Calculation of defect formation energies in UO 2
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Calculation of defect formation energies in UO2 Julia Wiktor1, Emerson Vathonne1, Michel Freyss1, Gérald Jomard1, Marjorie Bertolus1 1 CEA, DEN, DEC, Centre de Cadarache, 13108, Saint-Paul-lez-Durance, France ABSTRACT We present a physically justified formalism for the calculation of defect formation energies in UO2. The accessible ranges of chemical potentials of the two components U and O are calculated using the U-O experimental phase diagram and a constraint on the formation energies of vacancies. We then apply this formalism to the DFT+U investigation of the monovacancies and monointerstitials in UO2. The results of the most stable charge states of these defects are consistent with a strongly ionic system. Calculations predict similarly low formation energies for and in hyperstoichiometric UO2. INTRODUCTION A better understanding of atomic transport in nuclear fuels is essential to get further insight into irradiation driven micro-structural changes in these materials. These changes in turn control many basic material properties such as oxidation, actinide or fission product redistribution, fuel swelling and creep. Electronic structure calculations are invaluable tools to investigate these transport phenomena. Point defects in UO2 have been extensively studied using density functional theory [1,2,3,4,5,6,7,8]. Inconsistencies, however, exist in the formation energies of the defects obtained in these theoretical studies. First, different functionals are used for the description of interactions between electrons, in particular LDA, GGA, LDA+U, GGA+U or hybrid functionals. Second, not all DFT+U investigations deal with the spurious convergence to metastable states. Finally, the reference energies of O and U atoms used in formation energy calculations differ between the studies. Some authors choose O-rich conditions [5] where the oxygen chemical potential is set to its value in a O2 molecule, other authors change references from one defect to another [1,4] or consider two distinct references (O2 molecule and -uranium) [3]. We address the latter point in this paper. We present a physically justified formalism for the calculation of defect formation energies in UO2 and apply it to the DFT+U investigation of the monovacancies and monointerstitials in this material. FORMALISM FOR DEFECT FORMATION ENERGY CALCULATION The general expression for the calculation of the defect formation energies in UO2 is as follows: ,
,
,
(1)
where , is the total energy of the supercell with charge q containing the defect X, and are the numbers of uranium and oxygen atoms in the supercell, and are the is the electron chemical chemical potentials of uranium and oxygen atoms in UO2 and potential varying from the bottom to the top of the band gap.
The chemical potentials of uranium and oxygen atoms in UO2 are not known and cannot be obtained from the calculations. They depend on the stoichiometry of the material, which in turn depends on the composition of the gas surrounding the material, with which it is in equilibrium. We can write t
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