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

We present a study of the structural phase transition, mechanical and thermodynamic properties of UO$_{2}$ by means of the local density approximation (LDA)$+U$ approach. A phase transition pressure of 40 GPa, which agrees well with the experimental value of 42 GPa, is obtained from theory at 0 K. Pressure-induced enhancements of elastic constants, elastic moduli, elastic wave velosities, and Debye temperature of the fluorite phase are observed. Phonon spectrums 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 $\Gamma$$-$$X$ direction and soft phonon mode along the $\Gamma$$-$$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. Calculated temperature dependence of lattice parameter, entropy, and specific heat agree well with experimental observations in the low temperature domain. The difference of 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.