Carbon budget and isotope compositions of the Earth

Abstract

The carbon budget in the Earth interior is currently not well constrained because the sample of the Earth’s core is unavailable. Several ways have been used to estimate the Earth’s carbon inventory but their results vary more than one order of magnitude. Recently, using isotope signals to solve this kind of budget problem becomes an alternative way for various different isotope systems (Satish-Kumar et al., 2011; Shahar et al., 2011; Moynier et al., 2011; Lazar et al., 2012; Horita and Polyakov, 2015; Shahar et al., 2016; Elardo and Shahar, 2017; Liu et al., 2017). Here equilibrium carbon isotope fractionation factors for almost all kinds of carbon-bearing species in the deep Earth are provided by using first-principles methods. For the first time, silicate melts and iron melts are calculated directly other than using their crystalline analogues in the previous studies. We find that melts have very different compressibility than those crystalline analogues. Besides, compared to a fixed crystalline structure, melts have numerous local different configurations. A reasonable simulation of melts should considering the proper sampling of these local configurations to obtain a precise average result. Neglecting these differences between melts and crystalline analogues will let the estimations of isotope fractionation factors to be risky.In this study, we calculate the equilibrium isotopic fractionation factors of carbon between silicate melt, iron melt, magnesite, diamond, moissanite, and various iron-carbides at magma ocean conditions by first-principles density functional theory. The influences of pressure and redox condition on the chemical environment and isotope fractionation of carbon are also carefully investigated. The average value of δ13C of BSE is estimated to be about −7.2‰, according to the mantle derived diamonds (Cartigny et al., 2014). Although many people thought this signal can represent the carbon isotope composition of the whole mantle, we disagree with it. Diamonds can only represent the major C-bearing species at upper part of mantle, but not the major C-bearing species at lower mantle. Higher temperatures can destabilize diamond. Based on the mantle derived diamonds’ δ13C signal (−7.2‰) and those isotope fractionation factors we provided, we can deduce out the signal for the BSE. Our new carbon isotope fractionation results cannot compromise the mantle-core differentiation scenario at magma ocean period, no matter it is an equilibrium or a Rayleigh distillation process. However, if most of carbon was delivered from one or several giant impacts from the accretion feeding zone of Mars (i.e., with the similar chemistry), and with 2 times of the current mass of Mars to be delivered to the proto-Earth, all discrepancies will be resolved perfectly. This scenario coincides with the giant impact hypothesis of the Moon formation and the unexpected small size of Mars. Finally the carbon content of Earth’s core is estimated about 0.2wt% of the core. Carbon is not a major light element in the Earth's core.