Experimental constraints on the thermodynamics and sound velocities of hcp‐Fe to core pressures

Abstract

We report the high‐pressure thermoelastic and vibrational thermodynamic parameters for hexagonal close‐packed iron (ε‐Fe), based on nuclear resonant inelastic X‐ray scattering and in situ X‐ray diffraction experiments at 300 K. Long data collection times, high‐energy resolution, and quasi‐hydrostatic sample conditions produced a high‐statistical quality data set that comprises the volume‐dependent phonon density of states (DOS) of ε‐Fe at eleven compression points. From the integrated phonon DOS, we determine the Lamb‐Mössbauer factor (fLM), average force constant (Φ), and vibrational entropy (Svib) of ε‐Fe to pressures relevant to Earth's outer core. We find fLM = 0.923 ± 0.001 at 171 GPa, suggesting restricted thermal atomic motion at large compressions. We use Φ to approximate ε‐Fe's pressure‐ and temperature‐dependent reduced isotopic partition function ratios (β‐factors), which provide information about the partitioning behavior of iron isotopes in equilibrium processes involving solid ε‐Fe. In addition, we use the volume dependence of Svib to determine the product of ε‐Fe's vibrational thermal expansion coefficient and isothermal bulk modulus, which we find to be pressure‐independent and equal to 5.70 ± 0.05 MPa/K at 300 K. Finally, from the low‐energy region of each phonon DOS, we determine the Debye sound velocity (vD), from which we derive the compressional (vP) and shear (vS) sound velocities of ε‐Fe. We find vD = 5.60 ± 0.06, vP = 10.11 ± 0.12, and vS = 4.99 ± 0.06 km/s at 171 GPa, thus providing a new tight constraint on the density dependence of ε‐Fe's sound velocities to outer core pressures.