Vibrational and thermodynamic properties of MgSiO$_3$ post-perovskite

Recently a high pressure transformation in MgSiO$_3$ perovskite, the primary constituent of Earth's lower mantle, was identified near 125 GPa and 2500 K. In order to understand the importance of the new phase on mantle properties and dynamics it is necessary to determine its thermodynamic properties and contrast with those of perovskite. Here we perform first principles quasi-harmonic approximation calculations of the free energy of MgSiO$_3$ post-perovskite and derive several thermodynamic properties of interest up to and beyond core-mantle-boundary (CMB) pressures. It is found that in general its thermal properties are very similar to those of perovskite at relevant conditions, despite the great structural difference between these phases. The post-perovskite phase is found to be mechanically stable at ambient pressure and might be retrieved metastably at cryogenic temperatures.