Unusual Phonon Softening in $\delta$-Phase Plutonium

The phonon density of states and adiabatic sound velocities were measured on fcc-stabilized ${}^{242}\mathrm{Pu}_{0.95}{\mathrm{Al}}_{0.05}$. The phonon frequencies and sound velocities decrease considerably (soften) with increasing temperature despite negligible thermal expansion. The frequency softening of the transverse branch along the [111] direction is anomalously large (∼30%) and is very sensitive to alloy composition. The large magnitude of the phonon softening is not observed in any other fcc metals and may arise from an unusual temperature dependence of the electronic structure in this narrow $5f$-band metal.

Figure 1

Phonon densities of states of $\delta$-phase ${\mathrm{Pu}}_{0.95}{\mathrm{Al}}_{0.05}$ at four temperatures: 27, 65, 150, and 300 K. The dashed line represents the quadratic part of the DOS at each temperature, as estimated by the average sound velocity obtained from resonant ultrasound measurements.

Figure 2

Polycrystalline longitudinal, transverse, and average sound velocities versus temperature from 5 to 300 K obtained from resonant ultrasound measurements on ${\mathrm{Pu}}_{0.95}{\mathrm{Al}}_{0.05}$. $v_L$, $v_T$, and $\overline{v}$ decrease by about 12% upon warming to room temperature.

Figure 3

(a) $g(E)/E^2$ versus $E$ for ${\mathrm{Pu}}_{0.95}{\mathrm{Al}}_{0.05}$ at four temperatures: 27, 65, 150, and 300 K. The four symbols at $E=0$ indicate the elastic limit of the DOS ($D$) at each temperature as obtained from the average sound velocity. (b) Difference of the densities of states of ${\mathrm{Pu}}_{0.95}{\mathrm{Al}}_{0.05}$ at 300 and 27 K that has been smoothed using a three-point boxcar averaging. The frequency downshifting of the main Van Hove singularities (3, 7, and 12 meV) at high temperatures are especially clear.

Figure 4

The three panels on the left show the phonon dispersion curves along certain symmetry directions as calculated from a four-neighbor Born–von Kármán model for fcc ${}^{242}\mathrm{Pu}_{0.98}{\mathrm{Ga}}_{0.02}$ using the room temperature parameters of Wong et al. [6]. The dashed lines emanating from the origin reflect the slopes of the dispersion curves at low energies as obtained from the elastic constants. The rightmost panel shows the model phonon DOS for ${}^{242}\mathrm{Pu}_{0.98}{\mathrm{Ga}}_{0.02}$ (line), and the measured DOS of ${}^{242}\mathrm{Pu}_{0.95}{\mathrm{Al}}_{0.05}$ at room temperature (symbols). The calculated DOS has been convoluted with a Gaussian of standard deviation of 0.5 meV, intended to approximate the instrumental energy resolution.