Abstract
Ab initio calculations have been performed on all solid phases of U metal and U-Zr alloy, the basis of a promising metallic fuel for fast nuclear reactors. Based on generalized gradient approximation, both density functional theory (DFT) in its standard form and the so-called DFT plus Hubbard (DFT+) modification are evaluated. The evolution of calculated energetics, volume, magnetic moments, electronic structure, and -orbital occupation as functions of the effective Hubbard parameter, , is carefully examined at from 0 to 4 eV. DFT is found to overestimate energetics, underestimate volume, downward shift some bands near Fermi level and overestimate -orbital occupation against existing experimental and/or computational data. The error is ∼0.07 eV/atom in terms of enthalpy, which affects phase stability modeling for δ(U,Zr) and γ(U,Zr). DFT+ at eV offers clear improvement on these calculated properties (∼0.05 eV/atom in terms of enthalpy) and in general still neither promotes ordered magnetic moments nor opens unphysical band gaps, which occur at higher values. The empirical values of 1–1.5 eV are close to but smaller than the theoretical estimations of 1.9–2.3 eV that we obtain from the linear response approach. is found to vary only slightly (≤0.24 eV) between different phases and at different compositions of U and U-Zr; thus, a single eV, which is the statistical optimal from energetic fitting, is suggested for both U and U-Zr. Besides correlation, the relativistic effect of spin-orbit coupling (SOC) is also systematically explored. SOC is found to lower energy, increase volume, and split the 5 shell above Fermi level and reduce -orbital occupation. The effect predominates in the unoccupied states and is very small on all these calculated ground state properties (∼0.02 eV/atom in terms of enthalpy).
4 More- Received 21 June 2013
DOI:https://doi.org/10.1103/PhysRevB.88.235128
©2013 American Physical Society