First principles calculations of the structure and elastic constants of α, β and γ uranium

Beeler, Benjamin; Deo, Chaitanya; Baskes, M. I.; Okuniewski, Maria A.

doi:10.1016/j.jnucmat.2012.09.019

Cited by 97 publications

(66 citation statements)

References 38 publications

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“…However, there is a wealth of studies implying the opposite [4][5][6][7][8][9][10][11][12][13][14][15], namely that neither DFT+U nor SOC are necessary for an accurate description of uranium metal or its alloys with zirconium. We argue that the DFT+U approach for these systems leads to inconsistencies and inaccurate results for formation enthalpies, atomic volumes, and magnetic properties and should best be avoided, contrary to the conclusion of [1] where it is argued to be an improvement over conventional DFT.…”

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confidence: 99%

Comment on “Correlation and relativistic effects in U metal and U-Zr alloy: Validation ofab initioapproaches”

2014

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Comment on “Correlation and relativistic effects in U metal and U-Zr alloy: Validation ofab initioapproaches”

2014

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“…The tetragonal structure of uranium (β-U) has been acknowledged to exist in a small stable temperature interval, 945 − 1045 K, and it has 30 atoms in a unit cell [1,2]. The αand the γ-U and its compounds have been explored in detail through experimental investigations and theoretical simulations [3][4][5][6][7][8][9][10]. However, contradictions and uncertainties have existed in the case of the arrangement of the 30 atoms in the unit cell of β-U since the 1950s.…”

Section: Introductionmentioning

confidence: 99%

“…136, they thought, should be the best choice for β-U as a result of their data and symmetry analyses. With that, Beeler et al [10] systematically analyzed the structural and the elastic properties of the α-, β-, and γ-phase, the body-centered tetragonal (bct) and the face-centered cubic (fcc) structures.…”

Section: Introductionmentioning

confidence: 99%

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Simulation studies on the structural stability and properties of beta uranium

Gong¹,

Gao²,

Sun

et al. 2015

Journal of the Korean Physical Society

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The structural stability of beta uranium (β-U) is investigated by using the projector augmented wave (PAW) method based on the density function theory (DFT). Optimized lattice parameters are in agreement with other available data. Especially, the energy per atom and the phonon properties manifest that the model described by using space group No. 102 can be stabilized vibrationally and energetically. A reasonable agreement with the experimental data for the phonon entropy corresponding to the proper structure has been successfully achieved. Moreover, the thermodynamic functions are predicated at elevated temperatures.

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“…These publications suggest that LSDA+U is not necessary for the metals while for their oxides it is relevant, although the methodology itself is phenomenological. Focusing first on the uranium ground state, orthorhombic α-U, equilibrium and structural properties [11], elastic constants [11,15], phonon spectra [16], various defects [17][18][19], and even subtle electronic-structure details related to the chargedensity waves [20] are all satisfactorily described within conventional DFT. These results clearly imply that LSDA+U is not a relevant or necessary scheme for α-uranium.…”

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Electron correlation and relativity of the 5f electrons in the U–Zr alloy system

Söderlind

Sadigh

Lordi

et al. 2014

Journal of Nuclear Materials

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We address a recently communicated conception that spin-orbit interaction and strong electron correlations are important for the metal fuel U-Zr system. Here, we show that (i) relativistic effects only marginally correct the uranium metal equation-of-state and (ii) addition of onsite Coulomb repulsion leads to an unphysical magnetic ground state of the body-centered cubic (γ) phase and a grossly overestimated equilibrium volume.Consequently, LSDA+U is deemed unsuitable for describing the electronic structure of the U-Zr system. e-mail address to the corresponding author: soderlind@llnl.gov Recently, Xiong et al. [1] reported on thermodynamic modeling of the U-Zr system motivated by its potential as a nuclear fuel for fast breeder reactors. This work [1] came on the heels of another report by Landa et al.[2] on the same system, but with very different results for the formation enthalpies and ultimate conclusion on the U-Zr phase diagram. The authors [1] argue that their calculated energetics are significantly more accurate than that by Landa et al. [2], and they further attribute the difference to strong electron correlations and the relativistic spin-orbit interaction.In the present Letter we show that uranium metal, and thus the U-Zr metal nuclear fuel system, possess weakly correlated electrons that are adequately described within density-functional theory in the generalized gradient approximation, and that addition of onsite Coulomb repulsion using the LSDA+U formalism leads to finite magnetization of the γ phase in contradiction to experiments. Furthermore, we show that spin-orbit interaction is quite weak in uranium metal and that its inclusion will not significantly change the chemical bonding and formation enthalpies.In order to illustrate our arguments, we perform comparative electronic-structure (VASP) to the uranium f orbitals, which approximately corrects for their electron self interaction. An effective U eff = U -J is chosen to be 2 eV (J = 0), which appears to be realistic for uranium systems [7]. The spin-orbit interaction is included using the secondvariation method with scalar-relativistic orbitals as basis. This basis includes all eigenstates with energy less than 70 eV. In order to improve the description of the relativistic orbitals, the p 1/2 local orbitals are added to the basis set. For actinide metals, this technique for the spin-orbit coupling equals, with good approximation, that of the complete four-spinor Dirac formalism [8][9][10]. All calculations use a 12×12×12 Monkhorst-Pack k-point grid and a plane-wave cutoff of 23 Ry.In Table 1 we show our calculated equilibrium volumes (V) and bulk moduli (B) obtained with and without spin-orbit coupling (SOC) for bcc (γ) uranium metal using the Wien2K (VASP) codes. (The other component, Zr, is a light metal where relativistic effects are not important). The changes in V and B due to SOC are indeed quite small, consistent with results from previous publications [9,11], and within the scatter of the experimental data. The reason why the...

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First principles calculations of the structure and elastic constants of α, β and γ uranium

Cited by 97 publications

References 38 publications

Comment on “Correlation and relativistic effects in U metal and U-Zr alloy: Validation ofab initioapproaches”

Comment on “Correlation and relativistic effects in U metal and U-Zr alloy: Validation ofab initioapproaches”

Simulation studies on the structural stability and properties of beta uranium

Electron correlation and relativity of the 5f electrons in the U–Zr alloy system

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