Earth’s core could be the largest terrestrial carbon reservoir

Earth’s core is predominantly iron but must contain lighter elements to match seismologically inferred density and velocities. Carbon is a prime light-element candidate due to its cosmochemical abundance and strong siderophile behavior under core-forming conditions, partitioning preferentially into Fe-rich metallic melts. Despite consensus on its siderophile nature, the extent of carbon’s partitioning into the core and its present-day abundance remain debated, with accretion and differentiation models yielding core carbon contents from roughly 0.1 to 3 wt.%. Given uncertainties in geochemical partitioning, core temperatures, and phase relations, an independent, physics-based constraint on the density and elastic properties of Fe–C liquids at core pressures and temperatures is needed to refine the Earth’s carbon budget and assess whether the core could be the largest terrestrial carbon reservoir.

Prior high-pressure experiments and geochemical models show carbon is highly soluble in Fe-rich melts and typically exhibits metal/silicate partition coefficients much greater than unity, though reported magnitudes vary widely depending on alloy composition (effects of Si, O, S, N) and conditions. Phase diagram studies of Fe–C suggest limited carbon content in the inner core (<1 wt.% C) and modest contents in the outer core (~1 wt.% C) but cannot fully reconcile inner-core density deficit without additional light elements. Seismological and thermodynamic analyses have inferred that if carbon were the only light element, ~1.5–2 wt.% C in the outer core could satisfy the observed density deficit at the inner-outer core boundary, yet such amounts often overpredict compressional wave speeds. The applicability of Birch’s law (linear Vp–ρ relation) at extreme P–T is debated; some experiments on solids suggest deviations, and FPMD studies indicate complexities for metallic liquids. Previous FPMD work explored Fe liquids with various light elements (S, O, C, H), but datasets were sparse, limiting robust thermal EOS development and multi-component mixing assessments. These gaps motivate systematic simulations of Fe–C liquids across outer-core P–T, evaluation of Birch’s law for liquids, and ternary mixing analyses including other candidate light elements (O, S, H, Si, N).

• Performed first-principles molecular dynamics (FPMD) simulations using VASP within density functional theory (PAW method, GGA-PBE functional). Plane-wave cutoff energy was 400 eV. Canonical ensemble simulations were conducted with appropriate Brillouin zone sampling and thermal controls; a small volume-dependent pressure correction was applied to account for PAW-related effects. Magnetic moments were considered in tests to assess their influence on liquid properties at relevant conditions.
• Simulated liquid Fe–C binary alloys with approximately 4–6 wt.% and ~9 wt.% dissolved carbon across pressures 0–360 GPa and temperatures 4000–7000 K, encompassing outer-core conditions. Computed pressure–density data were fit with a thermal equation of state (EOS), yielding reference densities, bulk moduli and their pressure derivatives at specified temperatures (see summarized values in Table 1 of the paper).
• Derived compressional wave velocities (Vp) from FPMD outputs using thermodynamic relations involving the Grüneisen parameter and isothermal compressibility (dP/dV)T. Assessed Vp(ρ,T) along multiple isotherms to test the validity of Birch’s law for metallic liquids.
• Constructed an outer-core geotherm assuming an adiabatic profile anchored at the inner-core boundary temperature (ICB) in the range ~5500–6300 K, implying CMB temperatures near ~4400 K; evaluated sensitivity to different T_ICB choices.
• Compared calculated ρ and Vp for Fe–C liquids with PREM values at CMB and ICB to infer required carbon contents if carbon were the sole light element.
• Extended analysis to ternary mixtures (Fe–C–LE) where LE = O, S, H, Si, or N, using linear compositional derivatives for density and velocity from this and prior studies, neglecting cross terms between light elements, to identify combinations that can simultaneously match PREM ρ and Vp at CMB and/or ICB and the observed density discontinuity at the ICB.
• Benchmarked simulation results against available experimental data (X-ray absorption, diffraction, inelastic scattering) and prior FPMD studies at overlapping P–T conditions.

