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Landmark experiment opens up new research opportunities in actinides science

Researchers use high-resolution inelastic x-ray scattering and a microbeam approach to determine the first full phonon dispersion curves ever measured for any plutonium-bearing materials

Editor's note: The six scientists from Lawrence Livermore National Laboratory (LLNL) who co-authored this article have garnered an award for their groundbreaking research. The team recently received a Science and Technology Award, the highest honor granted by LLNL for science and technology accomplishments.

Understanding the physical basis for the intriguing properties of plutonium materials such as force constants, sound velocities, elasticity, phase stability, and thermodynamic properties critically hinges on the ability to produce high-quality experimental data. Of these, phonon dispersion curves (PDCs) are key to the elucidation of many of these physical phenomena.

A phonon is a lattice vibration, the acoustic equivalent of a photon, the basic quanta of light. PDCs in plutonium and its alloys have defied experimental determinations for the past 40 years because of the inability to grow the large single crystals (at least a few cubic millimeters in volume) necessary for inelastic neutron scattering (INS) measurements. Another obstacle was the high thermal-neutron absorption cross section of the most common isotope, plutonium-239.

Furthermore, only recently have theoretical computations of plutonium PDCs begun to overcome the difficulties in treating the f electrons accurately within the standard first-principles methods. Thus, the PDCs for plutonium-bearing systems have remained essentially unknown experimentally and theoretically.

The experimental difficulties associated with INS are circumvented in our experimental approach by employing inelastic x-ray scattering (IXS) with milli-electron volt (meV) energy resolution. With the advent of highly brilliant x-ray sources and high-performance focusing optics, samples with volumes as small as one ten-thousandth of a cubic millimeter can now be studied. These capabilities have opened up new experimental opportunities for materials that are only available in small quantities, as is the case for many actinide systems. The research is covered in detail in a paper published in August in Science magazine (see Science, Volume 301, page 1078 [2003]).

Our samples were large-grain polycrystalline specimens prepared from a plutonium-gallium alloy containing about 0.6 percent by weight of gallium produced by a strain-enhanced recrystallization technique. To extract the phonon energies, the spectra were fitted by convolving the experimentally determined resolution profile with a model function consisting of a Lorentzian for the elastic contribution and a pair of Lorentzians, constrained by the thermal phonon population factor, for the inelastic part.

The resulting PDCs along the three principal symmetry directions in the face-centered cubic (fcc) lattice are displayed in the figure below, together with a fit using a standard Born-von Kármán (B-vK) force constant model. An adequate fit to the experimental data is obtained if interactions up to the fourth-nearest neighbors are included and the calculated phonon density of states derived from the B-vK model is also shown. The dashed curves are recent dynamical mean field theory (DMFT) results.

Phonon dispersions along high-symmetry directions in a face-centered cubic plutonium-gallium alloy containing about 0.6 percent by weight of gallium. The experimental data are shown as circles. Along the [0xx] direction, there are two transverse branches [011]<01-1>(T 1) and [011]<100> (T2). Note the softening of the TA[xxx] branch toward the L point. The lattice parameter of our samples is a = 0.4621 nanometer (nm). The solid curves are the fourth-nearest neighbor Born-von Kármán model fit. The derived phonon density of states, normalized to three states per atom, is plotted in the right panel. The dashed curves are calculated dispersions for pure delta-plutonium based on dynamical mean field theory (DMFT).

The elastic moduli calculated from slopes of the experimental phonon dispersion curves near the G point are: C11 = 35.3 ±1.4 giga pascal (GPa), C12 = 25.5 ±1.5 GPa and C44 = 30.53 ±1.1 GPa. These values are in excellent agreement with those of the only other measurement on a similar alloy (1 percent atomic weight gallium) using ultrasonic techniques as well as with those recently calculated from a combined DMFT and linear response theory for pure delta-plutonium.

