Fig. 1. The most stable configuration of He₄, He₆, He₁₃, He₂₆ and He₅₅ clusters in tungsten. The balls represent helium atoms and the black sticks connect two helium atoms within the distance of 2.0 Å. The rainbow colors of the balls represent the atomic potential energies from −0.98 eV (blue) to 0.44 eV (red). The surface mesh is constructed and the transparency is 50% in order to show clearly.

Fig. 2. The average binding energy and trapping energy versus the size of the helium cluster.

Fig. 3. The behaviors of SIAs and the He₆ cluster at different temperatures: (a) the crowdion and the He₆ cluster tightly bind at 300 K; (b) the crowdion rotates and rearranges its location around the He₆ at 1000 K; (c) the crowdion even diffuses away from the He₆ at 1000 K; (d) the crowdion is not shown here and the He₆ dissociates into several separated helium atoms at 3500 K. The bigger and smaller balls represent helium and tungsten, respectively. The colors of balls with rainbow represent atomic potential energies from −8.00 eV (blue) to 1.13 eV (red). The black sticks connect two atoms within the distances of 2.0 Å and 2.5 Å for He and W, respectively. Only the tungsten atoms with high potential energy are shown here for clarity.

Fig. 4. The behaviors of SIAs and the He₁₃ cluster at different temperatures: (a) one crowdion and He₁₃ tightly combine at 300 K; (b) the crowdion rotates and rearranges its position around the He₁₃ at 1000 K; (c) and (d) an extra Frenkel pair is created to form a two-combined crowdion which rotates and change its position at 2000 K; (e) an extra Frenkel pair is created, and three crowdions separate and diffuse away from the He₁₃ at 3500 K. The graph settings are the same as Fig. 3.

Fig. 5. The behaviors of SIAs around the He₂₆ cluster at different temperatures. The configuration of dispersed crowdions is almost unchanged at (a) 300 K and (b) 1000 K; (c) the atomic structure of He₂₆; (d) at 2000 K, the SIAs change their positions and form a four-combined crowdion, and (e) the four-combined crowdion cluster rotates and changes its position; (f) extra one or (g) two Frenkel pairs are created to form a combined crowdion cluster at 3000 K, which can rotate and change its position around the He₂₆. The red arrows in the figure show the crowdions and their orientations. The graph settings are the same as Fig. 6.

Fig. 6. The behaviors of SIAs around the He₅₅ cluster at different temperatures: (a) eight insterstitial atoms disperse randomly around the He₅₅ and the atomic structure is almost unchanged at 300 K; (b) the SIAs self-assemble and form a dislocation loop (containing 10 SIAs) at 1000 K; the dislocation loop can rotate between (c) 〈100〉 and (d) 〈111〉 orientations at 2000 K. The graph settings are the same as Fig. 3.

Fig. 7. The variations of displacement of mass center of the He_n cluster with evolution time at different temperatures.

Table 1. The number of SIAs created by the He_n cluster at different temperatures. N_SIA and T represent the number of SIAs and temperature, respectively.

Table 2. The main features of SIAs and helium clusters at different temperatures. The “rotation” represents the rotation of dislocation loop (or crowdions), the “separation” represents the crowdion separating from the helium cluster, and the “dissociation” represents the helium cluster dissociating into separated helium atoms. The figures in the parentheses represent the number of crowdions in rotation.