary core formation. Proc. Natl. Acad. Sci. 116 (29), 14485–14494. http://dx.doi.org/10.1073/pnas.182079116, arXiv:https://www.pnas.org/doi/pdf/10.1073/pnas.182079116, URL https://www.pnas.org/doi/abs/10.1073/pnas.182079116.

Dalou, C., Hirschmann, M.M., Jacobsen, S.D., Le Losq, C., 2019b. Raman spectroscopy study of C-O-H-N speciation in reduced basaltic glasses: Implications for reduced planetary mantles. Geochim. Cosmochim. Acta 265, 32–47. http://dx.doi.org/10.1016/j.gca.2019.08.029.

Dalou, C., Hirschmann, M.M., von der Handt, A., Mosenfelder, J., Armstrong, L.S., 2017. Nitrogen and carbon fractionation during core-mantle differentiation at shallow depth. Earth Planet. Sci. Lett. 458, 141–151. http://dx.doi.org/10.1016/j.epsl.2016.10.026, URL https://www.sciencedirect.com/science/article/pii/S0012821X16305830.

Deng, J., Du, Z., Karki, B.B., Ghosh, D.B., Lee, K.K.M., 2020. A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nature Commun. 11 (1), 2007. http://dx.doi.org/10.1038/s41467-020-15757-0, http://www.nature.com/articles/s41467-020-15757-0.

Dixon, J.E., Stolper, E.M., Holloway, J.R., 1995. An experimental study of water and carbon dioxide solubilities in mid-ocean ridge basaltic liquids. Part II: Applications to degassing. J. Petrol. 3, http://dx.doi.org/10.1093/oxfordjournals.petrology.a037268.

Fiquet, G., Auzende, A.L., Siebert, J., Corgne, A., Bureau, H., Ozawa, H., Garbarino, G., 2010. Melting of peridotite to 140 gigapascals. Science 329 (5998), 1516–1518. http://dx.doi.org/10.1126/science.1192448, URL http://www.sciencemag.org/cgi/doi/10.1126/science.1192448.

Fischer, R.A., Cottrell, E., Hauri, E., Lee, K.K.M., Le Voyer, M., 2020. The carbon content of earth and its core. Proc. Natl. Acad. Sci. 117 (16), 8743–8749. http://dx.doi.org/10.1073/pnas.1919930117, arXiv:https://www.pnas.org/content/117/16/8743.full.pdf, URL https://www.pnas.org/content/117/16/8743.

Fischer, R.A., Nakajima, Y., Campbell, A.J., Frost, D.J., Harries, D., Langenhorst, F., Miyajima, N., Pollok, K., Rubie, D.C., 2015. High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O. Geochim. Cosmochim. Acta 167, 177–194. http://dx.doi.org/10.1016/j.gca.2015.06.026.

Fischer, R.A., Nimmo, F., 2018. Effects of core formation on the Hf-W isotopic composition of the Earth and dating of the Moon-forming impact. Earth Planet. Sci. Lett. 499, 257–265. http://dx.doi.org/10.1016/j.epsl.2018.07.030, URL https://linkinghub.elsevier.com/retrieve/pii/S0012821X18304369.

Gaillard, F., Bernadou, F., Roskosz, M., Bouhifd, M.A., Marrocchi, Y., Iacon Marziano, G., Moreira, M., Scaillet, B., Rogerie, G., 2022. Redox controls during magma ocean degassing. Earth Planet. Sci. Lett. 577, 117255. http://dx.doi.org/10.1016/j.epsl.2021.117255, URL https://www.sciencedirect.com/science/article/pii/S0012821X21005112.

Genda, H., Abe, Y., 2005. Enhanced atmospheric loss on protoplanets at the giant impact phase in the presence of oceans. Nature 433 (7028), 842–844. http://dx.doi.org/10.1038/nature03360.

Grewal, D.S., Asimow, P.D., 2023. Origin of the superchondritic carbon/nitrogen ratio of the bulk silicate earth – an outlook from iron meteorites. Geochim. Cosmochim. Acta 344, 146–159. http://dx.doi.org/10.1016/j.gca.2023.01.012, URL https://www.sciencedirect.com/science/article/pii/S0016703723000285.

Grewal, D.S., Dasgupta, R., Holmes, A.K., Costin, G., Li, Y., Tsuno, K., 2019a. The fate of nitrogen during core-mantle separation on Earth. Geochim. Cosmochim. Acta 251, 87–115. http://dx.doi.org/10.1016/j.gca.2019.02.009, URL https://www.sciencedirect.com/science/article/pii/S0016703719300869.

