**2. Simulation Details**

We employ the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software (Sandia National Laboratories, Albuquerque, NM, USA) to study the interaction between a dislocation loop and vacancy-type defects including a vacancy, di-vacancy, and vacancy cluster. A previous study indicated that nearly 60% of the dislocation loop is the 1/2[111] dislocation loop in W at 0.4–30 dpa and temperatures between 300 and 750 ◦C [21]. The size of the dislocation loop is usually less than 20 nm with most of them less than 6 nm [22]. Thus, we choose the 1/2[111] dislocation loop with its radius less than 6 nm. The embedded atom method (EAM) empirical interatomic potential developed by Marinica et al., denoted as "EAM2", is employed in our simulations, which has been used to investigate the properties of dislocation loop [30,31].

The direction of X, Y, and Z is set as [112], [110], and [111], respectively. The simulation box created by LAMMPS contains about 0.59 million atoms. Periodic boundary conditions are imposed on all boundaries of the simulation box. The 1/2[111] dislocation loop is placed at the center of the box and the vacancy-type defects are created at designed positions. The sketch of the simulation box and a schematic picture of the configuration of a 1/2[111] dislocation loop and a vacancy-type defect is shown in Figure 1.

**Figure 1.** (**a**) The sketch of the simulation box. The green ring represents the 1/2[111] dislocation loop. (**b**) The schematic picture of the configuration of a 1/2[111] dislocation loop and a vacancy-type defect. The vacancy-type defect is placed at the position that is along three different directions. Direction I is through the center of the dislocation loop and parallel to the Burgers vector. Position I is along the Direction I and has a distance of 15 Å to the habit plane (HP). Direction II is along the edge of the dislocation loop and parallel to the Burgers vector. Position II is along the Direction II and has the distance of 15 Å to the HP. Direction III is through the center of the dislocation loop on the HP.

Binding energies can be used to evaluate the static interaction between a dislocation loop and a vacancy-type defect. We first construct a 1/2[111] dislocation loop at the center of the simulation box. Then we insert a vacancy-type defect at a certain position (Position I and II) as shown in Figure 1b and relax the system to reach the equilibrium state by using the conjugate gradient method. The binding energy of the loop to a vacancy-type defect is given by:

$$E\_b = E\_1 - E\_2 \tag{1}$$

where *E*<sup>1</sup> stands for the minimum energy of the system with a vacancy-type defect that is far away from the dislocation loop to ensure that there is no interaction between them, and *E*<sup>2</sup> stands for the minimum energy of the system with a vacancy-type defect that is in a specific position. A positive *Eb* represents the attraction of the dislocation loop to a vacancy-type defect, while the negative value denotes the repulsion between them.

The elasticity theory is first used to verify our MS simulation results. A vacancy can be regarded as a sphere whose elastic constants are zero. On the one hand, the elastic constant of a vacancy is different from that of system, which will interfere with the existing elastic field and produce the interaction energy *E*<sup>1</sup> *int*. On the other hand, the stress produced by the vacancy will interact with the original elastic field and produce the interaction energy *E*<sup>2</sup> *int*. According to the linear elasticity theory, the total interaction energy is equal to the sum of the two energies *E*<sup>1</sup> *int* and *<sup>E</sup>*<sup>2</sup> *int* [32]. Then the interaction energy between a dislocation loop and a vacancy can be obtained. The HP of the dislocation loop is (*r*, *θ*) with a radius *R*. The center of the loop is at the origin and the Burgers vector is parallel to the Z axis. The interaction energy between a vacancy and a loop can be calculated by the following formula [32]:

$$\mathbb{E}\_{\text{int}}^{1}(\xi,\rho) = -\mathcal{K}^{2}(1-\sigma)\Omega \left\{ \frac{1}{3r} \frac{\left(1+\sigma\right)^{2}}{1-2\sigma} l\_{0}^{2} + \frac{15}{2\mu} \frac{1}{7-5\sigma} \left[ \frac{\left(1-2\sigma\right)^{2}}{3} \left(l\_{0}^{4}\right)^{2} + \xi^{2}l\_{0}^{2} + \xi^{2}l\_{1}^{2} + \rho^{-2}\Phi^{2} + \xi\rho^{-1}l\_{0}^{2}\Phi - \left(1-2\sigma\right)\rho^{-1}l\_{0}^{4}\Phi \right] \right\}, \tag{2}$$

$$E\_{int}^2(\xi,\rho) = -\frac{2}{3}\mathcal{K}(1+\sigma)\Delta\Omega I\_0^1\tag{3}$$

where:

$$
\zeta = \frac{z}{R} \tag{4}
$$

$$
\rho = \frac{r}{R} \tag{5}
$$

$$\mathbf{K} = \frac{b}{R} \frac{\mu}{2(1 - \sigma)}\tag{6}$$

$$I\_m^n(\xi,\rho) = \int\_0^\infty t^n f\_m(t\rho) f\_1(t) e^{-\xi t} dt \, (n,m=0,1,2) \tag{7}$$

$$\Phi(\xi,\rho) = (1 - 2\sigma)I\_0^1 - \xi I\_1^1 \tag{8}$$

where (*z*,*r*) is the position of the vacancy, *R* is the dislocation loop radius, *k* and *μ* represents the elastic constant tensor *C*<sup>12</sup> and *C*<sup>44</sup> of W, respectively. *k*<sup>1</sup> and *μ*<sup>1</sup> represent the elastic constant of the vacancy, which equals 0. *σ* is the Poisson's ratio. Ω is the volume of the vacancy, and *I<sup>n</sup> <sup>m</sup>*(*ξ*, *ρ*) is a complete elliptic integral. The used elastic constant tensors of W are *C*<sup>11</sup> = 523 GPa, *C*<sup>12</sup> = 203 GPa, and *C*<sup>44</sup> = 160 Gpa.

#### **3. Results and Discussion**

We first use the MS to calculate the binding energies of the 1/2[111] interstitial dislocation loop (IDL) and 1/2[111] vacancy dislocation loop (VDL) to a vacancy by varying the type and size of the loop at 0 K. The binding energies of the IDL to a vacancy are compared with that calculated by ET. We then simulate the binding energies of the IDL to a di-vacancy and a vacancy cluster. Finally, the effects of the temperature and position of the vacancy cluster on the mobility of the IDL are obtained by the MD simulations.
