[SY-B2] Influence of vibrational entropy on the concentrations of uranium vacancies in UO2
The wide deviations of the composition of UO2 around its nominal composition are accommodated by point defects or clusters of oxygen interstitials. The formation energies of these defects have been the subject of many studies DFT calculations. In the high temperature understoichiometric regime, atomistic calculations and experiment agree on the fact that oxygen vacancies are the dominant defect. At the opposite for the overstoichiometric material the formation energies predict uranium vacancies to dominate over oxygen interstitials. This contradicts experimental facts which show that oxygen interstitials, either isolated or clustered are accommodating the overstoichiometry in UO2+x. This so-called “uranium vacancy problem” has been noticed for many years [1] and has resisted the various calculations improvements, either methodological (e.g. use of DFT+U) or numerical (e.g. calculations made on bigger boxes).
Considering the vibrational entropy of the defects enables to solve this problem. We have combined ab initio formation energies of point defects and oxygen clusters in UO2 [2] with harmonic entropies calculated with a many body empirical potential with charge equilibration [3]. Including the vibrational contribution to the free energy of defects de-stabilizes the uranium vacancies compared to the oxygen defects. The latter are then predicted to be dominant at high temperatures or large overstoichiometry in agreement with experiments. However our calculations exhibit a composition and temperature domain where uranium vacancies may in fact be the majority defect in UO2+x. Some experimental observations (dilatometry, positron annihilation spectroscopy and uranium diffusion measurements) tend to confirm this prediction.
[1] J.P. Crocombette, et al., Phys. Rev. B 64, 104107 (2001).
[2] F. Bruneval, et al., Phys. Rev. Materials 2, 023801 (2018).
[3] A. Soulié, et al., Acta Mater. 150, 248 (2018).
Considering the vibrational entropy of the defects enables to solve this problem. We have combined ab initio formation energies of point defects and oxygen clusters in UO2 [2] with harmonic entropies calculated with a many body empirical potential with charge equilibration [3]. Including the vibrational contribution to the free energy of defects de-stabilizes the uranium vacancies compared to the oxygen defects. The latter are then predicted to be dominant at high temperatures or large overstoichiometry in agreement with experiments. However our calculations exhibit a composition and temperature domain where uranium vacancies may in fact be the majority defect in UO2+x. Some experimental observations (dilatometry, positron annihilation spectroscopy and uranium diffusion measurements) tend to confirm this prediction.
[1] J.P. Crocombette, et al., Phys. Rev. B 64, 104107 (2001).
[2] F. Bruneval, et al., Phys. Rev. Materials 2, 023801 (2018).
[3] A. Soulié, et al., Acta Mater. 150, 248 (2018).