Elastic constants, phonon density of states, and thermal properties of UO${}_2$

The elastic properties and phonon density of states of UO${}_2$ have been studied by first-principles spin-polarized electronic-structure calculations in both the local density approximation (LDA) and the generalized-gradient approximation (GGA) for the experimentally determined antiferromagnetic spin configuration. Calculations have also been done both with and without Hubbard corrections (LDA $+$ $U$ and GGA $+$ $U$). The elastic properties and phonon density of states are in very good agreement with experimental measurements when the Hubbard correction is included. The elastic constants and low-frequency (acoustic mode) phonons are in reasonably good agreement with experiment for all the different calculations. However, when Hubbard corrections are not included, the high-frequency phonons are pushed to lower frequencies and the optical phonons are significantly underestimated. The melting temperature is approximated by using an empirical equation, which uses elastic constants as input parameters, and is in good agreement with experiment. The first-principles calculations are also used to obtain the specific heat and entropy within the harmonic approximation at finite temperatures. It is shown that harmonic approximation is valid up to room temperature. The Debye temperature is estimated using two different methods. The predicted values are in excellent agreement with experimental results. It is shown that inclusion of the spin-orbit interaction does not significantly alter either the elastic or thermal properties.

Figure 1

(Top) A comparison of the phonon density of states of 48- and 96-atom cells. (Middle) The phonon density of states of ideal and distorted 96-atom cells. (Bottom) The phonon density of states of the 96-atom cell for different values of the $U$ parameter.

Figure 2

The phonon dispersion curves in two directions of high symmetry using a 192-atom cell. The experimental measurements[6] are shown by the open symbols.

Figure 3

(Top) The phonon density of states obtained from LSDA $+$ $U$, GGSA $+$ $U$, and shell model.[6] (Bottom) Calculated phonon density of states without Hubbard corrections.

Figure 4

Calculated specific heat and its comparison with experimental measurements. The low- (open square) and high- (open circles) temperature data are taken from Refs.5 and42, respectively.

Figure 5

Calculated entropy and its comparison with experimental measurements. The values of entropy (open circle) are taken from Ref.43.

Figure 6

Calculated vibrational entropy difference with and without quasiharmonic approximation (solid line and dashed line) and its comparison with experimental measurements (open circles).[43] The S${}_0$ is refered to the entropy at 35 K.