Phonon density of states in iron at high pressures and high temperatures

Abstract

The phonon density of states (DOS) in iron has been measured in situ by nuclear resonance inelastic X-ray scattering (NRIXS) at high pressures and high temperatures in a resistively heated diamond anvil cell. The DOS data provide a variety of thermodynamic and elastic parameters essential for characterizing iron at depth in the Earth interior, such as average sound velocity, Debye temperature, atomic mean square displacement, average kinetic energy, vibrational entropy and specific heat. The NRIXS data were collected at 6, 20, and 29 GPa and at temperatures up to 920 K. Temperatures were directly determined from the measured spectra by the ratio of intensities of the phonon creation/annihilation side bands that are determined only by the Boltzmann factor. The change of the DOS caused by the structural transition from α-Fe to ɛ-Fe is small and not resolvable within the experimental precision. However, the phonon energies in γ-Fe are clearly shifted to lower values with respect to α- and ɛ-Fe. The temperature dependence of derived thermodynamic parameters is presented and compared with those obtained by Debye’s model. The Debye temperatures that best describe the data decrease slightly with increasing temperature.