Influence of vibrational entropy on the concentrations of oxygen interstitial clusters and uranium vacancies in non-stoichiometric UO$_2$
Abstract
We combine density functional theory (DFT) formation energies and empirical potential calculations of vibrational free energies to calculate the free energies of formation of point defects and clusters of oxygen interstitials, and use a dilute defect model to calculate the concentrations of defects as a function of temperature and composition. We find that at high temperature oxygen interstitials are dominant, either in isolated form or in clusters depending on the deviation from stoichiometry. At temperatures lower than 1300 K we predict uranium vacancies to be dominant in the stoichiometric material. The disorder in UO2 therefore changes from Schottky to Frenkel type with increasing temperature. Uranium vacancies remain dominant up to deviations form stoichiometry as large as 0.045 at 800 K. Moreover, the concentration of uranium vacancies proves to be non-monotonous as a function of composition. These results are consistent with some experimental data on the evolution with stoichiometry of lattice constant, diffusion coefficients of uranium, positron lifetime and dilatometry measurements.
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