Grewal, D.S., Dasgupta, R., Hough, T., Farnell, A., 2021. Rates of protoplanetary accretion and differentiation set nitrogen budget of rocky planets. Nat. Geosci. 14 (6), 369–376. http://dx.doi.org/10.1038/s41561-021-00733-0.

Grewal, D.S., Dasgupta, R., Sun, C., Tsuno, K., Costin, G., 2019b. Delivery of carbon, nitrogen, and sulfur to the silicate Earth by a giant impact. Sci. Adv. 5 (1), http://dx.doi.org/10.1126/sciadv.aau3669, arXiv:https://advances.sciencemag.org/content/5/1/eaau3669-full.pdf, URL https://advances.sciencemag.org/content/5/1/eaau3669.

Grewal, D.S., Sun, T., Aithala, S., Hough, T., Dasgupta, R., Yeung, L.Y., Schauble, E.A., 2022. Limited nitrogen isotopic fractionation during core-mantle differentiation in rocky protoplanets and planets. Geochim. Cosmochim. Acta 338, 347–364. http://dx.doi.org/10.1016/j.gca.2022.10.025, URL https://www.sciencedirect.com/science/article/pii/S0016703722005658.

Halliday, A.N., 2013. The origins of volatiles in the terrestrial planets. Geochim. Cosmochim. Acta 105, 146–171. http://dx.doi.org/10.1016/j.gca.2012.11.015, URL https://www.sciencedirect.com/science/article/pii/S0016703712006680.

Hallis, L.J., Huss, G.R., Nagashima, K., Taylor, G.J., Halldórsson, S.A., Hilton, D.R., Mottl, M.J., Meech, K.J., 2015. Evidence for primordial water in Earth's deep mantle. Science 350 (6262), 795–797. http://dx.doi.org/10.1126/science.aac4834, arXiv:https://www.science.org/pdf/10.1126/science.aac4834, URL https://www.science.org/doi/abs/10.1126/science.aac4834.

Hin, R.C., Coath, C.D., Carter, P.J., Nimmo, F., Lai, Y.-J., Pogge von Strandmann, P.A.E., Willbold, M., Leinhardt, Z.M., Walter, M.J., Elliott, T., 2017. Magnesium isotope evidence that accretional vapour loss shapes planetary compositions. Nature 549 (7673), 511–515. http://dx.doi.org/10.1038/nature23899.

Hirose, K., Wood, B., Vočadlo, L., 2021. Light elements in the Earth's core. Nat. Rev. Earth Environ. 2 (9), 645–658. http://dx.doi.org/10.1038/s43017-021-00203-6.

Hirschmann, M.M., 2016. Constraints on the early delivery and fractionation of Earth's major volatiles from C/H, C/N, and C/S ratios. Am. Mineral. 101 (3), 540–553. http://dx.doi.org/10.2138/am-2016-5452.

Hirschmann, M.M., 2018. Comparative deep Earth volatile cycles: The case for C recycling from exosphere / mantle fractionation of major (H2O, C, N) volatiles and from H2O/Ce, CO2/Ba, and CO2/Nb exosphere ratios. Earth Planet. Sci. Lett. 1, 1–12. http://dx.doi.org/10.1016/j.epsl.2018.08.023.

Hirschmann, M.M., Bergin, E.A., Blake, G.A., Ciesla, F.J., Li, J., 2021. Early volatile depletion on planetesimals inferred from C-S systematics of iron meteorite parent bodies. Proc. Natl. Acad. Sci. 118 (13), e2062779118. http://dx.doi.org/10.1073/pnas.2026779118, arXiv:https://www.pnas.org/doi/pdf/10.1073/pnas.2026779118, URL https://www.pnas.org/doi/abs/10.1073/pnas.2026779118.

Huang, D., Badro, J., 2018. Fe-Ni ideality during core formation on Earth. Am. Mineral. 103 (10), 1701–1710. http://dx.doi.org/10.2138/am-2018-6651.

Huang, D., Badro, J., Siebert, J., 2020. The niobium and tantalum concentration in the mantle constrains the composition of Earth's primordial magma ocean. Proc. Natl. Acad. Sci. 117 (45), 27893–27898. http://dx.doi.org/10.1073/pnas.2007982117, URL https://www.pnas.org/content/117/45/27893.

Huang, D., Brodholt, J., Sossi, P., Li, Y., Murakami, M., 2022a. Nitrogen speciation in silicate melts at mantle conditions from Ab initio simulations. Geophys. Res. Lett. 49 (7), http://dx.doi.org/10.1029/2021GL095546, URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021GL095546, e2021GL095546 2021GL095546.