• Thermal EOS: Generated a consistent thermal EOS for liquid Fe–C at 4, 6, and 9 wt.% C over 0–360 GPa and 4000–7000 K. Reported reference densities and bulk moduli at high temperatures align in trend with available high-P–T experimental constraints.
• Velocity–density behavior: Along isotherms, Vp shows negligible dependence on density slope consistent with a breakdown of Birch’s law for metallic liquids; at fixed density, Vp increases with temperature. Overall, light-element addition modifies Vp by approximately −94 m/s per wt.% dissolved carbon at core conditions (sign as reported).
• Binary Fe–C cannot satisfy both constraints: For the Fe–C binary, about 1–4 wt.% C can match seismological Vp, but explaining the outer-core density deficit would require roughly 5–7 wt.% C, which then overpredicts Vp. Thus, a binary Fe–C outer core cannot simultaneously fit PREM ρ and Vp.
• Ternary mixtures: Considering Fe–C–LE with LE = O, S, or H and applying constraints from PREM and the density jump at the ICB yields viable solutions that satisfy both ρ and Vp either at CMB or ICB conditions. No unique simultaneous solution is found for Fe–C–Si or Fe–C–N due to similar compositional derivatives that preclude disentangling their effects.
• Outer-core carbon budget: Incorporating ternary effects and constraints, the outer core is inferred to contain about 0.3–2.0 wt.% C, corresponding to roughly 5.5–3.68 × 10^24 g of carbon, consistent with several previous geochemical and geophysical estimates. This range supports the outer core as potentially the largest reservoir of terrestrial carbon.

The study addresses whether carbon can be a significant light element in the Earth’s core while reconciling seismic constraints. Direct FPMD calculations of EOS and Vp for Fe–C liquids at core conditions show that a binary Fe–C composition cannot jointly reproduce PREM density and compressional wave velocity, clarifying discrepancies among prior experimental and modeling efforts. The breakdown of Birch’s law for metallic liquids at extreme P–T underscores the need for direct simulation- or experiment-based property evaluations rather than extrapolations from lower P–T regimes. By introducing additional light elements (O, S, H) into ternary mixtures, the authors identify combinations that align with both ρ and Vp at key core boundaries and with the observed density discontinuity at the ICB. The resulting carbon content of 0.3–2.0 wt.% fits within, and helps refine, prior geochemical partitioning models and phase diagram constraints. These results imply that the core, particularly the outer core, could host a substantial fraction of Earth’s carbon inventory, with implications for the deep carbon cycle, core thermodynamics, and the evolution of Earth’s interior. The findings bridge geophysical observations (seismology), computational mineral physics (FPMD), and geochemical constraints, strengthening the argument that multiple light elements jointly modulate the core’s properties and that carbon, while not the sole light element, is a significant contributor within a realistic compositional mix.

First-principles simulations of liquid Fe–C across outer-core pressures and temperatures yield a thermal EOS and compressional wave velocities demonstrating that a binary Fe–C composition cannot simultaneously satisfy PREM density and Vp. The analysis indicates Birch’s law does not hold for metallic liquids under core conditions. When additional light elements (O, S, H) are considered, simultaneous matches to seismic properties become feasible, implying an outer-core carbon content of approximately 0.3–2.0 wt.%. This makes the outer core a leading candidate for Earth’s largest carbon reservoir. Future work should target multi-component liquid alloys with improved experimental data at core P–T, refined compositional derivatives including cross terms, tighter constraints on the core geotherm, and explicit treatment of Ni and other minor constituents to further narrow the carbon budget.

• Sparse high-precision experimental data at true core P–T conditions necessitate reliance on simulations and extrapolations, introducing uncertainties.
• Application of small pressure corrections and assumptions within the DFT framework (functional choice, cutoff, k-point sampling) may affect absolute EOS and Vp values.
• The mixing model assumes linear compositional effects and neglects cross terms, which may not fully capture interactions among multiple light elements in liquid iron.
• Core temperature profile (ICB/CMB temperatures and adiabat) is uncertain; inferred compositions are temperature sensitive within plausible ranges.
• Nickel and other minor elements were not explicitly modeled; although expected to have small effects on Vp, their combined influence with other light elements remains to be fully quantified.
• Some reported comparative literature values exhibit variability; reconciling differing datasets and experimental conditions adds uncertainty to benchmark comparisons.