**1. Introduction**

Uranium dioxide (UO2) has been widely used as fuel for nuclear reactors owing to its properties, such as there being no specific deformation when it is strongly irradiated, having an unchanged lattice structure at high temperatures, being non-volatile and being chemically unreactive with water [1]. During the operation of nuclear reactors, the nuclear fuel elements are subjected to a harsh working environment and numerous radioactive fission products are produced during the fission of the fuel assembly in the reactor core. With the development of burnup, solid and gas fission products are produced in the fuel elements and their volume is greater than that of the material before fission. The volume of the fuel element increases with the development of burnup, which is called irradiation swelling. The radiation swelling of nuclear fuel induces interactions between fuel pellets and cladding, resulting in radial deformation and transverse tension of the cladding tube, causing damage to the cladding tube, which seriously threatens the safe operation of the reactor [2]. Swelling caused by solid fission products is simple and increases linearly with burnup; the behavior of gas fission products is complex and this field has not been extensively studied.

Due to the numerous radiation and structural changes experienced during the life of UO2 and storing, understanding and controlling the microstructural changes requires a comprehensive approach that considers all aspects of the material's behavior, from basic radiation damage processes to longer-term changes in the material microstructure. To better understand the fission gas behavior, such as microstructural changes and swelling,

**Citation:** Xia, Y.; Wang, Z.; Wang, L.; Chen, Y.; Liu, Z.; Wang, Q.; Wu, L.; Deng, H. Molecular Dynamics Simulations of Xe Behaviors at the Grain Boundary in UO2. *Metals* **2022**, *12*, 763. https://doi.org/ 10.3390/met12050763

Academic Editor: Alain Pasturel

Received: 21 March 2022 Accepted: 26 April 2022 Published: 29 April 2022

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many experimental and theoretical studies have been conducted [3–8]. It is difficult to analyze the behavior of xenon (Xe) atoms in UO2 through experiments [9–12] because the growth mechanism of Xe bubbles and the entire physical process are not well understood. Therefore, intragranular rare bubbles under dynamic conditions, cannot be studied through experiments, making computational simulations the only choice. Niemiec et al. proposed a basic evolution equation describing the kinetics of the nucleation and growth phase transitions to study phase transformation or microstructure formation kinetics in physical systems originally composed of several grains [13]. Atomistic simulations are vital to a provide good insight into the atomic structure and damage mechanisms.

To date, all simulations have been conducted in monocrystals. Gadomski et al. [14] studied the kinetic anomalies occurring in nucleation and growth phenomena in complex systems, such as polycrystalline partly ordered alloys, quasicrystal line assemblies, and mesomorphs, to understand the kinetics of the evolution of the microstructure and the system during growth. UO2 pellets are manufactured through traditional powder metallurgical processes; hence, they are polycrystalline materials composed of particles with a diameter of approximately 10 μm. The opening at the grain boundaries (GBs) is a crucial phenomenon since the energy of defects decreases near the GB and fission gas, which causes aggregation at the GB, and can be released to the outside of the fuel. As a result, the properties of UO2 GBs at the atomic scale have been studied [15–19]. In this study, we compare the early behavior of Xe bubbles in the GBs and the entire block of UO2. Previous numerical studies on this subject have mainly focused on metal systems, such as metallic tungsten [20–22]. Herein, we focus on the behavior of Xe atoms at the GBs and the bulk UO2, including the migration of a single Xe interstitial atom, the nucleation and growth of Xe bubbles and the bubble pressure and expansion associated with bubble growth. This study serves as a good reference for higher length scale simulation models.

## **2. Simulation Method**
