An equation of state for liquid iron and implications for the Earth's core

Abstract

An equation of state is presented for liquid iron based on published ultrasonic, thermal expansion, and enthalpy data at 1 bar and on pulse-heating and shock wave compression and sound speed data up to 10 Mbar. The equation of state parameters, centered at 1 bar and 1811 K (the normal melting point of iron), are density, ρ_0 = 7019 kg/m^3, isentropic bulk modulus, K_(S0) = 109.7 GPa, and the first- and second-pressure derivatives of K_S, K′_(S0) = 4.66 and K″_(S0) = −0.043 GPa^(−1). A parameterization of the Grüneisen parameter γ as a function of density ρ and specific internal energy E is γ = γ_0 + γ′(ρ/ρ_0)^n(E - E_0) where γ_0 = 1.735, γ′ = −0.130 kg/MJ, n = −1.87, and E_0 is the internal energy of the liquid at 1 bar and 1811 K. The model gives the temperature dependence of γ at constant volume as (∂γ/∂T)_(v|1bar,1811K) = −8.4 × 10^(−5) K^(−1). The constant volume specific heat of liquid Fe at core conditions is 4.0–4.5 R. The model gives excellent agreement with measured temperatures of Fe under shock compression. Comparison with a preliminary reference Earth model indicates that the light component of the core does not significantly affect the magnitude of the isentropic bulk modulus of liquid Fe but does decrease its pressure derivative by ∼10%. Pure liquid Fe is 3–6% more dense than the inner core, supporting the presence of several percent of light elements in the inner core.

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