Earth’s core could be the largest terrestrial carbon reservoir

The Earth's core, primarily composed of iron, necessitates the presence of lighter elements to account for its observed density, as determined by seismological observations. Identifying these light elements and their proportions remains a significant challenge in geochemistry. Carbon, with its chemical affinity for metallic phases and its cosmochemical abundance, is a strong candidate. Its solubility in iron-rich melts is substantial, reaching approximately 25% under high-temperature, magma ocean conditions. However, the carbon abundance in natural systems is likely well below saturation. The siderophile nature of carbon (preferential partitioning into metallic phases) is well-established, but the extent of this behavior remains debated, with estimated D_FeC/melt values varying considerably across studies. This variation, along with uncertainties in magma ocean processes, accretion, and core formation, leads to a wide range of estimated carbon content in the Earth's core (approximately 0.1 to 3 wt%). Therefore, an independent estimate of the present-day outer core's carbon budget, based on alternative approaches, is crucial to refine our understanding of the Earth's composition and evolution.

Previous research has explored various avenues to estimate the Earth's core carbon content. Studies utilizing partitioning behavior between liquid iron and combined phases of iron, ice, and FeS indicate a preference for carbon partitioning into liquid iron, suggesting a potential 1.5–2 wt% in the outer core to explain the density deficit at the inner-outer core boundary. However, this doesn't fully address the density deficit in the inner core. High-pressure and temperature phase diagrams of Fe-C alloys have also been employed, suggesting approximately 1 wt% carbon in the outer core and less in the inner core, but this fails to completely account for the observed density deficit. Additionally, the impact of light elements on the melting temperature of iron and its compounds has been investigated. Studies suggest that carbon can reduce melting temperature significantly, but in multi-component systems, determining light-element concentrations based solely on temperature is challenging. Independent constraints can be obtained by examining the effects of different elements on density (ρ) and compressional wave velocity (Vp) of iron alloys at core conditions. Challenges with high-pressure, high-temperature experiments often necessitate extrapolations using empirical relationships like Birch's law, whose validity at extreme core conditions is debated. Previous first-principles molecular dynamics (FPDM) simulations have explored various light element candidates (S, O, C, H), but often with limited data points, hindering the development of reliable empirical equations.

This study utilizes first-principles molecular dynamics (FPDM) simulations within the Vienna ab initio simulation package (VASP) to estimate the density and compressional wave velocity of liquid iron-carbon alloys. Density functional theory (DFT) with the projector-augmented wave (PAW) method and the generalized gradient approximation functional (GGA-PBE) were used. Simulations were performed at pressures ranging from 0 to 360 gigapascals (GPa) and temperatures from 4000 to 7000 Kelvin (K), covering the conditions relevant to Earth's core. Various carbon concentrations (4, 6, and 9 wt%) were investigated. The thermal equation of state was determined, and the validity of Birch's law was assessed by comparing the bulk sound velocities of liquid iron and iron-boron liquids along isotherms. The study also explores the effects of other light elements (O, S, H, Si, N) on density and compressional wave velocity in ternary systems (Fe-C-LE) to constrain the carbon content more accurately, considering the likely presence of multiple light elements in the Earth's core. A thermodynamic pressure correction was applied to refine the results. To account for the effect of limited elasticity, a volume-dependent paw protection was added to the pressure. The simulations were performed with magnetic moments to better reflect the conditions in the Earth’s core, considering that liquid iron exhibits magnetic moments at high pressures.

The FPDM simulations revealed that a simple iron-carbon binary system cannot simultaneously explain both the density and compressional wave velocity of the Earth's outer core. While a high carbon concentration (around 7 wt%) could explain the density deficit, it would result in compressional wave velocities exceeding observed values. A lower carbon concentration (around 1 wt%) is needed to match the observed velocities, but this is insufficient to explain the density. By incorporating other light elements into ternary systems (Fe-C-LE), the study identified scenarios that could simultaneously match both density and velocity. For example, in an Fe-C-O ternary system, the study found a unique solution for carbon content at both the core-mantle boundary (CMB) and inner-core boundary (ICB) conditions. However, unique solutions were not found for ternary systems including silicon or nitrogen. The analysis suggests that an outer core carbon content of 0.3–2.0 wt.% (5.5–3.68 × 10²⁴ g) is consistent with both density and velocity data, implying the outer core could hold a substantial fraction of the Earth’s total carbon. The study's analysis demonstrates the importance of considering multiple light elements to accurately constrain the carbon content of Earth’s core.

The findings address the longstanding challenge of determining the Earth's core carbon content by providing a refined estimate that considers both density and velocity constraints, unlike previous studies that often focused on one or the other. The 0.3–2.0 wt.% range proposed is consistent with some previous estimations, reducing the uncertainty considerably. This improved estimate significantly impacts our understanding of the Earth's overall carbon budget, which has a wide range of estimates in previous research. The study highlights the limitations of relying solely on binary systems and the necessity of considering multi-component systems to accurately model the complex interactions between elements in the Earth’s core. The methodological advancements employing FPDM simulations provide a valuable tool for future investigations of other planetary bodies.

This study provides a refined estimate of the carbon content in the Earth's outer core (0.3–2.0 wt%), suggesting it may be the planet's largest carbon reservoir. This estimate arises from a novel approach that simultaneously considers density and compressional wave velocity constraints using advanced FPDM simulations. The inability to reach a unique solution using simple binary Fe-C systems underscores the need to consider multi-component models. Future research could focus on exploring other light element combinations and refining the simulation techniques to further reduce uncertainties.

The study's reliance on FPDM simulations introduces inherent limitations associated with computational approximations and model parameters. While efforts were made to incorporate relevant physical phenomena like magnetic moments, other factors may influence the results. The uncertainty in the core's adiabatic temperature gradient can also affect the precision of carbon content estimations. Further experimental validation at core-relevant conditions would improve confidence in the findings.