P-T phase diagram for Rh(III) oxides from first principles

We present a detailed first principles study of the equilibrium lattice structures and the phase diagram for the three observed polymorphs of rhodium(III) oxide. The $P-T$ phase diagram is constructed by first calculating the thermodynamical Gibbs free energies as a function of $P$ and $T$ from the electronic energy, as well as vibrational energy and vibrational entropy contributions in a quasiharmonic approximation. Phase boundaries are then placed between each pair of phases by locating curves of intersection between the corresponding free energy surfaces. The resulting partitioning of phase space is consistent with the published experimental investigations. It is found that Rh$_{2}$O$_{3}$ I is the low-temperature and low-pressure form, Rh$_{2}$O$_{3}$ II is the high-pressure form and Rh$_{2}$O$_{3}$ III is high-temperature form. The calculations predict the existence of triple point for the three phases.