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 (f_(LM)), average force constant (Φ), and vibrational entropy (S_(vib)) of ε-Fe to pressures relevant to Earth's outer core. We find f_(LM) = 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 S_(vib) 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 (v_D), from which we derive the compressional (v_P) and shear (v_S) sound velocities of ε-Fe. We find v_D = 5.60 ± 0.06, v_P = 10.11 ± 0.12, and v_S = 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.

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