Structure, stability and diffusion of hydrogen in tungsten: A first-principles study

doi:10.1016/j.jnucmat.2009.01.277

Journal of Nuclear Materials

Volumes 390–391, 15 June 2009, Pages 1032-1034

https://doi.org/10.1016/j.jnucmat.2009.01.277 Get rights and content

Abstract

Using a first-principles method, we have investigated structure, stability and diffusion of hydrogen (H) in tungsten (W). We found that single H atom prefers to occupy the tetrahedral interstitial site with the formation energy of ∼−2.45 eV. Two H in the tetrahedral interstitial sites form a pairing cluster along the <1 1 0> directions with the H–H distance of ∼2.22 Å, while the corresponding binding energy is only 0.02 eV, indicating a very weak attractive interaction. This suggests that H itself is not capable of trapping other H atoms to form a H₂ molecule. The kinetics of H in intrinsic W is discussed, and the diffusion barrier of H that jumps between the tetrahedral interstitials is calculated to be 0.20 eV.

Introduction

Tungsten (W) and W alloys are the most promising candidates for plasma facing material (PFM) in Tokamak because of their good thermal properties and low sputtering erosion [1]. However, as a PFM, W will be exposed to extremely high fluxes of hydrogen (H) isotope ions. It must not only withstand radiation damage, but also keep intrinsic mechanical properties and structural strength. Previous experimental study shows that H isotope causes blistering at the W surface [2]. So far, however, the physical mechanism of H trapping and blistering in W is not well understood. It is still an open question as to how H blistering nucleates during plasma exposure.

First-principles method is one of widely-used computational methods, and plays more and more important role in investigating and predicting the structure and properties of many material systems [3], [4], [5], [6]. A recent first-principles study [7] shows that H prefers to occupy the tetrahedral interstitial site in W, and two H atoms interacts with an equivalent distance of 2.2 Å. In combination with the molecular dynamics and kinetic Monte-Carlo methods [7], it is demonstrated that H cannot be self-trapped in W, which explains the different bubble-formation depth of H from He as observed in the experiment. In order to understand the physical mechanism of H trapping in more detail and investigate the kinetics of H in the intrinsic W, in this paper, we have investigated the structure, stability and diffusion of H in W using the first-principles method. Our calculations will provide a useful reference for further exploration of the blistering mechanism of H in W.

Section snippets

Computation method

We employ a total-energy method based on density functional theory [8], [9] with generalized gradient approximation developed by Perdew and Wang [10] and the projector-augmented-wave potential. We use a kinetic energy cutoff of 350 eV for all calculations. The uniform grids of k-points are sampled by 5 × 5 × 5 for the 54-atom supercell and 3 × 3 × 3 for the 128-atom supercell. The calculations have been carried out by VASP [11], [12]. The calculated equilibrium lattice constant is 3.17 Å for a bcc W, in

Single H atom in W

The possible sites for single H atom involve both interstitial and substitutional sites. The results of formation energies in Table 1 show that the tetrahedral interstitial site is energetically more favorable for single H, in good agreement with both computational [7] and experimental results [13], [14], [15], [16]. For comparison, we also calculated formation energy of single vacancy, which is 3.14 eV for the 54-atom supercell and 3.11 eV for a 128-atom supercell, consistent with the calculated

Summary

We have studied structure, stability, and diffusion in a W single crystal using a first-principles method. Single H atom prefers to occupy the tetrahedral interstitial site in W with the formation energy of ∼−2.45 eV in comparison with the octahedral interstitial and substitutional case. Two H atoms in the tetrahedral interstitial sites form a pairing cluster along the <1 1 0> directions with the H–H equilibrium distance of 2.22 Å, while the corresponding binding energy is only 0.02 eV, indicating a

Acknowledgement

This work is supported by the National Natural Science Foundation of China (NSFC) with Grant No. 50871009.

References (21)

R. Causey et al.
J. Nucl. Mater.
(1999)
I.I. Arkhipov et al.
J. Nucl. Mater.
(2007)
S. Nagata et al.
J. Nucl. Mater.
(2000)
S.T. Picraux et al.
J. Nucl. Mater.
(1974)
C.S. Becquart et al.
Nucl. Instrum. Meth. Phys. Res. B
(2007)
T. Seletskaia et al.
J. Nucl. Mater.
(2006)
G.-H. Lu et al.
Phys. Rev. B
(2004)
G.-H. Lu et al.
Phys. Rev. Lett.
(2005)
G.-H. Lu et al.
Phys. Rev. B
(2006)
Y. Zhang et al.
Phys. Rev. B
(2007)

There are more references available in the full text version of this article.

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Structure, stability and diffusion of hydrogen in tungsten: A first-principles study

Abstract

Introduction

Section snippets

Computation method

Single H atom in W

Summary

Acknowledgement

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

Nucl. Instrum. Meth. Phys. Res. B

J. Nucl. Mater.

Phys. Rev. B

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B