Carbon and other light element contents in the Earth's core based on first-principles molecular dynamics

Abstract

Carbon (C) is one of the candidate light elements proposed to account for the density deficit of the Earth's core. In addition, C significantly affects siderophile and chalcophile element partitioning between metal and silicate and thus the distribution of these elements in the Earth's core and mantle. Derivation of the accretion and core-mantle segregation history of the Earth requires, therefore, an accurate knowledge of the C abundance in the Earth's core. Previous estimates of the C content of the core differ by a factor of ∼20 due to differences in assumptions and methods, and because the metal-silicate partition coefficient of C was previously unknown. Here we use two-phase first-principles molecular dynamics to derive this partition coefficient of C between liquid iron and silicate melt. We calculate a value of 9 ± 3 at 3,200 K and 40 GPa. Using this partition coefficient and the most recent estimates of bulk Earth or mantle C contents, we infer that the Earth's core contains 0.1-0.7 wt% of C. Carbon thus plays a moderate role in the density deficit of the core and in the distribution of siderophile and chalcophile elements during core-mantle segregation processes. The partition coefficients of nitrogen (N), hydrogen, helium, phosphorus, magnesium, oxygen, and silicon are also inferred and found to be in close agreement with experiments and other geochemical constraints. Contents of these elements in the core derived from applying these partition coefficients match those derived by using the cosmochemical volatility curve and geochemical mass balance arguments. N is an exception, indicating its retention in a mantle phase instead of in the core.

Fig. 1.

(Upper) Snapshot of atomic configuration in the simulation cell after the center of mass of the Fe cluster is moved to the center of the simulation cell and all of the atoms are moved accordingly by using the periodic conditions of the simulation cell. The encircled area marks the liquid metal phase domain and the surrounding area is the silicate melt domain. (Lower) The constructed alpha shape of the Fe cluster showing Fe atoms on the surface of the alpha shape and the Si and C atoms enclosed in the alpha shape.

Fig. 2.

Comparison of Si solubility in liquid iron obtained by FPMD with experimental data (33, 34). Temperatures and pressures are exactly as in the experiments (33, 34). The rectangles with numbers inside are the molar ratio of total cations to oxygen of the bulk system (metallic phase + silicate phase), controlling the oxidation state of the bulk system. The 1.08 is for the Si-bearing and 1.02 is for the O-bearing Earth models of Table 3, and 1.01 is for experimental data (33).

Fig. 3.

Comparison of Si, O, C, P, Mg, H, and N contents of the Earth’s core derived using different methods. Red diamonds [this work (A)] show an estimate of the core composition using C^C = C^E/[f + (1 − f)/D], where C^C represents core composition, C^E is bulk Earth composition (14), f is mass fraction of metallic core, and D is partition coefficients from Table 2. Blue triangles [this work (B)] show the core composition derived using the definition of partition coefficient, the C^C = D × C^M, where C^M is the primitive mantle composition (bulk silicate Earth) of ref. . Green circles [this work (C)] show the use of the most recent estimates of C, H, and N of the Earth’s mantle (22) and our ab-initio partition coefficients to calculate the corresponding core composition using C^C = D × C^M. Purple squares are the core compositions given by McDonough (14) based on volatility curve, cosmochemical constraints, and mass balance of geochemical reservoirs. With the exception of N, core compositions of light elements agree within an order of magnitude or better between different approaches.