Phonon density-of-states curves were obtained from inelastic neutron scattering spectra from the three crystalline phases of uranium at temperatures from 50 to 1213 K. The $\alpha$-phase showed an unusually large thermal softening of phonon frequencies. Analysis of the vibrational power spectrum showed that this phonon softening originates with the softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. It follows that thermal excitations of electronic states are more significant thermodynamically than are the classical volume effects. For the $\alpha -\beta$ and $\beta -\gamma$ phase transitions, vibrational and electronic entropies were comparable.

• Received 3 August 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.3076