High-temperature and high-pressure phase transitions in uranium

The phase diagram of uranium has been explored up to 100 GPa and 2000 K by means of ab initio molecular dynamics (AIMD) simulations. The lattice dynamics and energetics of the stable phases observed experimentally in this range of pressure and temperature are studied in this work. The phonon spectra of the $\alpha$ and $\gamma$ phases are shown to evolve strongly as a function of temperature, unveiling the huge anharmonic effects present in this material. If the elastics constants and the bulk and shear moduli of the $\gamma$ phase do not disclose any temperature effects, the shear modulus of the $\alpha$ phase decreases strongly as a function of temperature. Using the pressure- and temperature-dependent vibrational density of states and the Gibbs free energy of these two structures, we found a line transition between the $\alpha$ and $\gamma$ phases which slightly underestimates the experimental one. Coherently with experiments, the bct structure is never found stable between 0 and 100 GPa.

Figure 1

Phonon dispersions and density of states for $\alpha$-U at 300 and 900 K.

Figure 2

Phonon dispersions and density of states for $\alpha$-U at 19 and 88 GPa and 1600 K.

Figure 3

Bulk modulus $K$ and shear modulus $G$ of $\alpha$-U as a function of pressure and at several temperatures. The symbols are the calculated values and the lines are linear fits of these values.

Figure 4

Phonon dispersions and density of states for $\gamma$-U at 300, 900, and 1300 K using the TDEP method. The lower panel shows the phonon dispersions of $\gamma$-U at 0 K obtained with the DFPT method.

Figure 5

Phonon dispersions and density of states for $\gamma$-U at 11, 31, 51, and 89 GPa and 1600 K.

Figure 6

Bulk modulus $K$, shear modulus $G$, and $C^{\prime }$ of $\gamma$-U as a function of pressure and at several temperatures. For $K$ and $G$ the symbols are the calculated values and the lines are linear fits of these values. The dashed line is a linear fit of the values of $K$ for the $\alpha$-U structure. For $C^{\prime }$ the dashed lines are the transition pressures between $\alpha$ and $\gamma$-U corresponding to each temperature.

Figure 7

Free energies for $\alpha$ and $\gamma$-U as a function of temperature and volume.

Figure 8

Phase diagram of uranium. The black lines are the experimental transition lines [21] and the red circles are our results for the $\alpha \text{−}\gamma$ phase boundary. The inset shows the experimental (squares) and our theoretical (circles) volume changes in $\alpha \text{−}\gamma$ transitions as a function of pressure.