*3.3. Nucleation of Xe/Kr Cluster in UO2-Containing Point Defects*

Here, the Xe/Kr atoms cluster together at high temperatures. A similar phenomenon occurred while studying Mo. Zhang et al. [16] studied the clustering process of Xe atoms dispersed in Mo at high temperatures. They observed the formation of Xe bubbles when the concentration of Xe atoms exceeded the threshold concentration value. In this paper, we studied randomly distributed Xe/Kr atoms at octahedral interspaces in UO2. Figure 5 shows that, as the relaxation progresses to 5 ns, small Xe clusters form, and then the tiny clusters gradually grow larger by absorbing extra Xe atoms. The clusters are more evident and are larger, almost stable clusters at relaxation to 10 ns. To ensure the stability of clusters, we observed the clustering phenomenon until 20 ns, which was almost not very different from that at 10 ns. The simulation results were consistent with the growth model proposed by Turnbull [55]. The bubbles were heterogeneously nucleated in the wake of fission fragments. They grew by collecting gas by atomic diffusion for a time controlled by a resolution process.

**Figure 5.** System evolution of Xe clusters at different times at 2500 K (the yellow balls represent Xe atoms, the red circles mark the clusters); (**a**) 0 ns, (**b**) 5 ns, (**c**) 10 ns, (**d**) 20 ns.

In the system with the same defect concentration, the number of clusters formed increases as the interstitial Xe/Kr atomic concentration increases. Figure 6 shows that the number and size of clusters in the system with 5% interstitial Xe atoms added significantly exceeded those with 2% interstitial Xe atoms. The former are more likely to form larger clusters, with a considerable number of clusters over 50 atoms or even over 100 atoms in size. In comparison, the latter are mainly distributed in 2 to 50 atoms.

When there are equal interstitial atom concentrations, the system with more vacancies is more likely to form larger clusters. Similarly, the more interstitial atoms prearranged in the system, the more difficult it is for the Xe/Kr atoms to aggregate during relaxation. The system mainly forms many small clusters ranging in size from 2 to 10 atoms.

The W–S cell method was used to analyse the defect results of the five systems. Three systems were selected for a detailed demonstration, namely the defect-free system (bulk), the system with 1% vacancy concentration (1% vac), and the system with 2% vacancy concentration (2% vac). Figure 7 shows the final distribution of Xe atoms at 5% concentration and the distribution of vacancy atoms and interstitial atoms after defect analysis, respectively. The Xe/Kr atom cluster region overlaps with the position of the vacancy cluster. In other words, the nucleation of the Xe/Kr atom mainly occupied the vacancy position by squeezing out the atoms on the original lattice, which is consistent with the analysis of the stable occupation above. The Xe/Kr atoms squeeze out U atoms to form vacancies, and interstitial atoms moved away from clusters. In addition, Xe/vac is ~1.

**Figure 6.** The cluster sizes distribution of (**a**) 2% Xe, (**b**) 5% Xe, (**c**) 2% Kr, and (**d**) 5% Kr in different systems, respectively. The pink, light blue, dark blue, green and red bars are the systems with 2% interstitial concentration, with 1% interstitial concentration, perfect bulk without defects, with 1% vacancies concentration, with 2% vacancies concentration, respectively.

**Figure 7.** Xe clusters distribution and defects distribution at 5% concentration of Xe atoms in different systems. The green, red, and yellow balls represent the lattice U vacancies, U interstitials, and Xe atoms.
