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about 350K. Thus nature has provided us with a special alloy of Pu that behaves in most ways the same as pure Pu, but with the powerful benefit of not changing volume with tempera- ture. How can we use this to improve our understanding of this still-mysterious metal? Using RUS, the bulk modulus of Pu has been measured recently over the full temperature range of the first three phases of pure Pu,19-21 and moduli of
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ibility, varies wildly. How can this be? A second clue, provid- ed by RUS, is the absolute value of the elastic moduli. These are very low, even lower than Pb, making the amplitude of thermally-induced atomic vibrations very large for a given temperature. Can this be the answer? That is, electron local- ization occurs because for a fraction of the time the vibrating Pu are close together, and for a fraction of the time they are far apart, a consequence of the elastic softness of the materi- al. Thus acoustics suggests a dynamically-induced effect, something beyond the capability of current models.
A final word
The examples above have barely begun to unveil the many aspects of Resonant Ultrasound Spectroscopy for the study of materials. Many other accounts of RUS are available in literature. And many other applications of sound to vari- ous solid state problems have been reported. Acoustics has provided an important tool in materials research, and is expected to remain a useful instrument for understanding and testing new materials. After all, it is mainly through lis- tening that we learn.AT
References
1 E. Schreiber, O. L. Anderson, N. Soga, and N. Warren, “Sound velocity and compressibility for lunar rocks 17 and 46 and for glass spheres from the lunar soil,” Science 167, 732–734 (1970).
2 H. H. Demarest, Jr., “Cube-resonance method to determine the elastic constants of solids,” J. Acoust. Soc. Am. 49, 768–775 (1971). 3 W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162
(1991).
4 A. Migliori, J. L. Sarrao, W. M. Visscher, T. M. Bell, M. Lei, Z.
Fisk, and R.G. Leisure, “Resonant ultrasound spectroscopic
The findings are remarkable. Unlike ZrW2O8, Pu is an elemental metal and so has no complex structures to assist with an understanding of the zero thermal expansion alloy. But invar, which experi- ences a gradual change from one phase to another over a temperature range around room temperature, provides a clue. The high temperature phase has a smaller volume than the low temperature phase, so by adjusting composition, as temperature rises, just enough high temperature phase grows to keep the volume constant. Can the same thing happen with Pu? Maybe, and ultrasound certainly can help with understanding, if not providing the still unknown answer. From RUS measurements of the compressibility of δ-Pu-2.4 at. % Ga, we find that this alloy, now stable to well below room temperature, exhibits stunningly large (near 30%, com- pared to 3.5% for Cu) softening of its compressibility in a smooth way from 100K to above 4000K. Figure 7 shows this softening. The measurements are exceedingly difficult because of the safety and security issues involved, and the simplicity of RUS, with its lack of a transducer bond require- ment (glue doesn’t last long on highly radioactive materials) has made accurate and comprehensive studies possible for the first time. However, the results are both tantalizing and important. What we find is that even though the spacing between the constituent atoms is not changing at all, the elec- tronic structure, which is a key component of the compress-
the gallium-stabilized fourth phase as well.
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