Phonon spectrum, thermodynamic properties, and pressure-temperature phase diagram of uranium dioxide

TLDR: In this paper, the structural phase transition and the mechanical and thermodynamic properties of UO${}_{2}$ by means of the local density approximation (LDA)+$U$ approach were analyzed.

Abstract: We present a study of the structural phase transition and the mechanical and thermodynamic properties of UO${}_{2}$ by means of the local density approximation (LDA)+$U$ approach. A phase transition pressure of 40 GPa is obtained from theory at 0 K, and agrees well with the experimental value of 42 GPa. The pressure-induced enhancements of elastic constants, elastic moduli, elastic wave velocities, and Debye temperature of the ground-state fluorite phase are predicted. The phonon spectra of both the ground state fluorite structure and high-pressure cotunnite structure calculated by the supercell approach show that the cotunnite structure is dynamically unstable under ambient pressure. Based on the imaginary mode along the $\ensuremath{\Gamma}$$\ensuremath{-}$$X$ direction and soft phonon mode along the $\ensuremath{\Gamma}$$\ensuremath{-}$$Z$ direction, a transition path from cotunnite to fluorite has been identified. We calculate the lattice vibrational energy in the quasiharmonic approximation using both first-principles phonon density of state and the Debye model. The calculated temperature dependence of lattice parameter, entropy, and specific heat agrees well with experimental observations in the low temperature domain. The difference of the Gibbs free energy between the two phases of UO${}_{2}$ has predicted a boundary in the pressure-temperature phase diagram. The solid-liquid boundary is approximated by an empirical equation using our calculated elastic constants.