  Formation Gibbs free energy of point defects and oxygen clusters in uranium
dioxide at high-pressure high-temperature conditions are calculated from first
principles, using the LSDA+U approach for the electronic structure and the
Debye model for the lattice vibrations. The phonon contribution on Frenkel
pairs is found to be notable, whereas it is negligible for the Schottky defect.
Hydrostatic compression changes the formation energies drastically, making
defect concentrations depend more sensitively on pressure. Calculations show
that, if no oxygen clusters are considered, uranium vacancy becomes predominant
in overstoichiometric UO2 with the aid of the contribution from lattice
vibrations, while compression favors oxygen defects and suppresses uranium
vacancy greatly. At ambient pressure, however, the experimental observation of
predominant oxygen defects in this regime can be reproduced only in a form of
cuboctahedral clusters, underlining the importance of defect clustering in
UO2+x. Making use of the point defect model, an equation of state for
non-stoichiometric oxides is established, which is then applied to describe the
shock Hugoniot of UO2+x. Furthermore, the oxidization and compression behavior
of uranium monoxide, triuranium octoxide, uranium trioxide, and a series of
defective UO2 at zero Kelvin are investigated. The evolution of mechanical
properties and electronic structures with an increase of the oxidation degree
are analyzed, revealing the transition of the groundstate of uranium oxides
from metallic to Mott insulator and then to charge-transfer insulator due to
the interplay of strongly correlated effects of 5f orbitals and the shift of
electrons from uranium to oxygen atoms.
