Sound velocities and thermodynamical properties of hcp iron at high pressure and temperature

Sound velocities and thermodynamical properties of hcp iron have been computed using ab initio calculations over an extended density and temperature range, encompassing the conditions directly relevant for the Earth's inner core. At room temperature, and up to 350 GPa, an excellent agreement is obtained between present results and experimental data for many thermodynamical quantities: phonon density of states, vibrational entropy, heat capacity, Gruneisen parameter and thermal expansion. With increasing temperature, along an isochore, we observe a strong decrease of the phonon frequencies, demonstrating that intrinsic anharmonic effects cannot be neglected. We also carefully compare previous theoretical data for the sound velocities and try to explain the discrepancies observed with experiments. Finally, we propose a temperature dependant Birch's law that we compare with previous experimental work.