Point Defects Stability, Hydrogen Diffusion, Electronic Structure, and Mechanical Properties of Defected Equiatomic γ(U,Zr) from First-Principles

. 2022 Oct 24;15(21):7452. doi: 10.3390/ma15217452

U-Pu-Zr	Uranium-plutonium-zirconium
U-Zr	Uranium-zirconium
BCC	body-centered cubic
H	Hydrogen
DFT	Density functional theory
DFT + U	Density functional theory plus Hubbard parameter U
SOC	Spin-orbit coupling
$V_{U}$	Uranium vacancy
$V_{Z r}$	Zirconium vacancy
$H_{U}$	Uranium lattice occupied by hydrogen atom
$H_{Z r}$	Zirconium lattice occupied by hydrogen atom
$Perfect + O - site H_{i}$	Octahedral hydrogen interstitial in perfect cell
$Perfect + T - site H_{i}$	Tetrahedral hydrogen interstitial in perfect cell
$V_{U}$ $+ O - site H_{i}$	Octahedral hydrogen interstitial in uranium vacancy-containing cell
$V_{U}$ $+ T - site H_{i}$	Tetrahedral hydrogen interstitial in uranium vacancy-containing cell
CI-NEB	Climbing image nudged elastic band
SQS	Special quasi-random structure
E_cohesive	Cohesive energy
$N_{U}$	Number of uranium atoms
$N_{Z r}$	Number of zirconium atoms
$E_{U}$	Energy of an isolated uranium atom
$E_{Z r}$	Energy of an isolated zirconium atom
E[γ(U,Zr)]	Total energy of the γ(U,Zr) supercells
$E_{f} (V_{X})$	Formation energy of X type vacancy, X can be uranium or zirconium
$E [γ (U, Z r), V_{X}]$	Total energy of γ(U,Zr) supercells with a vacancy
$E (X)$	Energy of an isolated X atom, X can be uranium or zirconium
$E_{S}$	Hydrogen solution energy
E[γ(U,Zr),H]	Total energy of the γ(U,Zr) supercells with H atom
$E (H_{2})$	Energy of H2 molecular
$E [γ (U, Z r), V_{X}, H]$	Total energy of the γ(U,Zr) supercells with both X type vacancy and H atom, X can be uranium or zirconium
$E_{H_{i}}^{t r a p}$	Trapping energy of uranium vacancy on T-site $H_{i}$
TDOS	Total densities of states
PDOS	Partial densities of states
$N (E_{F})$	TDOS at the Fermi level
$N_{e} (U_{f})$	Number of valence electrons of U element at the Fermi energy level
$N_{e} (Z r_{d})$	Number of valence electrons of Zr element at the Fermi energy level
EOS	Equation of state
VRH approximations	Voight-Reuss-Hill approximations