Applicability of DFT + U to U metal and U-Zr alloy

TL;DR

This paper defends the use of DFT + U for modeling uranium and U-Zr alloys, countering recent critiques by providing experimental and computational evidence that supports its applicability and accuracy.

Contribution

It demonstrates that DFT + U remains a valid and valuable method for modeling uranium and U-Zr alloys, addressing previous criticisms and clarifying misconceptions.

Findings

DFT does not accurately model bulk modulus and elastic constants of αU.

DFT + U results are valid and can be useful for U and U-Zr modeling.

Criticisms based on specific phases and U_eff values are unfounded.

Abstract

In the Letter [J. Nucl. Mater. 444, 356 (2014)] and Comment [Phys Rev B 90, 157101 (2014)], Soderlind et al. argue that 1) DFT based on GGA already models U metal and U-Zr alloy accurately, and 2) DFT + U models them worse than DFT according to results they calculate or select from our recent study [Phys. Rev. B 88, 235128 (2013)]. Here we demonstrate in response to 1) that previously neglected and more recent experimental data indicate that DFT, even when implemented in all-electron methods, does not model the bulk modulus and elastic constants of {\alpha}U very accurately. Furthermore, Soderlind et al.'s claim that deficiency exists in our PAW calculation is unfounded and hence our results, including those that show DFT results compare unfavorably with experimental/computational references, are valid. We also demonstrate in response to 2) that Soderlind et al.'s arguments are unsound for three reasons. First, they focus on just the BCC phases {\gamma}U and {\gamma}(U,Zr)--which at the ab initio modeling temperature of 0 K are unstable and hence difficult to model and benchmar--as primary subjects of examination; however it is results for the stable phases mostly neglected by Soderlind et al. that are the primary evidence of our argument. Second, they make unfounded generalization of DFT + U results at selected U eff values to argue that DFT + U in general gives wrong or unsatisfactory results. Third, some key points in Soderlind et al.'s criticisms of DFT + U are not well supported, including the claims that for {\gamma}(U,Zr) DFT + U at Ueff = 1.24 eV gives positive deviations from linear dependence of composition that are unprecedentedly large and partially negative enthalpies of mixing that are inconsistent with the existence of miscibility gap in the experimental phase diagram. We therefore maintain our conclusion that DFT + U can be of value for modeling U and U-Zr.