Iron‐Carbon Alloy Under Shock Compression: Implications for the Carbon Concentration in Earth’s Inner Core

Abstract

AbstractCarbon has been proposed to be a potential light element in the Earth’s solid inner core. However, its presence and concentration in the core remain limited constrained. In this study, we measured the equation of state of an iron‐carbon alloy with ∼1.5 wt.% (∼6.64 at.%) carbon up to ∼185 GPa and ∼3,750 K via shock compression. The Hugoniot equation of state of the Fe‐1.5wt.%C alloy was determined to be Us (km/s) = 3.94 (0.15) + 1.62 (0.08) Up with an initial density of 7.77 (0.03) g/cm3, where Us and Up are the shock wave velocity and particle velocity, respectively. Hugoniot data combined with the Mie‐Grüneisen equation of state allow us to build the thermal equations of state of the Fe‐C alloy at high pressure‐temperature (P‐T) conditions. Investigations on the pressure‐density relation of Fe‐C alloys by the shock experiments and synchrotron X‐ray diffraction measurements by Pamato et al. (2020), https://doi.org/10.1029/2020jb020159 have indicated that carbon should occupy interstitial sites of iron lattice at high P‐T conditions. The thermal equation of state of the Fe‐1.5wt.%C alloy provided here shows that Fe‐1.5wt.%C is ∼1.65% denser than the inner core under conditions relevant to the inner‐core boundary. This study indicates that iron alloyed with an upper bound of ∼2.2 (0.3) wt.% (∼10.7 [1.6] at.%) carbon may match with the Preliminary Reference Earth Model (PREM) in the Earth’s inner core. Thus, interstitial carbon in iron helps to explain the observed density deficit of the inner core, although other light elements are also expected.