  At the atomic scale, uranium-plutonium mixed oxides (U,Pu)O_2 are
characterized by cationic chemical disorder, which entails that U and Pu
cations are randomly distributed on the cation sublattice. In the present work,
we study the impact of disorder on point-defect formation energies in (U,Pu)O_2
using interatomic-potential and Density Functional Theory (DFT+U) calculations.
We focus on bound Schottky defects (BSD) that are among the most stable defects
in these oxides. As a first step, we estimate the distance R_D around the BSD
up to which the local chemical environment significantly affects their
formation energy. To this end, we propose an original procedure in which the
formation energy is computed for several supercells at varying levels of
disorder. We conclude that the first three cation shells around the BSD have a
non-negligible influence on their formation energy (R_{D} = 7.0 \{AA}). We
apply then a systematic approach to compute the BSD formation energies for all
the possible cation configurations on the first and second nearest neighbor
shells around the BSD. We show that the formation energy can range in an
interval of 0.97 eV, depending on the relative amount of U and Pu neighboring
cations. Based on these results, we propose an interaction model that describes
the effect of nominal and local composition on the BSD formation energy.
Finally, the DFT+U benchmark calculations show a satisfactory agreement for
configurations characterized by a U-rich local environment, and a larger
mismatch in the case of a Pu-rich one. In summary, this work provides valuable
insights on the properties of BSD defects in (U,Pu)O_2, and can represent a
valid strategy to study point defect properties in disordered compounds.
