Invar model for δ-phase Pu: thermal expansion, elastic and magnetic properties

Lawson, A. C.; Roberts, J. A.; Martinez, B.; Ramos, Michael; Kotliar, Gabriel; Trouw, Frans; Fitzsimmons, M. R.; Hehlen, Markus P.; Lashley, J. C.; Ledbetter, Hassel; McQueeney, R. J.; Migliori, A.

doi:10.1080/14786430500155262

Cited by 51 publications

(79 citation statements)

References 34 publications

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“…This makes the 12-parameter fit of Lawson et al (1), and their analysis revealing a possible electronics-based free-energy driver for softening on heating, difficult to justify on fundamental grounds. Nevertheless, density and elasticity measurements point toward δ-Pu, pure or alloyed with Ga, being a mixture of at least two electronic configurations that are both thermally accessible below the melting point.…”

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confidence: 99%

“…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.…”

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confidence: 99%

“…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.…”

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confidence: 99%

“…δ plutonium | elastic moduli | thermal expansion | DFT 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.…”

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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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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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“…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].…”

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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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Diffraction and Thermal Expansion of Solids

Tyagi

Achary

2010

Thermodynamic Properties of Solids

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Thermal expansion of materials is a topic of age-old interest to mankind in view of the chronological development of several devices and technologies [1,2]. The concept of thermal expansion and knowledge of thermal expansion coefficient of materials remain important for any structural materials experiencing a temperature gradient. The structural materials include any material used in technology to build a mechanically or electronically integrated physical entity. In particular, the thermal properties are of interest when any structural assembly faces a temperature variation. Thermal expansion effects have been well considered right from the metals and ceramic parts of cookwares to the highly sophisticated mechanical structures, such as buildings, bridges, air/spacecraft, vessels, kilns, furnaces, and so on. In particular, metals such as steel, copper, and so on that are important structural parts show a significant expansion with temperature. Thus, in all these materials, thermal expansion was exploited either to enhance or to nullify any temperature-induced dimensional instability, for example, the utilization of thermal expansion in automatic cut-off switch using bimetals is well known. The discovery of Invar (an alloy of 35% Ni and 65% Fe) and subsequent modified compositions as Elinvar, Kovar, Alnico, and so on have found immense applications in modern technologies, such as design of high-accuracy clocks, shadow mask in television screen, and so on [3]. In addition, low thermal expansion in fused silica and controllable thermal expansion in materials with glass and glass-ceramic compositions have been discovered and used in precise optical instruments, mirror substrates, glass-metal junctions [4,5]. A large number of crystalline materials with low thermal expansion are also discovered [6]. Thermal expansion data of ceramics have been a prime consideration in the designing of electrolyte and electrodes of solid oxide fuel cells [7]. Similarly, thermal expansion data of nuclear fuel materials are significant in preventing detrimental effects of fuel-clad interaction and unwanted swelling of fuel pins [8]. Nuclear reactor performance is mainly restricted by the thermal expansion and thermal conductivity of the fuel pellets under irradiation conditions. In these j197 applications, the material property is more significant than the structural assembly and hence the structural materials are tuned as per their thermal expansion behavior. However, the thermal expansion behavior of electronic materials causing temperature-induced dimensional instability leading to circuit failure also needs to be dealt with. Considering such aspects, several Invar-type alloys and metal matrix composites are developed in recent years [9]. Thus, the thermal expansion data of any material are the first requisite for the development of most of the technologies.In general, it is known that all materials expand or contract with the rise or fall of temperature. The thermal expansion of any material is explained as a relative change in dimens...

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Invar model for δ-phase Pu: thermal expansion, elastic and magnetic properties

Cited by 51 publications

References 34 publications

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

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

Diffraction and Thermal Expansion of Solids

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