Non stoichiometric uranium dioxide experiences a shrinkage of its lattice constant with increasing oxygen content, for both the hypo- and the hyper-stoichiometric regimes. Based on ab initio calculations within the DFT+U approximation, we have developed a point defect model that accounts for the volume of relaxation of the most significant intrinsic defects of UO₂. Our model takes a special care about the treatment of the charged defects in the equilibration [1] and in the determination of reliable defect volumes of formation [2].
In the hypostoichiometric regime, the charged oxygen vacancies are dominant and explain the lattice constant variation
with their unexpected positive volume of relaxation.
In the hyperstoichiometric regime, the uranium vacancies are predicted to be the dominating defect in contradiction with experimental observations. However, disregarding uranium vacancies allows us to recover a good match for the lattice constant variation as a function of stoichiometry. This can be considered as a new clue that the stability of uranium vacancies within DFT+U is indeed spurious.

[1] J.P. Crocombette, D. Torumba, and A. Chartier, Phys. Rev. B 83, 184107 (2011).
[2] F. Bruneval, C. Varvenne, J.P. Crocombette, E. Clouet, Phys. Rev. B 91, 024107 (2015).