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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 a-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 a-b and b-g phase transitions, vibrational and electronic entropies were comparable. DOI: 10.1103/PhysRevLett.86.3076 PACS numbers: 63.20.-e, 64.30.+t, 78.70.Nx Although first known for its unusual nuclear properties, uranium exhibits several unusual solid-state properties that may originate with electronic instabilities. The thermally induced softening of the phonon density of states (DOS) for most elements originates with anharmonicity [1,2]. For the actinides, however, a distinction between the normal anharmonic softening and harmonic softening arising from a temperature-dependent harmonic potential has been suggested [3]. In a detailed assessment of the thermodynamic data on the six crystalline phases of Pu, it was concluded that the anharmonic and electronic contributions to the equation of state could not be separated [4]. The origin of this phonon softening is a fundamental issue for the equation of state. In this Letter, we use the power spectrum of atom motions to show that the thermal softening of the phonon DOS in a-U originates with the weakening of force constants in a harmonic solid, as opposed to the typical softening in an anharmonic potential. Temperature alters the electronic structure sufficiently to change the lattice dynamics. This Letter also addresses the entropy of phonons, and by deduction the entropy of electrons, for the three low-pressure phases of crystalline uranium metal.Previous lattice dynamics studies on uranium have been performed at room temperature and below [5,6], motivated in part by the discovery of several charge density wave transitions at low temperatures [7,8]. Independently, there has been recent interest in the vibrational entropy contribution to the high temperature phase stability of metals and alloys [9][10][11], motivated by the discovery that vibrational entropy plays a larger role in phase stability than previously expected [12]. Other experimental and theoretical work has shown that electronic contributions to the entropies of high temperature phase transitions can also be significant [13][14][15].Diffraction measurements on a-U at ambient pressure have shown that the Debye temperature decreases dramatically with increasing temperature [3,16]. This softening is consistent with decreases in the elastic constants [17,18]. Specifically, the Debye temperature was expressed by u Х ͑306 2 0.158T ͒ K, where T is temperature [3]. The magnitude of this softening suggests that the Debye temperature decreases...

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