Thermal equation of state of Fe₃S and implications for sulfur in Earth's core

Iron (Fe) and coexisting Fe 3 S were studied simultaneously using synchrotron X‐ray diffraction and a laser‐heated diamond anvil cell (DAC). The thermal equation of state (EOS) of Fe 3 S was investigated up to pressures of 80 GPa and temperatures of 2500 K. Fitting a third‐order Birch‐Murnaghan EOS to the room temperature data yielded bulk modulus K 0 = 156(7) GPa (values in parentheses are standard deviation) and pressure derivative K′ 0 = 3.8(3) calibrated against NaCl in the B2 structure. The room temperature data were also calibrated against the EOS of hcp‐Fe for comparison and aid in the determination of the thermal pressure contribution of Fe 3 S. This fit yielded bulk modulus K 0 = 113(9) GPa and pressure derivative K′ 0 = 5.2(6). The thermal pressure contribution of Fe 3 S was assumed to be of the form ΔP thermal = αK T ΔT, where αK T is constant. The best fit to the data yielded αK T = 0.011(2) GPa K −1 . Iron and Fe 3 S coexisted in the high‐pressure, high‐temperature experiments, and a density relationship between Fe and Fe 3 S was found to be linear and independent of temperature. Extrapolation of the data to the core‐mantle boundary (CMB), using an assumed temperature of 3500 K at the CMB, a 2% volume change associated with melting, and applying a small adjustment to account for the nickel content of the core indicates that 14.7(11) wt % sulfur is adequate to resolve the density deficit of the outer core.