Phonon density of states of $\alpha$- and $\delta$-plutonium by inelastic x-ray scattering

Inelastic x-ray scattering measurements of the phonon density of states (DOS) were performed on polycrystalline samples of pure $\alpha \text{-Pu}$ and $\delta {\text{-Pu}}_{0.98}{\text{Ga}}_{0.02}$ at room temperature. The heat capacity of $\alpha \text{-Pu}$ is well reproduced by contributions calculated from the measured phonon DOS plus conventional thermal-expansion and electronic contributions, showing that $\alpha \text{-Pu}$ is a “well-behaved” metal in this regard. A comparison of the phonon DOS of the two phases at room temperature showed that the vibrational entropy difference between them is only a quarter of the total entropy difference expected from known thermodynamic measurements. The missing entropy is too large to be accounted for by conventional electronic entropy and evidence from the literature rules out a contribution from spin fluctuations. Possible alternative sources for the missing entropy are discussed.

Figure 1

Phonon density of states of (a) $\delta {\text{-Pu}}_{0.98}{\text{Ga}}_{0.02}$ and (b) $\alpha \text{-Pu}$ measured at room temperature. The open circles were measured in this study, while the solid line was calculated from the force-constant-model fit to the measured dispersion curves by Wong et al. (Ref. 12) convoluted with the instrument resolution function. The $\alpha$-phase phonon DOS is clearly stiffer than the $\delta$ phase, which is expected given the higher density of monoclinic $\alpha \text{-Pu}$.

Figure 2

Heat capacity of pure $\alpha \text{-Pu}$ measured from 2 to 300 K. Contributions from the phonon DOS $\left(C_V^{\text{ph}}\right)$ volume expansion $\left(9B\nu {\alpha }^{2}T\right)$ and electronic excitations $\left(\gamma T\right)$ were calculated from measured data, as described in the text. For clarity error bars are shown on every fourth data point $f$.