Thermal evolution of vibrational properties of $\alpha$-U

By means of ab initio molecular dynamics calculations, the thermal evolution of vibrational properties in $\alpha$-U is studied at low temperature. The phase transition undergone by this material around 50 K was previously studied extensively using ab initio calculations in the framework of the linear response at 0 K. Although these previous efforts capture successfully the complexity of the experimental phonon spectrum at room temperature, in particular the soft-phonon mode and its pressure dependence, they fail to reproduce the transition to the charge-density-wave state at ambient pressure as a function of temperature. In the present work, by going beyond the quasiharmonic approximation and taking into account the temperature effects explicitly, we are able to reproduce the behavior of both phonon spectrum and elastic constants of U-$\alpha$ as a function of temperature.

Figure 1

Left: orthorhombic structure of the $\alpha$ phase of uranium. Right: ${\alpha }_1$ phase of uranium. The $\alpha$ structure is doubled in the $a$ direction and the blue and red atoms have been slightly displaced in opposite direction corresponding to a charge density wave with $q_x=1/2$ and $\varphi ={90}^{\circ }$.

Figure 2

Average atomic positions for AIMD simulations of $\alpha$-U at 300 K (in open red) and at 50 K (in full blue). The red box (dashed line) indicates the primite $\alpha$-U cell and the blue box indicates the ${\alpha }_1$-U cell. The sinusoidal modulations of the two $\alpha$-U atoms are represented by the blue lines. At the bottom, $P\left(x\right)$ describes the distribution of atomic positions along $x$.

Figure 3

Calculated phonon dispersion curves of $\alpha$-U at 300 K. Blue lines represent modes which appear to be primarily acousticlike while red lines represent modes which are mostly opticlike. Experimental neutron-scattering data [12] at room temperature are denoted by open and filled symbols.

Figure 4

Left: AIMD results at 50 (in blue), 300 (in red), and 900 K (in black) for the ${\mathrm{\Sigma }}_4$ and ${\mathrm{\Sigma }}_1$ mode of $\alpha$-U. Experimental neutron-scattering data [12] at room temperature are denoted by open and filled symbols and by the dashed line at 30 K [13]. Right: DFPT calculations with the cell parameters used in the AIMD simulations at 50, 300, and 900 K.

Figure 5

Low-frequency part of the ${\alpha }_1$-U phonon spectra for $u=0.2$ Å (in red and blue solid lines). The dashed lines are the phonon branches of the $\alpha$-U structure $(u=0$ Å).

Figure 6

Relative variation of the $\alpha$-U bulk modulus (with respect to its maximum) as a function of the temperature. The black line is the ultrasound data [43, 45]. The red filled and open squares are the AIMD results for both ideal $\alpha$-U and ${\alpha }_1$-U, respectively, and the blue dashed line is the results from QHA [16].