*3.3. Static Interaction of an IDL to a Di-Vacancy and a Vacancy Cluster*

To investigate the interaction between the IDL to a di-vacancy and a vacancy cluster, we calculate their binding energies along the Direction II and Direction III, respectively. The configuration of the divacancy considered is 1NN, which was reported stable in W [6]. Figure 6 shows the distribution of the calculated binding energies between the different sized IDLs and a di-vacancy as a function of their distance along the Direction I and II, respectively. The variations of the binding energies with the distance and loop radius are very similar to that of an IDL and a vacancy as shown in Figure 2. The largest binding energy of the IDL to a divacancy is generally larger than that of the IDL to a vacancy. Along the Direction I as shown in Figure 6a the largest binding energy decreases from 0.45 eV to 0.03 eV with increasing the radius of the IDL from 10.0 Å to 50.0 Å. The binding energy reaches zero when the distance is larger than 40.0 Å for all sized IDLs. While along the

Direction II as shown in Figure 6b, the largest binding energy decreases from 5.8 eV to 1.2 eV with increasing the radius of the loop from 10.0 Å to 50.0 Å. The calculated absorption distance ranges from 15.0 Å to 27.0 Å.

**Figure 6.** The distribution of binding energies of the different sized IDLs to a divacancy as a function of their distance when the divacancy is placed along (**a**) the Direction I and (**b**) Direction II, respectively. The inset figure shows the binding energies at a small energy scale.

Figure 7 depicts the calculated binding energies between the different sized IDLs and a vacancy cluster as a function of their distance along the Direction I and II. Comparing to the binding energies of the IDL to a vacancy and a di-vacancy as shown in Figures 5 and 6, the distribution of the binding energies of IDL to a vacancy cluster as a function of their distance shows a similar trend but larger values. Figure 7a shows the binding energy decreases with the increase of their distance and the loop radius along the Direction I. The largest binding energy decreases from 3.4 eV to 0.05 eV with increasing the radius of the loop from 10.0 Å to 50.0 Å. The binding energy is almost zero when the distance is longer than 40.0 Å for all sized IDLs. While along the Direction II as shown in Figure 7b, the largest binding energy decreases from 12.0 eV to 6.2 eV as the IDL radius increases from 10.0 Å to 50.0 Å. The absorption distance ranges from 22.0 Å to 32.0 Å. Therefore, as the number of vacancies increases, the binding energies increase gradually for the same sized IDL and the same distance. Besides, the distribution of the binding energies of the IDL to various vacancy-type defects as a function of the distance along the Direction I and II is similar. Based on the same trend of the distribution of the binding energies between the IDL and vacancy-type defects, we can conclude that they have similar interaction behaviors.
