**1. Introduction**

Uranium dioxide (UO2) is widely used as a nuclear fuel in the nuclear industry for various nuclear power reactors [1]. Thus, the safe operation of a nuclear reactor correlates strongly with the stability of UO2. However, under extreme conditions, different radiation defects (e.g., vacancies, interstitials, and voids) would be created within the nuclear fuel due to irradiation. These defects would lead to severe degradation of the physical, thermal, and mechanical properties of the nuclear fuels [2–4]. For example, irradiation-induced fission products and vacancies can produce bubbles and voids, causing swelling and fragmentation which thus deteriorates the performance of fuels [5]. Therefore, to investigate the effect of radiation-induced defects on the thermo-mechanical properties of uranium dioxide is essential.

In the literature, numerous experimental and theoretical studies have been performed to understand the impact of fission products, porosities, and other defects on thermal transport in UO2. For example, Hobson et al. analyzed porous UO2 with porosity levels of 4.11 to 8.58% and observed the relationship of reductions in thermal conductivity to the temperature [6]. An experimental study on the effect of soluble fission products on thermal conductivity was also performed, which found that at lower temperatures the thermal

**Citation:** Wang, Z.; Yu, M.; Yang, C.; Long, X.; Gao, N.; Yao, Z.; Dong, L.; Wang, X. Effect of Radiation Defects on Thermo–Mechanical Properties of UO2 Investigated by Molecular Dynamics Method. *Metals* **2022**, *12*, 761. https://doi.org/10.3390/ met12050761

Academic Editor: Enrique Jimenez-Melero

Received: 8 April 2022 Accepted: 25 April 2022 Published: 29 April 2022

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conductivity would decrease with an increase in fission product concentration; however, at higher temperatures the concentration of fission products has only a slight influence on thermal transport [7].

In addition to experiments, computer simulations have also provided an effective tool to analyze the specific mechanism of fuels at the atomic level. Liu et al. investigated the effect of uranium vacancies, oxygen vacancies, and fission products on the thermal conductivity of uranium. They also observed a stronger effect on the reduction in thermal conductivity by uranium vacancies compared to that by oxygen vacancies [8]. Chen et al. performed molecular dynamics (MD) simulations to examine the effect of Xe bubble size and pressure on the thermal conductivity of uranium dioxide and demonstrated that the dispersed Xe atoms could result in a lower thermal conductivity than by clustering them into bubbles [9]. Uchida et al. performed molecular dynamics simulations to evaluate the effect of Schottky defects on the thermal properties in UO2 and reported that thermal conductivity decreased with the increasing concentration of Schottky defects [10]. Furthermore, the thermal transport of ThO2, as an alternative to conventional uranium nuclear fuel, was also investigated extensively. For example, Park et al. [11] investigated the effect of vacancies and substitutional defects on the thermal transport of ThO2 by employing reverse non-equilibrium molecular dynamics (NEMD). The authors reported that the effect of thorium vacancy defects on the thermal transport of ThO2 is even more detrimental than that of oxygen vacancy defects. In addition, compared to vacancy defects, substitutional defects in ThO2 slightly affect the thermal transport [11]. To investigate the effect of irradiation-induced fission products on the thermal conductivity of thorium dioxide, Rahman et al. [5] examined the effect of Xe and Kr with impurity concentrations of 0 to 5% on the thermal conductivity of ThO2 with the molecular dynamics method, and found that Xe and Kr resulted in significant reductions in the thermal conductivity of ThO2.

In order to use nuclear fuels safely in reactors, the mechanical feature of fuels after irradiation is also an important property which needs to be considered [12]. For example, Jelea et al. examined the thermo-mechanical properties of a UO2 matrix containing different concentrations of porosity and observed that the elastic modulus decreased with an increase in porosity concentration [13]. Rahman et al. examined the effect of fission products (Xe and Kr) and porosity on mechanical properties of ThO2 within 300–1500 K using molecular dynamics simulations. By comparing the effect of fission products and porosity, the authors reported that the fission products resulted in a stronger reduction in elastic modulus than the porosity [14].

Although the effects of fission products and porosity on thermo-mechanical properties of UO2 have been studied by different groups, to our best knowledge no investigation has been performed about the effect of Frenkel defects and antisites on the thermo-mechanical properties of irradiated UO2. Considering its importance, in this work, the influences of Frenkel defects and antisites on the thermal expansion coefficient and elastic modulus of uranium dioxide are investigated extensively via molecular dynamics simulations. The thermal expansion coefficient of perfect and damaged systems is evaluated from changes in lattice parameters. Three independent elastic constants are calculated for each system, which are used to estimate the elastic modulus. The reduction in the elastic modulus induced by Frenkel defects and antisites is also calculated as a function of concentrations of defects in the system. A comparison is finally made between the effects of Frenkel defects and antisite defects to provide more understanding about the structure and property changes of UO2 after irradiation. In the following sections, the computational method is first presented. The results and discussion are provided in Section 3. The conclusion is made in the last section.
