**1. Introduction**

Pure uranium (U) is limited to a considerable extent in the production of fuel elements due to its questionable properties. α-U, which is stable at low temperatures, has pronounced anisotropy and comparatively low strength characteristics at elevated temperatures. Meanwhile, the existence of high-temperature body-centered cubic (bcc) γ-U and intermediate tetragonal β-U indicates harmful allotropic transformations during cyclic heat treatment. Moreover, U shows high chemical activity in corrosion behaviors [1,2]. A common solution of problems above is the utilization of uranium alloys, which retains the isotropic structure of γ-U at room temperature. So far, molybdenum (Mo) and zirconium (Zr), along with a few other elements appear to be promising options in U alloys for nuclear fuel. In particular, alloying U with Mo remarkably improves its mechanical properties, corrosion resistance, and dimensional stability, along with providing other benefits such as high thermal conductivity and low thermal expansion [3,4]. Enhanced mechanical properties enable U-Mo alloys to be utilized for the production of cores of fuel elements of arbitrary configurations. High corrosion resistance in water of high parameters and reliable dimensional stability under irradiation are deciding factors governing the choice of U-Mo alloys as fuel materials. It is also deemed expedient in all cases for U-Mo alloys to be included in the construction of fast-neutron reactors [1].

However, the introduction of alloy elements also brings about some peculiar physical phenomena whose fundamental mechanism remains to be understood. During the cooling of U-Mo alloys, several metastable phases have been observed in a sequence of bcc γ → bcc with doubled lattice constant <sup>γ</sup><sup>S</sup> → body-centered tetragonal (bct) <sup>γ</sup><sup>0</sup> → monoclinic

**Citation:** Ouyang, W.; Lai, W.; Li, J.; Liu, J.; Liu, B. Atomic Simulations of U-Mo under Irradiation: A New Angular Dependent Potential. *Metals* **2021**, *11*, 1018. https://doi.org/ 10.3390/met11071018

Academic Editor: Ayrat Nazarov

Received: 5 June 2021 Accepted: 19 June 2021 Published: 24 June 2021

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α" → orthorhombic α' [5,6]. The addition of Mo was suggested to stiffen the U lattice against shear, thus hindering and also complicating the transition progress. However, during service life, Mo has been observed to be depleted from grain boundaries (GBs) among a wide range of compositional banding [7], which could lead to an onset of phase decomposition. In particular, the elemental redistribution near GBs could also be implicated in the generation of irradiation-induced recrystallization (IIR) [8], where fuel grains are subdivided into nano-sized grains from the GBs during service life. Meanwhile, IIR is suggested as an important culprit behind accelerated swelling behavior of nuclear fuel alloys [9], which enhances the reach of GBs into the fuel grains, destroying low swelling intra-granular fission gas bubbles (FGBs) and producing high swelling inter-granular FGBs.

To shed light on the underlying mechanism of microstructure evolution under irradiation at U-Mo fuel operation temperatures, constructing corresponding potential for molecular dynamics simulation has been under research in recent years. An embedded atom method (EAM) potential for U-Mo-Xe has been developed by the force matching method [10], through which the properties of U2Mo and α-U-Mo could be reproduced well, even without taking them into account in the fitting process. However, traces of overfitting were observed, suggesting the limitation of EAM for the description of a U-Mo system. By the use of the interatomic potential proposed by Smirnova et al. [10], attempts to reveal cascade effects on residual defects in U-Mo alloys have also been reported [11]. Also based on the U-Mo-Xe EAM potential, Hu et al. [12] have investigated the relationship between the pressure, equilibrium Xe concentration, and radius of Xe bubbles in U-10 wt% Mo by molecular dynamics (MD) simulations. Utilizing a formalism improved on the basis of EAM, namely Angular-Dependent Potential (ADP), Smirnova et al. have qualitatively reproduced the properties of cubic and tetragonal phases of γ-U-Mo alloys [13] and improvements were also made in reproduction of the density, coefficient of thermal expansion, and diffusion behavior [14]. It was also suggested that a successful capture of atomic properties in γ-U and γ-U-Mo systems requires utilization of a potential form, with its level of complexity no lower than the ADP. Moreover, Starikov et al. [15] have also constructed an ADP with the same form as that developed by Smirnova, which paid special attention to the description of metastable phases of U-Mo solid solution in the fitting process.

For the present work, we first constructed a U-Mo interatomic potential using the ADP formalism proposed by the author's group [16]. The ADP formulas were further modified such that it can more accurately reproduce the threshold displacement energy surface as well as many-body repulsion at intermediate and short interatomic distances. We then applied the obtained potential in MD simulations to study the U-Mo system under irradiation.
