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# Rates of protoplanetary accretion and differentiation set nitrogen budget of rocky planets

## Abstract

The effect of protoplanetary differentiation on the fate of life-essential volatiles such as nitrogen and carbon and its subsequent effect on the dynamics of planetary growth is unknown. Because the dissolution of nitrogen in magma oceans depends on its partial pressure and oxygen fugacity, it is an ideal proxy to track volatile redistribution in protoplanets as a function of their sizes and growth zones. Using high-pressure/temperature experiments in graphite-undersaturated conditions, here we show that the siderophilic (iron-loving) character of nitrogen is an order of magnitude higher than previous estimates across a wide range of oxygen fugacity. The experimental data combined with metal–silicate–atmosphere fractionation models suggest that asteroid-sized protoplanets, and planetary embryos that grew from them, were nitrogen depleted. However, protoplanets that grew to planetary embryo size before undergoing differentiation had nitrogen-rich cores and nitrogen-poor silicate reservoirs. Bulk silicate reservoirs of large Earth-like planets obtained nitrogen from the cores of the latter type of planetary embryos. Therefore, to satisfy the volatile budgets of Earth-like planets during the main stage of their growth, the timescales of planetary embryo accretion had to be shorter than their differentiation timescales; that is, Moon- to Mars-sized planetary embryos grew rapidly within ~1–2 Myrs of the Solar System’s formation.

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## Data availability

The data supporting the findings of this study are available within the article and its Supplementary Information files. All new data associated with this paper will be made publicly available at https://doi.org/10.6084/m9.figshare.14191079.

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## Acknowledgements

The manuscript benefitted from constructive criticism from S. Mikhail. G. Costin is acknowledged for help with electron microprobe analyses. D.S.G. received support from NASA FINESST grant 80NSSC19K1538. NASA grants 80NSSC18K0828 and 80NSSC18K1314 to R.D. supported the work. D.S.G. acknowledges additional support from a Lodieska Stockbridge Vaughn Fellowship by Rice University.

## Author information

Authors

### Contributions

D.S.G. conceived and developed the central ideas presented in this study. R.D. helped in refining the ideas. D.S.G. and R.D. designed the experiments. T.H. and D.S.G. performed the experiments. A.F. performed the FTIR analyses. D.S.G. analysed the experiments and developed the models. D.S.G. and R.D. interpreted the data. D.S.G. wrote the manuscript with inputs from R.D.

### Corresponding author

Correspondence to Damanveer S. Grewal.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

Peer review information Nature Geoscience thanks Sami Mikhail and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Rebecca Neely.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Comparison of the silicate melt compositions of this study with previous studies as a function of oxygen fugacity.

Below IW–1.5 (fO2 range explored in this study), the silicate melt compositions of this study are more mafic, that is, have higher NBO/Ts, relative to the silicate melt compositions used to determine $$D_N^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ in previous studies. Therefore, the silicate melt compositions of this study are more representative of magma oceans of inner Solar System rocky planets. Primitive mantle compositions are used to estimate the magma ocean compositions of Earth60, Mars61 and Mercury62. NBO/T is a measure of degree of silicate melt polymerization and is expressed as total non-bridging oxygens per tetrahedral cations; NBO/T = (2 × Total O)/T – 4, where T = Si + Ti + Al + Cr + P). The calculated error bars for NBO/T represent ±1-σ deviation based on the replicate electron microprobe analyses and are smaller than the symbol sizes for all data from this study.

### Extended Data Fig. 2 Time series to determine the experimental duration necessary to reach equilibrium.

N contents in the (a) alloy and (b) silicate melts, and consequently (c) $$D_N^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ show no variation beyond the uncertainties of the measurements as a function of time for experiments conducted at 3 GPa and 1600 °C for 0.5, 2, 6, and 12 hours (Experiment numbers: X63, G634, X74, and G639). These demonstrate that N exchange between the two phases had attained equilibrium at less than 0.5 hours in our experimental conditions. Also, an almost unchanged N content in alloy and silicate melts with increase in time means that there was no loss of N from the alloy + silicate melt system with increase in experimental run time. d, NBO/T of the silicate melt compositions also show no variation with time beyond the uncertainties of the measurements, which illustrates that the silicate melt compositions had also reached steady state. All experiments were conducted with a fixed starting composition of alloy + silicate mixture (70%ThB1+30%Fe-5Ni-5N-17.5Si). Error bars in all panels are ±1-σ deviation based on replicate electron microprobe analyses and where absent the error bars are smaller than the symbol size.

### Extended Data Fig. 3 Thickness normalized FTIR spectra of the peaks associated with nitrogen species in the experimental silicate glasses of this study.

The only detectable, IR-active N-bearing peak was that of N-H stretching, marked by the grey band. No C-species were detectable.