Huang, D., Li, Y., Khan, A., Sossi, P., Giardini, D., Murakami, M., 2023. Thermoelastic properties of liquid fer-rich alloys under martian core conditions. Geophys. Res. Lett. 50 (6), http://dx.doi.org/10.1029/2022GL012271, arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2022GL012271, URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022GL012271, e2022GL012271 2022GL012271.

Huang, D., Murakami, M., Brodholt, J., McCammon, C., Petitgirard, S., 2022b. Structural evolution in a pyrolitic magma ocean under mantle conditions. Earth Planet. Sci. Lett. 584, 117473. http://dx.doi.org/10.1016/j.epsl.2022.117473, URL https://www.sciencedirect.com/science/article/pii/S0012821X22001091.

Huang, D., Siebert, J., Badro, J., 2021. High pressure partitioning behavior of Mo and W and late sulfur delivery during Earth's core formation. Geochim. Cosmochim. Acta 310, 19–31. http://dx.doi.org/10.1016/j.gca.2021.06.031, URL https://www.sciencedirect.com/science/article/pii/S0016703721003896.

Jackson, C.R.M., Cottrell, E., Du, Z., Bennett, N.R., Fei, Y., 2021. High pressure redistribution of nitrogen and sulfur during planetary stratification. Geochem. Perspect. Lett. 18, 37–42. http://dx.doi.org/10.7185/geochemlet.2122, URL http://www geochemicalperspectivesletters.org/article2122.

Jennings, E.S., 2020. Using complementary microanalytical techniques to analyse diamond anvil cell experiments. IOP Conf. Ser.: Mater. Sci. Eng. 891 (1), 012015. http://dx.doi.org/10.1088/1757-899X/891/1/012015.

Johnson, B., Goldblatt, C., 2015. The nitrogen budget of Earth. Earth-Sci. Rev. 148, 150–173. http://dx.doi.org/10.1016/j.earscirev.2015.05.006, URL https://www.sciencedirect.com/science/article/pii/S0012825215000896.

Kadik, A.A., Kurovskaya, N.A., Ignat'ev, Y.A., Kononkova, N.N., Koltashev, V.V., Plotnichenko, V.G., 2011. Influence of oxygen fugacity on the solubility of nitrogen, carbon, and hydrogen in FeO-Na2O-SiO2-Al2O3 melts in equilibrium with metallic iron at 1.5 GPa and 1400°C. Geochem. Int. 49, 429–438.

Kegerreis, J.A., Eke, V.R., Catling, D.C., Massey, R.J., Teodoro, L.F.A., Zahnle, K.J., 2020. Atmospheric erosion by giant impacts onto terrestrial planets: A scaling law for any speed, angle, mass, and density. Astrophys. J. Lett. 901 (2), L31. http://dx.doi.org/10.3847/2041-8213/abb5fb.

Kerridge, J.F., 1985. Carbon, hydrogen and nitrogen in carbonaceous chondrites: Abundances and isotopic compositions in bulk samples. Geochim. Cosmochim. Acta 49 (8), 1707–1714. http://dx.doi.org/10.1016/0016-7037(85)90141-3, URL https://www.sciencedirect.com/science/article/pii/S0016703785901413.
Li, J., Bergin, E.A., Blake, G.A., Ciesla, F.J., Hirschmann, M.M., 2021. Earth's carbon deficit caused by early loss through irreversible sublimation. Sci. Adv. 7 (14), eabd3632. http://dx.doi.org/10.1126/sciadv.abd3632, arXiv:https://www.science.org/doi/pdf/10.1126/sciadv.abd3632, URL https://www.science.org/doi/abs/10.1126/sciadv.abd3632.

Li, Y., Marty, B., Shcheka, S., Zimmermann, L., Keppler, H., 2016. Nitrogen isotope fractionation during terrestrial core-mantle separation. Geochem. Perspect. Lett. 2, 138–147. http://dx.doi.org/10.7185/geochemlet.1614, URL https://www geochemperspectivesletters.org/article1614.

Li, Y., Wiedenbeck, M., Monteleone, B., Dasgupta, R., Costin, G., Gao, Z., Lu, W., 2023. Nitrogen and carbon fractionation in planetary magma oceans and origin of the superchondritic C/N ratio in the bulk silicate Earth. Earth Planet. Sci. Lett. 605, 118032. http://dx.doi.org/10.1016/j.epsl.2023.118032.

