A. Takayama

A.M. Ito

H. Nakamura

S. Saito

National Institute for Fusion Science (NIFS-Repository)

First-principles calculations of the binding ener-gies between helium atoms and mono-vacancies of tung-sten are performed with the ‘OpenMX’ code package,which is designed for nano-scale material simulationsbased on density functional theories (DFT). The gen-eralized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional is used for exchange-correlation potential and norm-conserving pseudo-potentials and pseudo-atomic localized basis functionsare employed for core Coulomb potential.Total energies are calculated for a body-cubic-center(bcc) supercell composed of 54 tungsten atoms (3 ×3 × 3 × 2) E[W54], a supercell of 53 atoms with mono-vacancy E[W53V1], and supercells with n helium atomstrapped within the mono-vacancy E[W53V1Hen]. TheBrillouin zone with 6×6×6 k-points sampling using theMonkhorst-Pack method is employed.The ‘OpenMX’ uses numerical pseudo-atomic or-bitals (PAOs) as basis function to expand one-particleKohn-Sham wave functions. We employ the 2 s-state, 2p-state, 1 d-state, and 1 f-state radial functions with cut-oﬀ radius of 8.0 a.u. for tungsten, and the 2 s-state, 1p-state, and 1 d-state radial functions with cut-oﬀ radiusof 6.0 a.u. for helium.Cohesive energy Ec of tungsten is estimated byEc = E(W)− E(W54)/54, (1)where E(W) is the energy of isolated tungsten atom.The lattice constant is obtained by minimizing Ec, andis 3.220 A˚ in the present calculation parameter set. Weemploy lattice constant of 3.220 A˚ for present calcula-tions, although this value is rather large compared to aliterature data, 3.165 A˚ (at 298K). In this case, Ec of 8.92eV is obtained, which is comparable to an experimentalobservation. Parameters used for present calculationsare summarized in the table I.Binding energies of helium atoms trapped withinthe mono-vacancy are given byEn←(n−1)B = E[W53V1Hen−1] + E[W54He1] (2)−E[W53V1Hen]− E[W54],where E[conﬁguration] is a total energy of the given con-ﬁguration.In order to search stable conﬁgurations with sin-gle and multiple helium atoms trapped in a mono-vacancy, samples consisted of octahedral-site (O-site)or tetrahedral-site (T-site) helium atom(s) and mono-vacancy tungsten are prepared. Iterative calculationsTable I: Parameters for calculationtarget material tungsten bccsupercell 3× 3× 3(54 lattice points)lattice constant 3.220 A˚k-grids 6× 6× 6PAOs W 8.0-s2p2d1f1He 6.0-s2p1d1of self-consistent ﬁeld (SCF) convergence and moleculardynamics (MD) according to the resulting force are per-formed, and we obtain a relaxation state. The ﬁnal stateof sample with the lowest total energy for each sampleof the same number of helium atoms is regarded as themost stable state. The conﬁgurations obtained by theabove mentioned method are used for the calculation ofbinding energy, eq. (2).Figure 1 depicts calculated values of the binding en-ergy EB as a function of the number of helium atomstrapped within a tungsten mono-vacancy, deﬁned ineq.(2). The binding energy gradually decreases as thenumber of the trapped He atoms increases, steeply dropsat 7 trapped He, and then recovers. When a binding en-ergy EB takes negative value, the conﬁguration is lessstable than the conﬁguration whose tungsten is less byone. It is inferred that tungsten mono-vacancy can con-tain at least 6 helium atoms from Fig. 1. In the case of 6helium trapped within the tungsten mono-vacancy, the6 mono-vacancy-trapped helium atoms form octahedralconﬁguration. He atoms are tightly bounded around amono-vacancy located at center of W cube, and make akind of cluster structure. The formation of this clusterstructure may be related to helium bubble generation.Fig. 1: Binding energy as function of the number of Heatom trapped within a W mono-vacancy.382§11. First Principles Investigation on Trapping of Multiple Helium Atoms within a Tungsten Mono-vacancyTakayama, A., Ito, A.M., Nakamura, H.,  Saito, S. (Nagoya Univ.)

First Principles Investigation on Trapping of Multiple Helium Atoms within a Tungsten Mono-vacancy

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