Vibrational Softening in α-Uranium

Energy Transfer About the time this issue of Los Alamos Science was going to press, we obtained new experimental results on atomic vibrations in uranium. These results help answer questions raised when Andrew Lawson and coworkers of Los Alamos rediscovered vibrational softening in the early 1990s. Although softening had been observed at least three times earlier, the most important questions about the phenomenon were never addressed experimentally: What is the nature of vibrational softening? Is it an anharmonic or electronic effect? This article summarizes preliminary inelastic neutron-scattering results that address both questions. Our full results will be published in a journal article (Manley et al. 2000a). Lawson’s measurements of Debye-Waller factors—mean-square atomic displacement, 〈u2〉—suggest that the average phonon frequency decreases by about 40 percent as the temperature is raised from room temperature (300 kelvins) to uranium’s β-phase transition temperature (940 kelvins), a much larger decrease than the quasi-harmonic theory of anharmonicity would normally predict (see the article “Atomic Vibrations and Melting in Plutonium” on page 190). In the quasi-harmonic approximation, anharmonic vibrations are assumed to be independent harmonic modes whose frequencies are not fixed but, instead, depend on volume (V). In this approximation, the vibrational entropy S of a collection of vibrational modes can be written as