Thermodynamic stability of theUO2surfaces: Interplay between over-stoichiometry and polarity compensation

The thermodynamic stability of ${\mathrm{UO}}₂$ surfaces is investigated using ab initio calculations. We employ the GGA+$U$ framework to properly model the strong electronic correlations of the uranium $5f$ electrons. Among the seven terminations of the (100), (110), and (111) orientations studied in this paper, we predict that the stoichiometric O-(111) is the most stable one under oxygen-poor or -intermediary environments. At odds with other fluorite surfaces, the overstoichiometric and polar ${\mathrm{O}}₂$-(100) and ${\mathrm{O}}₂$-(111) terminations become the most stable in oxygen-rich environments. For the latter, strong modifications of the electronic structure appear within the upper layers, in order to fulfill the polarity compensation criterion. Some U-$5f$ states are emptied, leading to higher oxidation $5+$ and $6+$ states for uranium in the outermost layers, but leaving the surface insulating. This unexpected polarity compensation mechanism is not observed for other charge transfer compounds (such as ${\mathrm{PuO}}₂$) and can be related to the $f\text{\ensuremath{-}}f$ Mott-Hubbard band gap of the ${\mathrm{UO}}₂$ material. By considering the most stable stoichiometric and overstoichiometric terminations, the Castell's ratio can be fulfilled, explaining the Wulff shape of nanovoids in ${\mathrm{UO}}₂$ crystals.