Helium bubble nucleation and growth in α-Fe: insights from first–principles simulations

Abstract

We have carried out a first-principles study on the nucleation and early-stage growth of He bubbles in Fe. The energetics, atomic and electronic structure of He-vacancy complexes, involving both a monovacancy and a nine-vacancy cluster, are examined. Based on the energetics, we then perform thermodynamics analysis to gain deeper insights into He bubble nucleation and growth. We have determined the energy cost for the nucleation of He bubbles and found that up to eight He atoms can be trapped at a single vacancy. In order to capture more He atoms, the vacancy has to emit Frenkel pairs to release the substantial stress building on the surrounding Fe lattice. Compared to the monovacancy, the nine-vacancy cluster has a lower energy cost for He bubble nucleation and growth. He atoms at the vacancy repel the surrounding electronic charge and redistribute it on the neighboring Fe atoms. The thermodynamic analysis reveals that He chemical potential provides a driving force for He bubble nucleation and growth. There are two critical He chemical potentials that are of particular importance: one of them marks the transition from single He occupation to multiple He occupation at a monovacancy while the other sets off He-induced superabundant vacancy formation.

Energetic Study of Helium Cluster Nucleation and Growth in 14YWT through First Principles

“…Without a vacancy, the He atom prefers the tetrahedral interstitial site with a lower formation energy; otherwise, the He atom is trapped in the vacancy as a substitution. These results match well with recently-published data [47], which are also based on VASP calculations. These results are slightly higher than other published data [4,36,48,49], mainly due to different Density Functional Theory (DFT) solvers and setups.…”

“…The formation energy and He trapping energy variations with the number of He atoms in the He${}_n$X clusters are presented in Figure 4. In both cases, the formation energy of the He${}_n$X cluster increases monotonically with the number of He atoms, consistent with previous Molecular Dynamics (MD) calculations [38] and DFT calculations [47]. The slope of $E_{\mathrm{f}}$ represents the energy penalty rate for the growth of the small He${}_n$X cluster.…”

“…Recently, Dr. Lu’s group proposed that up to eight He atoms can be trapped at a single vacancy in an α -iron matrix. In order to capture more He atoms, the vacancy has to emit Frenkel pairs to release the substantial stress building on the surrounding Fe lattice [47]. During the He accumulation within the local environment of the vacancy/O:Vac pair, significant pressure has been produced, causing significant distortion of the local lattice structure.…”

“…The formation energy is defined as:$E_{\mathrm{normalf}}(\mathrm{ref}+n\mathrm{He})=E(\mathrm{ref}+n\mathrm{He})-E\left(\mathrm{ref}\right)-nE\left(\mathrm{He}\right)$ where $\mathrm{ref}+n\mathrm{He}$ denotes the reference unit with n number of He atoms in the super-cell; subscript f denotes the formation energy. E(He) = $-0.0046$ eV is the energy of an isolated He atom in the vacuum space [47]. During the He cluster formation, the He trapping energy is an important parameter to determine whether the n -th He atom can be trapped into the He${}_{(n-1)}$ cluster.…”

Effects of Cr and W additions on the stability and migration of He in bcc Fe: A first-principles study

“…Inside the structural materials, He atom is mobile and easily to be trapped by point defects, forming He bubbles [10][11][12][13], leading to void swelling and He embrittlement. Thus, many attentions have been paid to investigate the behavior of single He impurity and He clusters in point defects and grain boundaries using first-principles calculations and molecular dynamics (MD) simulations [10][11][12][13][14][15][16][17][18][19], such as He solution and migration, formation of He-vacancy clusters, and He-to-vacancy ratio in bcc Fe. So far, most theoretical studies focused on He impurities in pure Fe solid.…”