Point defects and clustering in uranium dioxide by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>LSDA</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi></mml:mrow></mml:math>calculations

Abstract

A comprehensive investigation on point defects and their clustering behavior in nonstoichiometric uranium dioxide $\mathrm{U}{\mathrm{O}}_{2\ifmmode\pm\else\textpm\fi{}x}$ is carried out using the $\mathrm{LSDA}+\mathrm{U}$ method based on density functional theory. Accurate energetic information and charge transfers available so far are obtained. With these energies that have improved more than 50% over that of pure generalized gradient approximation and local density approximation, we show that the density functional theory predicts the predominance of oxygen defects over uranium ones at any compositions, which is possible only after properly treating the localized $5f$ electrons. Calculations also suggest an upper bound of $x\ensuremath{\sim}0.03$ for oxygen clusters to start off. The volume change induced by point uranium defects is monotonic but nonlinear, whereas for oxygen defects, increasing $x$ always reduces the system volume linearly, except dimers that require extra space for accommodation, which has been identified as a metastable ionic molecule. Though oxygen dimers usually occupy Willis ${\mathrm{O}}^{\ensuremath{''}}$ sites and mimic a single oxygen in energetics and charge state, they are rare at ambient conditions. Its decomposition process and vibrational properties have been studied carefully. To a general clustering mechanism in anion-excess fluorites systematically obtain, we also analyze the local stabilities of possible basic clustering modes of oxygen defects. The result shows a unified way to understand the structure of Willis-type and cuboctahedral clusters in $\mathrm{U}{\mathrm{O}}_{2+x}$ and $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{U}}_{4}{\mathrm{O}}_{9}$. Finally, we generalize the point defect model to the independent cluster approximation to include clustering effects; the impact on defect populations is discussed.