Libourel, G., Marty, B., Humbert, F., 2003. Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity. Geochim. Cosmochim. Acta 67 (21), 4123–4135. http://dx.doi.org/10.1016/S0016-7037(03)00259-X.

Lichtenberg, T., Drązkowska, J., Schönbächler, M., Golabek, G.J., Hands, T.O., 2021. Bifurcation of planetary building blocks during Solar System formation. Science 371 (6527), 365–370. http://dx.doi.org/10.1126/science.abb3091, arXiv:2101.08571, URL https://www.science.org/doi/10.1126/science.abb3091.

Lodders, K., 2003. Solar system abundances and condensation temperatures of the elements. Astrophys. J. 591 (2), 1220. http://dx.doi.org/10.1086/375492.

Marty, B., 2012. The origins and concentrations of water, carbon, nitrogen and noble gases on Earth. Earth Planet. Sci. Lett. 313–314 (1), 56–66. http://dx.doi.org/10.1016/j.epsl.2011.10.040.

Marty, B., Almayrac, M., Barry, P.H., Bekaert, D.V., Broadley, M.W., Byrne, D.J., Ballentine, C.J., Caracausi, A., 2020. An evaluation of the C/N ratio of the mantle from natural CO2-rich gas analysis: Geochemical and cosmochemical implications. Earth Planet. Sci. Lett. 551, 116574. http://dx.doi.org/10.1016/j.epsl.2020.116574.

Mcdonough, W.F., 2003. Compositional model for the Earth's core. Treatise Geochem. 2, 547–568. http://dx.doi.org/10.1016/B0-08-043751-6/02015-6.

Mcdonough, W., Sun, S.-s., 1995. The composition of the Earth. Chem. Geol. 120 (3), 223–253. http://dx.doi.org/10.1016/0009-2541(94)00140-4, URL http://www.sciencedirect.com/science/article/pii/0009254194001404.

Nakajima, M., Stevenson, D.J., 2015. Melting and mixing states of the Earth's mantle after the Moon-forming impact. Earth Planet. Sci. Lett. 427, 286–295. http://dx.doi.org/10.1016/j.epsl.2015.06.023, URL https://www.sciencedirect.com/science/article/pii/S0012821X15003805.

Pearson, V.K., Sephton, M.A., Franchi, I.A., Gibson, J.M., Gilmour, I., 2006. Carbon and nitrogen in carbonaceous chondrites: Elemental abundances and stable isotopic compositions. Meteorit. Planet. Sci. 41 (12), 1899–1918. http://dx.doi.org/10.1111/j.1945-5100.2006.tb00459.x, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1945-5100.2006.tb00459.x, URL https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1945-5100.2006.tb00459.x.

Piani, L., Marrocchi, Y., Rigaudier, T., Vacher, L.G., Thomassin, D., Marty, B., 2020. Earth's water may have been inherited from material similar to enstatite chondrite meteorites. Science 369 (6507), 1110–1113. http://dx.doi.org/10.1126/science.aba1948, http://www.ncbi.nlm.nih.gov/pubmed/32855337, https://www.sciencemag.org/lookup/doi/10.1126/science.aba1948.

Roskos, M., Bouhifd, M.A., Jephcoat, A.P., Marty, B., Mysen, B.O., 2013. Nitrogen solubility in molten metal and silicate at high pressure and temperature. Geochim. Cosmochim. Acta 121, 15–28. http://dx.doi.org/10.1016/j.gca.2013.07.007.

Rubie, D.C., Jacobson, S.A., Morbidelli, A., Brien, D.P.O., Young, E.D., Vries, J.D., Nimmo, F., Palme, H., Frost, D.J., 2015. Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed Solar System bodies and accretion of water. ICARUS 248, 89–108. http://dx.doi.org/10.1016/j.icarus.2014.10.015.

Rubie, D.C., Melosh, H.J., Reid, J.E., Liebske, C., Righter, K., 2003. Mechanisms of metal-silicate equilibration in the terrestrial magma ocean. Earth Planet. Sci. Lett. 205, 239–255.

Rudge, J.F., Kleine, T., Bourdon, B., 2010. Broad bounds on Earths accretion and core formation constrained by geochemical models. Nat. Geosci. 3 (6), 439–443. http://dx.doi.org/10.1038/ngeo872.

Schönbächler, M., Carlson, R.W., Horan, M.F., Mock, T.D., Hauri, E.H., 2010. Heterogeneous accretion and the moderately volatile element budget of earth. Science 328 (5980), 884–887. http://dx.doi.org/10.1126/science.1186239, arXiv:https://science.sciencemag.org/content/328/5980/884.full.pdf, URL https://science.sciencemag.org/content/328/5980/884.

