Invar effect in Pu-Ga alloys

Lawson, A. C.; Roberts, J. A.; Martinez, B.; Richardson, J. W.

doi:10.1080/13642810208222945

Cited by 40 publications

(41 citation statements)

References 16 publications

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“…IV.A. The double-well minima offer a natural explanation for the negative volume expansion in pure delta Pu and its dependence on Ga concentration ͑Kotliar, 2002; Lawson et al, 2002Lawson et al, , 2005Kotliar and Savrasov, 2003͒. The calculated spectral density of states for the fcc structure using the volume V / V ␦ = 0.8 and 1.05 corresponding to the ␣ and ␦ phases has been reported ͑Savrasov et al,…”

Section: Plutoniummentioning

confidence: 99%

Electronic structure calculations with dynamical mean-field theory

et al. 2006

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A review of the basic ideas and techniques of the spectral density-functional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the one-electron description breaks down. The method is illustrated with several examples where interactions play a dominant role: systems near metal-insulator transitions, systems near volume collapse transitions, and systems with local moments.

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Section: Plutoniummentioning

confidence: 99%

Electronic structure calculations with dynamical mean-field theory

et al. 2006

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“…This technique (9) measures the mechanical resonance frequencies to determine the complete elastic tensor. The rectangular parallelepiped specimens used for the temperature dependence were 0.1311 g, 0.1995 × 0.2045 × 0.2078 cm 3 with geometrically determined density of 15.466 g/cm 3 at 295 K, and 1.3396 g, 0.4746 × 0.3768 × 0.4843 cm 3 with geometric density of 15.467 g/cm 3 at 295 K. The absolute error in the determination of bulk modulus B and shear modulus G was ∼0.3%. The errors were primarily caused by errors in the geometry, thus the precision of the measured temperature dependence is substantially greater than the accuracy.…”

Section: Experimental Methodsmentioning

confidence: 99%

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

Migliori

Söderlind

Landa

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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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...

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“…The increase in β (0) upon increasing temperature incorporates several important effects compared to the temperature independent parameterization, (1) it introduces strong phonon softenings enhancing anharmonicity; (2) it enhances the weight of the non-spherically symmetric fluctuations in the positions of the neighboring atoms; (3) it lowers the energy of the competing phases which have smaller volumes. Fluctuations into those phases decrease the volume in a way reminiscent of the Invar model [9,10], without having to include explicit Ising degrees of freedom as was done recently by Lee et al in Ref. 38.…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore the transition from α to δ phase is characterized by a large excess of entropy beyond the phonon contribution, but no comprehensive microscopic theory of the excess entropy is available. [7,8] A very useful phenomenology for δ-Pu and its alloys has been constructed by Lawson and his collaborators, by using analogies with the Invar model of iron [9,10].…”

Section: Introductionmentioning

confidence: 99%

Temperature-dependent electronic structures, atomistic modelling and the negative thermal expansion ofδPu

Yin

Deng

Basu

et al. 2014

Philosophical Magazine Letters

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We introduce a temperature-dependent parameterization in the modified embedded-atom method and combine it with molecular dynamics to simulate the diverse physical properties of the δ and ε phases of elemental plutonium. The aim of this temperature-dependent parameterization is to mimic the different magnitudes of correlation strength of the Pu 5f electrons at different temperatures. Compared to previous temperature independent parameterization, our approach captures the negative thermal expansion and temperature dependence of the bulk moduli in the δ-phase. We trace this improvement to a strong softening of phonons near the zone boundary and an increase of the flike partial density and anharmonic effects induced by the temperature-dependent parameterization upon increasing temperature. Our study suggests it is important to include temperature-dependent parameterization in classical force field methods to simulate complex materials such as Pu.

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Invar effect in Pu-Ga alloys

Cited by 40 publications

References 16 publications

Electronic structure calculations with dynamical mean-field theory

Electronic structure calculations with dynamical mean-field theory

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

Temperature-dependent electronic structures, atomistic modelling and the negative thermal expansion ofδPu

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