*3.2. Na Atom and O Atom Adsorption*

The adsorption behaviors of Sodium atom on both Mo (110) and Mo-Re (110) surfaces are investigated firstly. In the current calculations, the adsorption energy for the Na atom adsorbed on the Mo (110) or Mo-Re (110) surfaces is defined as:

$$E\_{\rm ads} = E\_{(Mo/Mo-Rc)-Na} - E\_{(Mo/Mo-Rc)slab} - E\_{Na} \tag{2}$$

Here *E*(*Mo*/*Mo*−*Re*)−*Na* is the total energy of the adsorbate–substrate system, *E*(*Mo*/*Mo*−*Re*)*slab* is the total energy of the clean Mo/Mo-Re surface, and *ENa* is the average energy of BCC Na. A negative *Eads* value indicates the attractive interaction between the adsorbate and the substrate. The more negative adsorption energy implies the stronger attractive interaction between the adsorbate and the substrate.

Figure 2 shows the Initial states and final states of Na adsorption Mo (110) and Mo-Re (110) surfaces. The adsorption energies and structural parameters of Na on Mo or Mo-Re (110) surfaces are given in Table 2. For the Mo (110) surface, the hollow site is the energetically most favored for Na adsorption and the corresponding energy is −0.51 eV. The Bridge site is second preferred for Na adsorption with the adsorption energy of −0.44 eV. The Top site is a stable one for Na adsorption, but the adsorption energy is only −0.35 eV. For Mo-Re (110) surface, all un-equivalent Top, Hollow and Bridge sites are considered for Na adsorption. For each type of adsorption site, only the initial and final sites with the lowest energy are collected and shown in Figure 2 and Table 2. Compared with the pristine Mo (110) surface, Mo-Re (110) surface provides stronger affinity to the Na atom. It is worth noting that the Na atom initially placed at the Bridge site moves towards the Re atom after the structure optimization, as can be seen in Figure 2f, and this configuration delivers the lowest adsorption energy of −0.60 eV. The adsorption energies of Na adsorption on the Top site and Hollow site of Mo-Re (110) surface are −0.43 eV and −0.56 eV, respectively. The average vertical distance between adsorbed Na atom and the top layer (*dNa*−*sur*) is also listed in Table 2. It is interesting to found that the Na adsorption energy is proportional to *dNa*−*sur f* (Figure 3). A shorter distance between the Na atom and the top layer indicates a stronger attractive interaction. Both energetical and geometric parameters indicate that the Re atom can strengthen the attractive interaction between Na and the Mo surface. The electronic structure is analyzed for understanding the effect of Re atom on Na adsorption. On the Mo (110) surface, the Na atom only interacts with Mo atoms in the upmost layer, as shown in Figure 4a. The Re atom can significantly affect the charge redistribution induced a by Na adsorption. As shown in Figure 4b, electrons from the Mo settled in the second atomic layer migrate to the first layer, resulting to great electron accumulation. In this case, the columbic attraction between the Na atom and the substrate is enhanced and lead to a lower adsorption energy.

**Figure 2.** Initial and final configurations of Na adsorption on Mo (110) and Mo-Re (110) surfaces. Snaps (**a**–**c**) show Na atoms initially placed at Top site, Hollow site and Bridge site of Mo (110) surface. Snaps (**d**–**f**) show Na atoms initially placed at Top site, Hollow site and Bridge site of Mo-Re (110) surface. Blue and green spheres represent Mo atoms in the first layer and the second layer. Yellow and purple spheres represent Re atoms and Na atoms, respectively.


**Table 2.** Adsorption energy of Na on Mo (110) and Mo-Re (110) surfaces. *Eads* is the adsorption energy, and *dNa*−*sur f* is the vertical distance between the adsorbate and the top layer of the slab model.

**Figure 3.** Na adsorption energy as the function of the average distance between the Na atom and the top layer of the substrate.

**Figure 4.** Difference charge density of Na adsorption at the hollow site of (**a**) Mo (110) surface and (**b**) Mo-Re (110) surface. The red isosurface represent the electron accumulation region, while the green isosurface represent the electron depletion region. The Re atom is located in the center of Mo (110) surface, as shown in Figure 1c.

The adsorption energies of O on Mo and Mo-Re (110) surfaces are also investigated in the present study (Table 3). The adsorption energy for the O atom adsorbed on the Mo/Mo-Re (110) surfaces is defined as

$$E\_{\rm ads} = E\_{\rm (Mo/Mo-Rc)-O} - E\_{\rm (Mo/Mo-Rc)slab} - \frac{1}{2}E\_{O\_2} \tag{3}$$

where *E*(*Mo*/*Mo*−*Re*)−*<sup>O</sup>* is the total energy of the adsorbate–substrate system, *E*(*Mo*/*Mo*−*Re*)*slab* is the total energy of clean Mo/Mo-Re surfaces, and *EO*<sup>2</sup> is the energy of an isolated O2 molecule. The adsorption energy of a single O atom on the surface is always calculated to characterize the oxygen-substrate interactions for refractory materials, and the energy of an O atom is usually referenced to the half of the O2 molecule [35–37].


