2.2.1. Stable Occupation of Xe/Kr Cluster in UO2-Containing Point Defects

In addition to studying the stable occupation of Xe(Kr) clusters in defect-free bulk UO2, the influence of different defects in UO2 on the stable occupation of Xe(Kr) clusters was studied, such as U, O, UO double, Schottky, and double Schottky vacancies. A cubic box of 25 *a*<sup>0</sup> × 25 *a*<sup>0</sup> × 25 *a*<sup>0</sup> (*a*<sup>0</sup> is the lattice constant of the UO2 fluorite structure at 0 K) containing 187,500 atoms was used. MD simulation was performed after generating each configuration to equilibrate the system. After energy minimisation, the first atom was introduced into the system. The site with the lowest energy formation was searched through energy minimisation again to determine the stable site of the first atom. Afterwards, the second atom was introduced around the first atom, and the process was repeated to obtain a stable space for the two atoms. Further, the same process was performed until stable positions for six atoms were found successfully.

The formation energy of a Xe/Kr cluster in defect-free UO2 bulk is defined as follows:

$$E\_{N\text{ }\chi\text{e}/\text{Kr}}^{f} = E\_{N\text{ }\chi\text{e}/\text{Kr}}^{\text{Int}} - E^{P} - NE^{\chi\text{e}/\text{Kr}} \tag{1}$$

where *EInt <sup>N</sup>* Xe/Kr is the energy of the UO2 system containing the Xe (or Kr) cluster, *<sup>E</sup><sup>P</sup>* is the energy of perfect UO2, *N* is the number of Xe (or Kr) atoms, and *E*Xe/Kr is the energy of a single-isolated Xe (or Kr) atom (this value is zero for the interatomic potential under consideration).

The formation energy of a Xe/Kr cluster in defective UO2 is defined as

$$E\_{N\text{ }\text{Xe/Kr}}^{f} = E\_{N\text{ }\text{Xe/Kr}}^{Int} - E\_{VD}^{m} - NE^{\text{Xe/Kr}} \tag{2}$$

where *EInt <sup>N</sup>* Xe/Kr is the total energy of the system with the Xe (or Kr) cluster added on *VD* (represent different vacancy-type defects), *E<sup>m</sup> VD* is the total energy of systems containing the *VD*, *m* is the number of vacancies for *VD*, *N* is the number of Xe (or Kr) atoms, and *E*Xe/Kr is the energy of a single-isolated Xe (or Kr) atom.

The binding energy of an additional X (X = Xe or Kr) atom to a VD-X cluster in UO2 is defined as follows:

$$E^b(\mathbf{X} + \mathbf{VD} - \mathbf{X}\text{ cluster}) = E^f(\mathbf{X}) + E^f(\mathbf{VD} - \mathbf{X}\text{ cluster}) - E^f(\mathbf{X} + \mathbf{VD} - \mathbf{X}\text{ cluster}) \tag{3}$$

where *Ef* (X) is the formation energy of a Xe (or a Kr) atom located on the most stable interstitial site in bulk UO2.
