**1. Introduction**

In recent years, photovoltaic cells, electrochemical energy storage devices and wind turbines have been greatly improved to reduce the energy risk and environmental problems caused by the utilization of fossil fuels [1–4]. However, these sustainable energy technologies have not met the demand of the fast developed modern society. Going beyond the technologies discussed above, nuclear fission has been delivering green and reliable energy for half a century, and nuclear energy is a competitive candidate to mitigate energy risks [5–7]. In addition, nuclear energy is also expected to power spacecraft [8,9].

Heat pipes (HPs) are the key device in the nuclear energy system for achieving a high efficiency and safety. In nuclear reactors, the high-temperature HPs usually use liquid sodium (Na) as the heat transfer medium, because liquid Na possesses a high latent heat of vaporization, low saturated vapor pressure and outstanding heat conductivity [10]. Molybdenum (Mo) alloys with a low rhenium (Re) content can be used as structural materials in high-temperature HPs for nuclear application due to its high melting point, good mechanical properties and adequate irradiation resistance [11,12]. The Mo-based HPs accompanied with liquid Na working fluid can be operated at the temperature window of approximately 1000 K to 1700 K [13]. Comparing with other refractory metals, Mo also exhibits a relatively higher corrosion resistance to liquid alkali metal. Inoue et al. [14] reported that Mo alloys showed a better corrosion resistance than Nb alloys in a liquid Na environment. Saito et al. [15] studied the corrosion of niobium (Nb)-based alloys and Mo-based alloys, and found that the weight of the corrosion product of Mo alloys was ten times smaller than that of the Nb alloys in liquid lithium (Li). In addition, their results also demonstrated that metal elements in Nb alloys are dissolved more easily.

The dissolution, migration and precipitation of alloy elements in HPs can change the properties of the material surface, which is harmful for the performance of HPs [16–18]. For Mo-based HPs using Na as the working fluid, it is still not well understood how Mo and Re atoms diffuse and accumulate in the Na solvent at the atomic scale. In the last few years, ab initio molecular dynamics (AIMD) have been successfully employed to investigate the properties of liquid alkali metal at extreme conditions [19–21]. In our present study, AIMD simulations are performed to reveal the interactions between liquid Na and Mo or Re solute atoms.

## **2. Computational Methods**

All simulations in this study were performed on Vienna ab initio Simulation Package (VASP) [22,23] based on the density functional theory (DFT) [24,25]. The projector augmented-wave (PAW) method [26] was employed for describing the ion—electron interactions and the Perdew−Burke−Ernzerhof (PBE) functional [27] was used to describe the electron—electron exchange correlations. All AIMD simulations were carried out using NVT ensemble with the 400 eV energy cutoff of plane wave basis sets. AIMD simulations were run for at least 60 ps with a timestep of 2 fs. Only the Γ point was sampled in the first Brillouin zone.

The liquid metal model was constructed by randomly distributing Na atoms in a <sup>15</sup> × <sup>15</sup> × 15 Å<sup>3</sup> box with a three-dimensional boundary condition. The number of Na atoms was determined by the liquid Na density reported by Argonne National Laboratory [28]. In this study, three temperature conditions of 700 K, 1100 K and 1600 K are considered, and corresponding number of Na atoms in the model are 75, 67 and 56, respectively, which correspond to the liquid Na density of 852 kg/m3, 756 kg/m3 and 626 kg/m3, as reported in Ref. [28].