Shi, L., Lu, W., Kagoshima, T., Sano, Y., Gao, Z., Du, Z., Liu, Y., Fei, Y., Li, Y., 2022. Nitrogen isotope evidence for Earth's heterogeneous accretion of volatiles. Nature Commun. 13 (1), 4769. http://dx.doi.org/10.1038/s41467-022-32516-5, URL https://www.nature.com/articles/s41467-022-32516-5.

Siebert, J., Badro, J., Antonangeli, D., Ryerson, F.J., 2012. Metal-silicate partitioning of Ni and Co in a deep magma ocean. Earth Planet. Sci. Lett. 321–322, 189–197. http://dx.doi.org/10.1016/j.epsl.2012.01.013.

Siebert, J., Badro, J., Antonangeli, D., Ryerson, F.J., 2013. Terrestrial accretion under oxidizing conditions. Science 339 (6124), 1194–1197. http://dx.doi.org/10.1126/science.1227923.

Sossi, P.A., Burnham, A.D., Badro, J., Lanzirotti, A., Newville, M., O'Neill, H.S., 2020. Redox state of Earth's magma ocean and its Venus-like early atmosphere. Sci. Adv. 6 (48), http://dx.doi.org/10.1126/sciadv.abd1387, arXiv:https://advances.sciencemag.org/content/6/48/eabd1387.full.pdf, URL https://advances.sciencemag.org/content/6/48/eabd1387.

Sossi, P.A., Klemme, S., O'Neill, H.S., Berndt, J., Moynier, F., 2019. Evaporation of moderately volatile elements from silicate melts: experiments and theory. Geochim. Cosmochim. Acta 260, 204–231. http://dx.doi.org/10.1016/j.gca.2019.06.021, URL https://www.sciencedirect.com/science/article/pii/S0016703719303606.

Speelmanns, I.M., Schmidt, M.W., Liebske, C., 2018. Nitrogen solubility in core materials. Geophys. Res. Lett. 45 (15), 7434–7443. http://dx.doi.org/10.1029/2018GL079130.

Speelmanns, I.M., Schmidt, M.W., Liebske, C., 2019. The almost lithophile character of nitrogen during core formation. Earth Planet. Sci. Lett. 510, 186–197. http://dx.doi.org/10.1016/j.epsl.2019.01.004.

Suer, T.-a., Siebert, J., Remusat, L., Menguy, N., Fiquet, G., 2017. A sulfur-poor terrestrial core inferred from metal-silicate partitioning experiments. Earth Planet. Sci. Lett. 469, 84–97. http://dx.doi.org/10.1016/j.epsl.2017.04.016, URL http://linkinghub.elsevier.com/retrieve/pii/S0012821X17301954.

Takahashi, E., 1986. Melting of a dry peridotite KLB-1 up to 14 GPa: Implications on the Origin of peridotitic upper mantle. J. Geophys. Res. 91 (B9), 9367. http://dx.doi.org/10.1029/JB091iB09p09367, URL http://doi.wiley.com/10.1029/JB091iB09p09367.

Wang, Z., Becker, H., 2013. Ratios of S, Se and Te in the silicate Earth require a volatile-rich late veneer. Nature 499 (7458), 328–331. http://dx.doi.org/10.1038/nature12285.

Wang, W., Li, C.-H., Brodholt, J.P., Huang, S., Walter, M.J., Li, M., Wu, Z., Huang, F., Wang, S.-J., 2021. Sulfur isotopic signature of Earth established by planetesimal volatile evaporation. Nat. Geosci. 14 (11), 806–811. http://dx.doi.org/10.1038/s41561-021-00838-6.

Wasson, J.T., Kallemeyn, G.W., 1988. Compositions of chondrites. Phil. Trans. R. Soc. A 325 (1587), 535–544. http://dx.doi.org/10.1098/rsta.1988.0066, URL http://rsta.royalsocietypublishing.org/cgi/doi/10.1098/rsta.1988.0066.

Yoshioka, T., Nakashima, D., Nakamura, T., Shcheka, S., Keppler, H., 2019. Carbon solubility in silicate melts in equilibrium with a CO-CO2 gas phase and graphite. Geochim. Cosmochim. Acta 259, 129–143. http://dx.doi.org/10.1016/j.gca.2019.06.007, URL https://www.sciencedirect.com/science/article/pii/S0016703719303461.