*3.2. Diffusion of Xe/Kr Cluster in UO2*

Based on empirical potential calculations, the diffusivity of Xe/Kr clusters in bulk UO2 has been calculated. Since the first U interstitial atom was excited by adding four Xe atoms or five Kr atoms to the bulk UO2, we studied the Xe/Kr clusters with less than four atoms. Xe usually diffuses due to a vacancy-assisted mechanism. The diffusion of Xe at U, O, UO, one U, two O vacancies, and vacancy clusters (comprising two U vacancies and zero, one, or two O vacancies) has been studied in most studies. Earlier studies concluded that Xe atoms occupied trap sites that contained at least one uranium vacancy and, in many cases, one or two additional oxygen vacancies [49,50]. The conclusion showed that triple vacancy was the main diffusion pathway of Xe in UO2. Previous DFT data [51–53] have shown the activation energies of Xe from 2.87 to 3.95 eV and prediffusion factors from <sup>5</sup> × <sup>10</sup>−<sup>4</sup> m2/s to 2.9 × <sup>10</sup>−<sup>12</sup> m2/s. Due to experimental factors, Lawrence et al. [21] found that the diffusion coefficients between different studies have many orders of magnitude. Herein, the interstitial diffusion mechanism of Xe/Kr was investigated. The simulation estimated the diffusion barrier of Xe atoms as 2.11 eV and the pre-diffusion factor index as 1.8 × <sup>10</sup>−<sup>5</sup> <sup>m</sup>2/s at temperatures between 1800 and 2300 K, and the simulation estimated the diffusion barrier of Kr atoms as 2.31 eV and the prediffusion factor index as 0.12 × <sup>10</sup>−<sup>3</sup> <sup>m</sup>2/s. Tables <sup>1</sup> and <sup>2</sup> show the detailed data of the Xe/Kr atom and clusters. Torres et al. [54] calculated the migration energies of Xe/Kr in bulk UO2 by a direct mechanism, and the results were 4.09 and 4.72 eV, respectively.

**Table 1.** Diffusion energy barrier and diffusion prefactor of small interstitial Xe clusters in UO2.


**Table 2.** Diffusion energy barrier and diffusion prefactor of small interstitial Kr clusters in UO2.


The activation energy of the Xe cluster was ~2 eV, and the diffusion coefficient can be seen in Figure 4, which shows the diffusion coefficient for Xe and Kr clusters in bulk UO2. Figure 4 illustrates the difficulty of cluster diffusion. It is consistent with the data proposed by Davies et al., indicating that clusters are not easy to diffuse. By analysing the movement of the atoms during migration, we find that, when studying the diffusion of individual atoms, evidently, individual atoms are fast and have a wide range of motion. When studying clusters with two atoms, the atoms move mainly by the rotating bypass method. In the diffusion process, atom A was stapled at random, and then atom B rotated around atom A to find a stable position, and then spread over continuously. When there were three atoms in a cluster, a small cluster was formed with one of the atoms pinned together, and the remaining atoms rotated slightly, causing the whole cluster to move and spread out. These trajectories suggested that the diffusion of interstitial clusters is more complicated and may require more complex conditions. In fact, there are little data on experimental interstitial diffusion.

**Figure 4.** The diffusion coefficient for (**a**) Xe and (**b**) Kr clusters in bulk UO2. The lines are linear Arrhenius fits.