**Table 3.** Adsorption energy of O on Mo/Mo-Re (110) surface.

As listed in Table 3, The Hollow site is energetically preferred for O adsorption on the Mo (110) surface with the adsorption energy of −4.09 eV. It is worth noting that the O atom initially placed at the Bridge site will spontaneously move to the Hollow site after the structure optimization as shown in Figure 5c. The O atom can also be stabilized at the Top site, but the adsorption energy is only −2.80 eV. As with Na on Mo (110) surface, the shorter vertical distance between O atom and the substrate (*dO*−*sur f*) leads to a lower (more negative) adsorption energy. For the Mo-Re (110) surface, the Hollow site is also the most favored for O adsorption and the corresponding adsorption energy is −4.14 eV, which is even 0.05 lower than the adsorption energy of O at the Hollow site of Mo (110) surface. It is worth mentioning that all un-equivalent Hollow sites around the Re atoms are checked, and Figure 5 as well as Table 3 demonstrates configurations with the lowest energy. As with the pristine Mo (110) surface, the O atom initially placed at the Bridge site of the Mo-Re (110) surface will move to the Hollow site after the structure relaxation. In addition, the O atom can be stabilized at the Top site with a much higher adsorption energy of −2.82 eV. As with Na adsorption, the Re atom in the surface can also strengthen the attractive interaction between the adsorbed O atom and the Mo-based substrate.

**Figure 5.** Initial and final configurations of O adsorption on Mo (110) and Mo-Re (110) surfaces. Scheme 110. surface. Snaps (**a**–**c**) show O atoms initially placed at Top site, Hollow site and Bridge site of Mo (110) surface, while snaps (**d**–**f**) show O atoms initially placed at Top site, Hollow site and Bridge site of Mo-Re (110) surface. Blue and green spheres represent Mo atoms in the first layer and the second layer. Yellow and red spheres represent Re atoms and O atoms, respectively.

#### *3.3. Impact of O on Na Adsorption and Diffusion*

O is the key impurity in liquid metal for the high-temperature heat pipe. The impact of pre-adsorbed O on Na adsorption behavior is also investigated. The configurations of pre-adsorbed O atom are adopted from Figure 6b,e. The adsorption energy for the Na on surface with a pre-adsorbed O is defined as

$$E\_{\rm ads} = E\_{\rm (Mo-O/Mo-Rc-O)-Na} - E\_{\rm (Mo-O/Mo-Rc-O)slab} - E\_{\rm Na} \tag{4}$$

where *E*(*Mo*−*O*/*Mo*−*Re*−*O*)−*Na* is the total energy of the adsorbate–substrate system, *E*(*Mo*−*O*/*Mo*−*Re*−*O*)*slab* is the total energy of Mo or Mo-Re surface with a pre-adsorbed O atom, and *ENa* is the energy of an Na atom in the BCC structure. In Equation (4), the subscript Mo-O represents the Mo (110) surface with a pre-adsorbed O atom and Mo-Re-O represent the Mo-Re (110) surface with a pre-adsorbed O atom.

All un-equivalent sites are considered and only the configurations with the lowest energies are shown in Figure 6. Adsorption energies and geometric parameters are given in Table 4. It is found that Na atoms initially placed at Top and Bridge sites move to Hollow sites after the optimization. The former one occupied the Hollow site which is 6.02 Å away from the pre-adsorbed O atom, and latter one occupied the Hollow site which is only 2.35 Å away from the O atom. However, these two final configurations lead to the same adsorption energy of 0.52 eV. For the Na atom initially placed at the Hollow site, the adsorption energy is −0.53 eV with *dNa*−*<sup>O</sup>* = 2.36 Å. It can be inferred that the O atom does not affect the adsorption behavior of the Na atom.

**Figure 6.** The initial and final configurations of Na atom adsorption on Mo-O (110) and Mo-Re-O (110) surface. Snaps (**a**–**c**) show Na atoms initially placed at Top site, Hollow site and Bridge site of Mo-O (110) surface, while snaps (**d**–**f**) show Na atoms initially placed at Top site, Hollow site and Bridge site of Mo-Re-O (110) surface. Blue and green spheres represent Mo atoms in the first layer and the second layer. Yellow, purple and red spheres represent Re atoms, Na atoms and O atoms, respectively.


**Table 4.** Na adsorption energy on different surface models.

For the Mo-Re (110) surface with a pre-adsorbed O, Na initially placed at the top site will spontaneously move to a Hollow site which is close to the O atom (*dNa*−*<sup>O</sup>* = 2.37 Å) as shown in Figure 6d. However, it should be noticed that the Na atom at the Hollow site which is closer to a Re atom has lowest adsorption energy of −0.61 eV in Figure 6e. The adsorption energy of Na at the Bridge site is −0.57 eV, which is also closer to the Re atom in Figure 6f and has a lower adsorption energy than the Na atom shown in Figure 6d. For the Na adsorption on the clean Mo-Re (110) surface, the adsorption energies of the Hollow site and Bridge site are −0.56 eV and −0.60 eV. As with the Mo (110) surface, pre-adsorbed O on the Mo-Re (110) surface cannot affect the Na adsorption behavior significantly.

Figure 7 show the energy barrier of Na migration from one most stable site to its first-nearest most stable site is also calculated in this work using CI-NEB method. Our theoretical results show that the diffusion barrier of Na on Mo (110) surface is 0.037 eV, while it is 0.063 eV on the Mo-Re (110) surface. It can be inferred that the Re atom can slower down the Na diffusion kinetics on the Mo surface. The impact of pre-adsorbed O on the Na diffusion is also investigated. For the Mo (110) surface, the pre-adsorbed O atom can increase the diffusion barrier to 0.087; for the Mo-Re (110) surface, the pre-adsorbed O can significantly increase the Na diffusion barrier to 0.221 eV. Therefore, it can be inferred

that both the existence of O impurity and Re alloy atoms can block the Na diffusion on the Mo surface.

**Figure 7.** Calculated diffusion energy profiles for a Na atom diffusion on different surfaces: (**a**) Na diffusion on pure Mo (110) surface; (**b**) Na diffusion on Mo-Re (110) surface; (**c**) Na diffusion on Mo (110) surface with an adsorbed O atom; (**d**) Na diffusion on Mo-Re (110) surface with an adsorbed O atom.