The small difference between C11 and C44 is very unusual for a metal with a face-centered cubic structure. The shear moduli C44 and C' = (C11 - C12)/2 differ by a factor of six. This is in contrast to that of a "normal" fcc metal such as aluminum: 1.2 and is significantly higher than values in other "unusual" fcc metals such as gamma-cerium: 2.8, lanthanum: 4.1, and thorium: 3.6.

Published results support the conclusion that delta-plutonium-gallium is the most elastically anisotropic fcc metal known. Furthermore, we observe a large deviation, D, from the Cauchy criterion. Our measurement yields D = (C44 -C12)/C12 = 0.9, which differs significantly from zero and implies that the interatomic forces have a strong noncentral component.

Joe Wong and his colleagues used the high-resolution inelastic x-ray scattering beam line at the European Synchrotron Radiation Facility in Grenoble, France, to obtain the first-ever experimentally determined phonon dispersion curves of a plutonium alloy. ESRF is a third-generation synchrotron, and the only facility with a beam line capable of measuring plutonium's lattice vibration energy.

The most striking feature of the experimental PDCs is a soft-mode behavior for the TA branch along [111]. A similar feature (but occurring at about twice the energy and at a higher crystal momentum toward the L point) is also seen in a recent DMFT calculation for delta-plutonium. The cubic fcc crystal structure of delta-plutonium can be viewed as being composed of hexagonally close-packed atomic planes stacked along the [111] direction with a specific stacking arrangement. The soft transverse mode at L suggests that each atomic plane could easily slide relative to its immediate neighboring atomic planes to form new stacking arrangements.

Pure delta-plutonium, on lowering temperature, transforms into the gamma phase, which has a face-centered orthorhombic structure. This structure can be described in terms of a stack of slightly distorted hexagonally packed atomic layers, and indeed is the type of structure that could be easily obtained by layer parallel shear in the fcc phase.

Thus, the soft mode at L is likely a key feature associated with the delta-to-gamma transition, even though this transition is suppressed by gallium stabilization in the present case. This notion is indeed substantiated by the fact that the first interplanar force constant (derived from the B-vK model) of the T[111] mode is more than an order of magnitude smaller than those of the transverse modes in the other two directions.

The small amount of gallium in the sample is sufficient to allow the system to bypass the gamma and beta phases and make a transition directly to a monoclinic alpha-prime phase at about -110oC. The alpha-prime phase, despite its apparent complexity, is also a slightly distorted hexagonal close-packed structure, and is easily accessible from the fcc phase through the same shear mechanism.

A similar soft-mode behavior has been observed in gamma-cerium and lanthanum. In those cases, the transition leads, instead, to a double-hexagonal-close-packed structure, but the same general concept of layer parallel shear applies.

As evident by the data presented in the figure on the previous page, our IXS experiment validates the main qualitative predictions of a recent DMFT calculation for delta-plutonium in terms of a low shear elastic modulus C', a Kohn-like anomaly in the T1[011] branch, and a large softening of the T[111] modes. Such experimental-theoretical agreements give credence to the DMFT approach for the theoretical treatment of 5f electron systems. However, while there is good qualitative agreement between theory and experiment, quantitative differences are evident. These differences provide the benchmark for refined theoretical treatments and further experiments with plutonium and other 5f elements.

Acknowledgements

This work was performed under the auspices of the Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48 and the Department of Energy by the University of Illinois Frederick Seitz Materials Research Laboratory under Grant No. DEFG02-91ER45439. We are thankful to Francesco Sette, European Synchrotron Radiation Facility (ESRF) for his support and encouragement in this project, and to Paul Berkvens and Patrick Colomp, also with ESRF, for their advice and technical assistance.

This article was contributed by Joe Wong, Daniel Farber, Florent Occelli, Adam J. Schwartz, Mark Wall, and Carl Boro of Lawrence Livermore National Laboratory; Michael Krisch of the European Synchrotron Radiation Facility, Grenoble, France; and Tai-C. Chiang and Ruqing Xu, of the Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign.


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