### Extended Data Fig. 4 Carbon and nitrogen contents in the alloy melts as a function of oxygen fugacity.

a, C content in the alloy melt in graphite-undersaturated experiments of this study is substantially lower (0.11–0.80 wt.%) than the graphite-saturated experiments of the previous studies10,11,12,13,22,27. b, In agreement with previous studies in graphite-saturated conditions, N content in the alloy melt decreases with decrease in fO2 in graphite-undersaturated conditions. However, at any given fO2, N in graphite-undersaturated alloys is substantially greater than graphite-saturated alloys. $$D_N^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ for graphite-saturated alloys has been determined only in N-undersaturated conditions, therefore, N content in the alloys from only two previous studies10,11 was compared with the data from the present study because of similar N contents in the starting mixtures. Error bars represent ±1-σ deviation based on the replicate electron microprobe analyses; where absent, the error bars are smaller than the symbol size.

### Extended Data Fig. 5 $$D_N^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ as a function of oxygen fugacity and (a) silicon content in the alloy and (b) temperature.

a, In addition to the effect of fO2, when Si content in the alloy melt and FeO content in the silicate melt are coupled to each other, incorporation of Si into the alloy melt on its own has a strong negative effect on N content in the alloy at a similar logfO2 (~IW–4; here shown by grey rectangle). A similar effect has been observed in a previous study11 albeit at a higher logfO2 (~IW–2.5) because in graphite-saturated alloys, Si expels N from the alloy melt even at low concentrations (as low as 0.1 wt.% Si). b, In contrast to the observations of previous studies11,12 in graphite-saturated conditions, temperature does not have any discernible effect on $$D_N^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ in the limited temperature range explored in this study. Error bars represent ±1-σ deviation obtained by propagation of ±1-σ deviation on N content in the alloy and silicate melts; where absent, the error bars are smaller than the symbol size.

### Extended Data Fig. 6 Comparison between nitrogen content in the final products and starting mixtures.

Similar to the observation in all previous studies that estimated $$D_N^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ in graphite capsules10,11,12,13,22,27, the reconstructed N content in the final products of this study in MgO capsules is less than the N content in the starting mixture. Mass balance suggests that the extent of recovery of initial N content lies in the range of ~50–85%. Loss of N has been explained by the storage of N in the pores of the capsule walls or diffusive loss across the capsule wall11,12. Error bars represent ±1-σ deviation obtained by propagation of ±1-σ deviation on N content in the alloy and silicate melts; where absent, the error bars are smaller than the symbol size.

### Extended Data Fig. 7 Predicted $$D_{\mathrm{N}}^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ using the parametrization developed in this study and comparison between the $$D_{\mathrm{N}}^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ values predicted by this study and two previous studies.

a, Predicted $$D_{\mathrm{N}}^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ using the parametrization developed in this study plotted against experimentally determined $$D_{\mathrm{N}}^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ for Fe-Ni-N±C±S±Si alloy melt-silicate melt equilibration. ‘n’ represents the total number of experiments that were used to calibrate the parameterized equation in this study. Solid line represents 1:1 fit while the dashed lines represent error within a factor of 2. b, The predicted $$D_{\mathrm{N}}^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ values in C-free and graphite-undersaturated alloys, in agreement with the experimental data of this study, are an order of magnitude higher than the predicted $$D_{\mathrm{N}}^{{\mathrm{alloy}}/{\mathrm{silicate}}}$$ values of graphite-saturated alloys at logfO2> IW–5 and the gap between the predicted values decreases with decrease in fO2 (see Methods).

### Extended Data Fig. 8 The effects of (a) the extent of atmosphere retention after final-step of Earth’s accretion and (b) the extent of emulsification of the impactor’s core in the target’s magma ocean on N budget of the BSE.

For scenario 10 (as defined in Fig. 5a) and 50 ppm of accreted N, it can be seen that N budget of the present-day BSE can be satisfied for ~60–100 % of atmosphere retention on Earth after its final accretion event (a) and for ~50–100 % emulsification of the impactor’s core in the target’s MO (b) during every step of accretion. Lesser extent of final-stage atmospheric retention or lesser degree of emulsification of the impactor’s core would require higher amount of accreted N (>50 ppm) in the seed planetary embryos (here Mars-sized) to satisfy the N budget of the present-day BSE.

### Extended Data Fig. 9 Comparison between the calculated nitrogen solubility constants (SN) from this study and the fixed values used in previous studies.

The effective solubility constants for N vary with the size of protoplanetary bodies with variations in the range of an order of magnitude from a Vesta-sized to a Mars-sized protoplanet. Therefore, using a fixed solubility constant, as used in previous studies3,4,10 to calculate the solubilities of N in magma oceans for rocky bodies having different sizes can give erroneous results.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–3 and Tables 1–7.

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

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• DOI: https://doi.org/10.1038/s41561-021-00733-0

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