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

By studying the position and energy changes of Xe/Kr atoms in UO2, it is found that, after adding Xe/Kr atoms into UO2, the Xe/Kr atoms move to the octahedral interstitial sites after structural optimization. Figure 1a shows that, when a Xe atom is randomly inserted into the bulk UO2, it moves to the nearest octahedral site. The energy is lowest at the octahedral interstitial site, with a formation energy of 9.79 eV. The phenomenon is the

same for the Kr atom, but, because the Kr atom is smaller than the Xe atom, its formation energy is smaller at 8.45 eV. When two interstitial Xe or two interstitial Kr atoms are added into UO2, after relaxation, the energy of the two atoms forming a dimer is the lowest. The formation energies of Xe2 and Kr2 are 16.44 and 15.60 eV, respectively. The stable structure of three interstitial atoms is shown as an equilateral triangle. The formation energies of Xe3 and Kr3 are 22.49 and 21.53 eV, respectively. After the addition of the fourth Xe atom and complete relaxation (Figure 1b), the positions of the four atoms appear as triangular cones at different octahedral sites. The first lattice U atom is squeezed out of the cluster, and the Xe atoms cluster around the U vacancy. However, the interstitial U atom moves away from the cluster, and the formation energy of Xe4 is 27.92 eV. The Kr4 cluster slightly differs from Xe4. The four Kr atoms are located on different octahedral gaps, forming a planar quadrilateral. However, no interstitial atoms are squeezed out of clusters, and the formation energy of Kr4 is 27.38 eV. After inserting the fifth atom, the first lattice U atom in the Kr cluster is squeezed out. After adding the sixth atom, the second lattice U atom is squeezed out of the Xe cluster (Figure 1c). The formation energies of Xe5, Kr5, Xe6, and Kr6 are 32.19, 32.41, 39.79, and 37.21 eV, respectively.

**Figure 1.** Relaxation configuration diagrams of different UO2 systems after adding Xe atoms. (**a**–**c**) are 1, 4, and 6 Xe in the defect-free system, respectively; (**d**–**f**) are 1, 3, and 6 Xe in the system containing U vacancies, respectively. (**g**–**i**) are 1, 3, and 6 Xe in the system containing double Schottky vacancies, respectively. The dashed frames are the schematics of the squeezed interstitial atoms. The red, yellow, green, and purple balls represent U atoms, Xe atoms, U vacancies, and U interstitial atoms, respectively. The O atoms are ignored.

Additionally, the stabilities of Xe/Kr atoms in configurations with different defects are compared. As shown in Figure 1d, in the configuration containing a single U vacancy, the addition of one Xe/Kr atom occupies the vacancy. When adding three or six Xe/Kr atoms in this system (Figure 1e,f), the atoms occupy the vacancy and distribute in the octahedral interstitial sites around the vacancy. The configuration of a single O vacancy is consistent with that of a single U vacancy. In the case of the UO double vacancy, one Xe/Kr atom was added to occupy the U vacancy. Two Xe/Kr atoms are evenly distributed into the central region of the two vacancy centres; when multiple atoms are added, they take the central region as the origin and occupy the surrounding octahedral interstitial sites. Figure 1g–i shows that, when there is a double Schottky vacancy, the Xe/Kr atom moves to the position near the central vacancy region. When more than one atom is present in the box, the Xe/Kr atoms are mainly distributed in the central vacancy region or the surrounding octahedral interstitial sites.

Figure 2 shows that, as the number of Xe/Kr atoms increases, the formation energy of the configuration with various defect types increases gradually. The formation energy of the O vacancy was 5 eV larger than that of the U vacancy on average at each stage. The Xe/Kr atom was more accessible to form in the U vacancy than in the O vacancy. Further, Figure 2 shows that the formation energy of Xe/Kr clusters in the six systems can be divided into three layers. The first layer contains the bulk UO2 and the system with O vacancy. They are characterized by no U vacancy, and the formation energy difference is very small. The second layer contains U, UO double, and Schottky vacancies, which contain only one U vacancy. The third layer contains double Schottky vacancies, which contain two U vacancies. Additionally, the volume of the U vacancy is much larger than that of the O vacancy, which provides more space for clusters. Thus, the stability of Xe/Kr clusters depends on the number of U vacancies. Figure 3 shows that, as the number of Xe/Kr atoms increases, the binding energy of Xe/Kr and cluster decreases and stabilises. The overall trends of adding Xe or Kr atoms are consistent, and the changes caused by different defects in the system are similar. The double Schottky configuration has a more vital ability to adsorb Xe atoms and weaken. When additional atoms are adsorbed to a certain extent, the adsorption capacities of all defective configurations tend to be the same, which mainly depends on the number of vacancy defects contained in the configurations.

**Figure 2.** The formation energy (eV) of (**a**) Xe clusters and (**b**) Kr clusters in UO2 with and without defects as a function of the number of Xe or Kr atoms in the formed cluster.

**Figure 3.** The binding energy (eV) of (**a**) an additional Xe atom and (**b**) an additional Kr atom to a cluster as a function of the number of Xe or Kr atoms in the formed cluster.
