A. Takayama

A.M. Ito

H. Nakamura

Y. Oda

National Institute for Fusion Science (NIFS-Repository)

First-principles calculations of the bindingenergies1) of hydrogen-helium atoms interstitially-trapped in tungsten are carried out with the ‘OpenMX’code package, which is designed for nano-scale materialsimulations based on density functional theories (DFT)and developed by Dr. Ozaki at Japan AdvancedInstitute of Science and Technology2).The ‘OpenMX’ uses numerical pseudo-atomic or-bitals (PAOs) as basis function to expand one-particleKohn-Sham wave functions. The generalized gradi-ent approximation (GGA) with Perdew-Burke-Ernzerhof(PBE) functional is used for exchange-correlation poten-tial and norm-conserving pseudo-potentials and pseudo-atomic localized basis functions are employed for coreCoulomb potential. The Brillouin zone with 4× 4× 4 k-points sampling using the Monkhorst-Pack method isemployed.In this study, total energies are calculated for abody-cubic-center (bcc) supercell composed of 128 tung-sten atoms (4 × 4 × 4 × 2) E[W128] and supercells withm-hydrogen and n-helium atoms interstitially-trapped intungsten E[W128HmHen].The lattice constant is obtained by minimizing thecohesive energy Ec, and is 3.186 A˚ in the present cal-culation parameter set. We employ a lattice constantof 3.186 A˚ for present calculations, although this valueis slightly large than that in the literature, 3.165 A˚ (at298K).Iterative calculations of self-consistent ﬁeld (SCF)convergence and molecular dynamics (MD) accordingto the resulting force are performed, and a relaxationstate is obtained. For the geometry optimization, theBroyden-Fletcher-Goldfarb-Shanno (BFGS) method isemployed. The ﬁnal state with the lowest total energyfor each sample having the same number of hydrogen andhelium atoms is regarded as the most stable state. Theconﬁgurations obtained by the above mentioned methodare used for the calculation of binding energy.Solution energies of hydrogen and helium againsttungsten are evaluated as -1.46 eV and 6.17 eV, respec-tively. This means that hydrogen is fusible in tungsten,meanwhile helium is hardly-soluble.Figures 1 and 2 depict the total binding energiesEB evaluated in this study as a function of the numberof helium and hydrogen atoms interstitially-trapped intungsten, respectively. It is inferred from these ﬁguresthat interstitially-trapped helium atoms have a tendencyto gather in tungsten once they are trapped. On theother hand, though hydrogen is easy to solve in tung-sten, interstitially-trapped hydrogen hardly form a clus-ter. They, however, can gather in tungsten with thehelp of interstitially-trapped helium. This result indi-cates that diﬀusion of helium in tungsten can be dis-turbed and that hydrogen retention in tungsten may beenhanced.Fig. 1: Total binding energy as a function of the numberof interstitially-trapped He atom.Fig. 2: Total binding energy as a function of the numberof interstitially-trapped H atom.1) A. Takayama, A. M. Ito, et al., “First-principles In-vestigation on Trapping on Multiple Helium Atomswithin a Tungsten Monovacancy”, Jpn. J. Appl.Phys., (2013) vol. 52, 01AL03.2) http://www.openmx-square.org/420§18. First-principles Investigations of Hydrogen-helium Atoms  Interstitially-trapped in TungstenTakayama, A., Ito, A.M., Oda, Y., Nakamura, H.

First-principles Investigations of Hydrogen-helium Atoms Interstitially-trapped in Tungsten

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