Statistical model and first-principles simulation on concentration of HenV cluster and He bubble formation in α-Fe and W

Using first-principles calculations, we investigate the stabilities of He and Hen-vacancy (HenV) clusters in α-Fe and W. Vacancy formation energies are 2.08 eV in α-Fe and 3.11 eV in W, respectively. Single He in both α-Fe and W prefers to occupy the tetrahedral interstitial site. We recalculated the He solution energy considering the effect of zero-point energy (ZPE). The ZPEs of He in α-Fe and W at the tetrahedral (octahedral) interstitial site are 0.072 eV (0.031 eV) and 0.078 eV (0.034 eV), respectively. The trapping energies of single He at vacancy in α-Fe and W are −2.39 eV and −4.55 eV, respectively. By sequentially adding He into vacancy, a monovacancy trap up to 10 He atoms distributing in the vacancy vicinity. Based on the above results combined with statistical model, we evaluate the concentrations of all relevant HenV clusters as a function of He chemical potential. The critical HenV concentration is found to be ∼10−40 (atomic) at the critical temperature T = 600 K in α-Fe and T = 1600 K in W, respectively. Beyond the critical HenV concentrations, considerable HenV aggregate to form HenVm clusters. By further growing of HenVm, the HenVm clusters grow bigger resulting in the larger He bubble formation.