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Results of ab initio density-functional theory calculations of the migration energies of oxygen vacancies and interstitials in stoichiometric UO 2 are reported. The diffusion of oxygen vacancies in UO 2 is found to be highly anisotropic, and the ͓1 0 0͔ direction is energetically favored. The atomic relaxations play an important role in reducing the migration barriers. Within the generalized gradient approximation ͑GGA͒, we find that the migration energies of the preferred vacancies and interstitials paths are, respectively, 1.18 and 1.09 eV. With the inclusion of the Hubbard U parameter to account for the 5f electron correlations in GGA+ U, the vacancy migration energy is lowered to 1.01 eV while the interstitial migration energy increases slightly to 1.13 eV. We find, however, that the correlation effects have a drastic influence on the mechanism of interstitial migration through the stabilization of Willis-type clusters. Indeed, in contrast to GGA, in GGA+ U there is an inversion of the migration path with the so-called "saddle-point" position being lower in energy than the usual starting position. Thus while the migration barriers are nearly the same in GGA and GGA+ U, the mechanisms are completely different. Our results clearly indicate that both vacancies and interstitials contribute almost equally to the diffusion of oxygen in UO 2 .

Barium and zirconium behavior in nuclear fuels is investigated using density functional theory ͑DFT͒. More particularly, incorporation and solution energies of Ba and Zr in preexisting trap sites of UO 2 ͑vacancies, interstitials, U-O divacancy, and Schottky trio defects͒ are calculated using the projector-augmented-wave method as implemented in the Vienna ab initio simulation package ͑VASP͒. Correlation effects are taken into account within the DFT+ U approach. Our results are discussed in relation to those based on conventional functionals and with available experimental data. For both functionals, zirconium is found to be much more soluble than barium. However, the most favorable solution site depends on the treatment of correlation effects, the difference between DFT+ U and DFT based results being more pronounced for Zr than for Ba. We also demonstrate that the solution process for more complex phases like BaO, ZrO 2 , BaUO 3 , and BaZrO 3 are very sensitive to the correct description of correlation effects in UO 2 .

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A theoretical study of molybdenum and caesium solution in uranium dioxide is carried out. Calculations are performed using the density functional theory with the projector-augmented-wave method as implemented in the Vienna ab initio simulation package (VASP). Correlation effects are taken into account within the DFT+U approach. Molybdenum is preferentially inserted in uranium-oxygen divacancies for understoichiometric urania and uranium vacancies for overstoichiometric urania. The favourable sites for caesium solution are the Schottky defect for understoichiometric urania and U vacancies and U-O divacancies for overstoichiometric urania. Using the stability of many binary and ternary compounds in comparison to soluted atoms, we show that caesium and molybdenum are insoluble in uranium dioxide whatever the stoichiometric regime.

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