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            This project is an investigation of the lattice dynamics of selected f-electron systems, including Pu, U, Ce, their alloys and compounds, and other related materials that are relevant to energy generation and national security. The underpinning scientific theme is the quantification and understanding of electron correlation effects which can play a dominant role in controlling the physical properties of these complex electronic systems. Such correlation effects modulate interatomic forces and lead to strongly competing interactions involving itinerant bonding, localization, and directional bonding of the f electrons, which can in turn lead to a host of complex phenomena including soft phonons, anharmonicity, negative thermal expansion, large volume changes across phase boundaries, pressure-induced volume collapse, charge and spin density waves, orbital ordering, magnetism, superconductivity, heavy Fermion behavior, etc. Alloying and compound formation can create additional levels of complexity. Many of the effects and phenomena are not yet understood in detail, and calculations based on density functional methods often fail to describe the experimental results. The physics of f-electron-containing systems represents a frontier area for fundamental research and a fertile ground for scientific discoveries.

            In the past year we have focused our work on two systems. One of them is Pu alloyed with 0.6 wt% of Ga. Pure Pu at room temperature has a complex crystal structure characterized by the monoclinic symmetry (alpha phase). With Ga alloying, its structure becomes fcc (delta phase). Upon cooling to ~170 K, the alloy makes a martensitic transformation to an alpha-prime phase. This low temperature transition is of great interest. Inelastic x-ray scattering studies at room temperature have shown a pronounced soft mode at the L point in the Brillouin zone. A lattice dynamics analysis shows that this soft mode is likely related to the low temperature phase transition. In our work, we apply the method of x-ray thermal diffuse scattering (TDS) to examine the temperature dependence and critical behavior, if any, of this mode as the sample temperature is lowered toward the transition temperature.

            X-ray TDS transmission patterns were recorded using synchrotron radiation at the Advanced Photon Source. Our analysis employed a fourth-neighbor Born-von Kármán force constant model to generate theoretical TDS images for a fit to the data. The planar force constants responsible for (111) atomic layer sliding and the L-point mode softening were treated as fitting parameters, while the other force constants were held fixed at the values known from prior work. The results of the analysis revealed that the soft mode remained unchanged over a wide temperature range. There was no further softening at temperatures very close the transition temperature. This is very unusual. Specifically, there are two other fcc elemental metals, Ce and La, that show similar soft modes at the L point, and both undergo similar first-order transitions. In both cases, significant phonon softening was observed as T approaches the transition temperature from above, and the behavior is in good accord with the usual picture of first-order martensitic transitions in terms of a free energy analysis.

            For the present case, the lack of temperature dependence of the soft mode suggests a different type of behavior for the free energy. The question is then: what drives the phase transition? It is likely that the unusual behavior of Pu-Ga is related to the 5f electronic structure near the Fermi level. The phase transition in question involves a partial local-itinerant (insulator-metal) transformation of the f electrons. Such electronic interactions can be highly nonlinear and abrupt. The fairly constant phonon frequency is also consistent with recent results demonstrating the robustness of the Pu electronic structure as the crystal is expanded by Am doping. Further theoretical studies using advanced computational tools would be needed for a detailed understanding of the relationship between electronic effects and soft phonon modes in this case.

            The other system that we are working on is Ce, which has a 4f electronic structure with instabilities somewhat similar to the Pu case. At room temperature, Ce under pressure undergoes a transformation from the gamma phase to the alpha phase with a sbstantial volume collapse, but both phases have the same fcc lattice structure. There has been a long debate about the relative importance of the lattice contribution and the electronic contribution to the entropy change related to the transition. In a collaboration with Michael Krisch of ESRF, we have analyzed the data from inelastic x-ray scattering and deduced the force constants for the two phases. Large changes are observed and the phonon entropies and free energies have been computed. The data and results are being further analyzed. We have noticed evidence indicating anomalies in the speed of sound and valence changes which could provide key clues for a better understanding of the nature of the transition.

            The work on Pu and Ce will continue. Other phase transitions in these and other systems as well as the behavior under extreme conditions will be explored. We have secured a grant from DOE to set up a diamond anvil cell system for high pressure studies of f-electron materials at low temperatures. The equipment will be located at Sector 30 of the Advanced Photon Source. We are in the process of organizing a PUP (Partner User Proposal) at the Advanced Photon Source for work on quantum phase transitions.