Alpha-plutonium's polycrystalline elastic moduli over its full temperature range

Indications of flat bands driving the δ to α volume collapse of plutonium

On cooling from the melt, plutonium (Pu) undergoes a series of structural transformations accompanied by a ≈ 28% reduction in volume from its δ phase to its α phase at low temperatures. While Pu's partially filled 5f-electron shells are known to be involved, their precise role in the transformations has remained unclear. By using calorimetry measurements on α-Pu and gallium-stabilized δ-Pu combined with resonant ultrasound and X-ray scattering data to account for the anomalously large softening of the lattice with temperature, we show here that the difference in electronic entropy between the α and δ phases dominates over the difference in phonon entropy. Rather than finding an electronic specific heat characteristic of broad f-electron bands in α-Pu, as might be expected to occur within a Kondo collapsed phase in analogy with cerium, we find it to be indicative of flatter subbands. An important role played by Pu's 5f electrons in the formation of its larger unit cell α phase comprising inequivalent lattice sites and varying bond lengths is therefore suggested.

Electronically driven collapse of the bulk modulus in δ-plutonium

A long-standing mystery in the material science of actinides concerns the question of why the bulk modulus of plutonium metal undergoes an anomalously large softening with increasing temperature compared to other metals. We show that a crucial step to understanding this phenomenon is taking into consideration the compressibility of thermally excited electronic configurations. We find this to lead to a previously unknown electronic softening contribution to the bulk modulus and a collapse of the bulk modulus when there exists a large partial pressure between different configurations.

Plutonium metal exhibits an anomalously large softening of its bulk modulus at elevated temperatures that is made all the more extraordinary by the finding that it occurs irrespective of whether the thermal expansion coefficient is positive, negative, or zero—representing an extreme departure from conventional Grüneisen scaling. We show here that the cause of this softening is the compressibility of plutonium’s thermally excited electronic configurations, which has thus far not been considered in thermodynamic models. We show that when compressible electronic configurations are thermally activated, they invariably give rise to a softening of the bulk modulus regardless of the sign of their contribution to the thermal expansion. The electronically driven softening of the bulk modulus is shown to be in good agreement with elastic moduli measurements performed on the gallium-stabilized δ phase of plutonium over a range of temperatures and compositions and is shown to grow rapidly at small concentrations of gallium and at high temperatures, where it becomes extremely sensitive to hydrostatic pressure.

Alpha-plutonium's Grüneisen parameter

Reported Grüneisen parameters γ of alpha-plutonium range from 3.0 to 9.6, which is remarkable because typical Grüneisen parameter uncertainty seldom exceeds ± 0.5. Our six new estimates obtained by different methods range from 3.2 to 9.6. The new estimates arise from Grüneisen's rule, from Einstein model and Debye model fits to low-temperature ΔV/V, from the bulk modulus temperature dependence, from the zero-point-energy contribution to the bulk modulus, and from another Grüneisen relationship whereby γ is estimated from only the bulk modulus and volume changes with temperature (or pressure). We disregard several high estimates because of the itinerant-localized 5f-electron changes during temperature changes and pressure changes. Considering all these estimates, for alpha-plutonium, we recommend γ = 3.7 ± 0.4, slightly high compared with values for all elemental metals.

Polycrystalline gamma-plutonium's elastic moduli versus temperature

Resonant ultrasound spectroscopy was used to measure the elastic properties of pure polycrystalline (239)Pu in the gamma-phase. Shear and longitudinal elastic moduli were measured simultaneously and the bulk modulus was computed from them. A smooth, linear, and large decrease in all elastic moduli with increasing temperature was observed. The Poisson ratio was calculated and an increase from 0.242 at 519 K to 0.252 at 571 K was found. These measurements on extremely well-characterized pure Pu are in agreement with other reported results where overlap occurs. We calculated an approximate Debye temperature Theta(D)=144 K. Determined from the temperature variation in the bulk modulus, gamma-Pu shows the same Gruneisen parameter as copper.