Origin of the multiple configurations that drive the response of δ-plutonium’s elastic moduli to temperature

Abstract

The electronic and thermodynamic complexity of plutonium has resisted a fundamental understanding for this important elemental metal. A critical test of any theory is the unusual softening of the bulk modulus with increasing temperature, a result that is counterintuitive because no or very little change in the atomic volume is observed upon heating. This unexpected behavior has in the past been attributed to competing but never-observed electronic states with different bonding properties similar to the scenario with magnetic states in Invar alloys. Using the recent observation of plutonium dynamic magnetism, we construct a theory for plutonium that agrees with relevant measurements by using density-functional-theory (DFT) calculations with no free parameters to compute the effect of longitudinal spin fluctuations on the temperature dependence of the bulk moduli in δ-Pu. We show that the softening with temperature can be understood in terms of a continuous distribution of thermally activated spin fluctuations.T he plutonium δ-phase (face-centered cubic, fcc), depending on gallium concentration, can on heating expand (above ∼2 at % Ga), contract (less than ∼2 at % Ga), or maintain volume independent of temperature from approximately 500 to 800 K (∼2 at % Ga) (1). Reminiscent of the Invar effect (2, 3), Lawson et al. (1) made the critically important observation that this could be modeled by assuming that two configurations were thermodynamically accessible in δ-Pu. This assumption introduces a strong constraint on a microscopic theory. Separated by 1,400 K, the higher energy configuration is assumed to have smaller volume than the lower energy one. Thus, as temperature rises, the Boltzmann factor increases the occupied fraction of the higher energy state, compensating for ordinary thermal expansion effects. This model could be made to fit δ-Pu's volume versus temperature dependence as measured by elastic neutron scattering for the range of Ga concentrations typically used to stabilize the δ-phase (4). However, measurements of the elastic moduli of polycrystalline Pu-Ga alloys by Suzuki et al. (5) showed that the bulk modulus softened substantially on warming in temperature regions where the atomic volume remained fixed. In an attempt to include elastic softening as temperature increased and volume decreased, Lawson et al.(1) made the unusual conjecture that the higher energy state with smaller volume, required to get the thermal expansion correct, must make no contribution to the bulk modulus. The usual situation is that a higher energy state with lower volume is stiffer, not softer as required here. Although the multiple-configuration assumption is now strongly supported by recent measurements (6), the yet-unexplained anomalous behavior (softening on warming with no volume change) remains a critical missing component of a fundamental understanding of δ-Pu.The detailed issue then is that the bulk and shear moduli of δ-Pu soften with temperature at a rate an order of magnitude greater than other metals with similar...

Relevance of Kondo physics for the temperature dependence of the bulk modulus in plutonium

“…First, we note that, contrary to the comments in Migliori et al (1), the results of our recent inelastic neutron experiments (2) do not contradict the results of earlier experiments (3)(4)(5), which show that the ground state is nonmagnetic. All of these experiments are consistent with the interpretation that δ-Pu has a nonmagnetic fluctuating valence ground state.…”

“…The recent PNAS paper by Migliori et al (1) attempts to explain the unusually strong temperature dependence of the bulk modulus of fcc plutonium (δ-Pu) by use of the disordered local moment (DLM) model. It is our opinion that this approach does not correctly incorporate the dynamic magnetism of δ-Pu.…”

“…Second, Söderlind et al (1,7) attempt to explain the small susceptibility observed in δ-Pu by assuming a complete cancellation of the spin and orbital angular momentum contributions. The spin and orbital moments in Pu do partially cancel, but we have performed a careful experimental analysis (2,8) to show that a net magnetic moment of 0.6 ± 0.2 μ B is present in the excited state.…”

“…This idea is based on comparison with rare earth valence fluctuation systems, such as CePd 3 and CeBe 13 , which exhibit bulk moduli anomalies as large as 10% because of the Kondo thermal excitation (10). In any case, careful examination of the results of Migliori et al (1) shows that the DLM model, which calculates a 6% decrease in the bulk modulus in the temperature range 300-500 K, underestimates the measured effect by a factor of four.…”

Physical mechanism of δ-δ′-ε phase stability in plutonium

“…The physical picture behind this reduction is given by the longitudinal thermal spin fluctuations 31 , which is due to the particular energy versus magnetic moment curve of Pu stabilizing lower local magnetic moments at high temperature, as compared to the static DLM moment. As shown in Fig.…”