Concentration dependent hydrogen diffusion in tungsten

doi:10.1016/j.jnucmat.2016.06.044

Journal of Nuclear Materials

Volume 479, October 2016, Pages 195-201

https://doi.org/10.1016/j.jnucmat.2016.06.044 Get rights and content

Highlights

•
The recommended value of 0.39 eV for the H in W migration barrier should be changed to 0.25 eV.
•
The random oscillation of atoms around the equilibrium position can be dealt with in diffusion simulations.
•
Hydrogen diffusion in tungsten is highly concentration dependent.

Abstract

The diffusion of hydrogen in tungsten is studied as a function of temperature, hydrogen concentration and pressure using Molecular Dynamics technique. A new analysis method to determine diffusion coefficients that accounts for the random oscillation of atoms around the equilibrium position is presented. The results indicate that the hydrogen migration barrier of 0.25 eV should be used instead of the presently recommended value of 0.39 eV. This conclusion is supported by both experiments and density functional theory calculations. Moreover, the migration volume at the saddle point for H in W is found to be positive: ΔV_m ≈ 0.488 Å³, leading to a decrease in the diffusivity at high pressures. At high H concentrations, a dramatic reduction in the diffusion coefficient is observed, due to site blocking and the repulsive H-H interaction. The results of this study indicates that high flux hydrogen irradiation leads to much higher H concentrations in tungsten than expected.

Introduction

Tungsten (W) is one of the strongest candidates to be used as the divertor plate material for the next step fusion device (ITER) due to its high melting point, low erosion rate, good thermal conductivity and low hydrogen retention. Such combination of properties makes W a promising plasma-facing wall material. However, continuous bombardment with low energy hydrogen isotopes is seen to introduce defects in plasma facing materials. Open volume defects, such as vacancies, are known to trap hydrogen (H) and thus are the main reasons for H retention in W. In fusion reactors this is a critical issue due to the tritium retention.

The presence of H strongly affects most of the W properties, due to phenomena like vacancy formation and blistering [1], [2]. Moreover, H is known to be trapped in impurities, vacancies, dislocations and grain boundaries [3], [4], [5], affecting the micro-structure evolution of the material. In order to be able to predict and calculate the evolution of the micro-structure, tritium retention, and other thermal and mechanical properties, it is essential to know the H concentration present in the material.

The H atom is an endothermic impurity in W with a solution energy E_sol of about 1 eV [6]. This means that the equilibrium H concentration C_H,eq in W is very low unless a large H₂ pressure (P) is present at the W surface at high temperature (T); $C_{H, e q} \propto \sqrt{(P)} \exp (- (E_{s o l} - T Δ S) / k_{B} T)$ , where ΔS is the entropy change and k_B is the Boltzmann constant. However, large H flux from a fusion device, plasma source or ion implanter can result in concentrations that considerably exceeds equilibrium value in W. This H concentration is proportional to the incoming flux and inverse proportional to the H diffusivity. The H diffusivity, however, is a function of the concentration itself. At high concentrations, the diffusivity should decrease due to the adjacent interstitial site blocking [7], and due to the short-range H-H repulsion [8], [9]. Hence, the decreasing diffusivity will increase the concentration, affecting the properties of the W material. To our knowledge, no data on concentration dependent H diffusion in W is found in the literature.

In this study, using molecular dynamics simulations we derive equations showing H diffusion coefficient dependence on the H concentration. We present a new analysis method to determine diffusion coefficients that accounts for the random oscillation of atoms around the equilibrium position. Moreover, we review the H diffusion coefficient at low concentrations in W, and suggest that the commonly used H diffusion parameters should be revised.

Section snippets

Computational method

Our modelling of H diffusion in W is done employing molecular dynamics simulations (MD) [10] using the bond-order potential by Li et al. [11] to describe the forces between W-W, W-H and H-H atoms. We use the Berendsen thermostat to control the atom velocity distribution, which for large systems of over hundreds of atoms approximately generates a correct canonical ensemble. Since the timestep is proportional to $M^{- 1 / 2}$ [10], where M is the atom mass, heavy hydrogen isotope deuterium (D) is chosen

Diffusion coefficient at low concentrations

The simulation of D diffusion coefficient for low D concentration (D/W = 1/2000) is done in the temperature range between 300 and 1500 K, and diffusion times between 1 and 20 ns. The D position during simulation is tracked using the Wigner-Seitz cell analysis, where the closest tetrahedral interstitial site (TIS) is found and is assigned to be the D position in the diffusion coefficient analysis. Fig. 1 illustrates the real X-position of the D atom, and the one used in the analysis as a

Conclusions

We have shown how the random oscillation of atoms around the equilibrium position can be dealt with in diffusion simulations. The derived method is general and only the mean oscillation distance squared around the atomic equilibrium position is needed. It improves the accuracy of determining the diffusion coefficient at all temperatures, but the main advantage is that it makes it possible to simulate atomic diffusion, and determine the corresponding diffusion coefficients at lower temperatures

Acknowledgements

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Grants of computer time from the Centre for Scientific Computing in Espoo, Finland, are gratefully acknowledged.

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View full text

Concentration dependent hydrogen diffusion in tungsten

Highlights

Abstract

Introduction

Section snippets

Computational method

Diffusion coefficient at low concentrations

Conclusions

Acknowledgements

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

Comput. Mater. Sci.

J. Nucl. Mater.

J. Nucl. Mater.

J. Nucl. Mater.

Mechanism of vacancy formation induced by hydrogen in tungsten

AIP Adv.

Hydrogen interaction with point defects in tungsten

Phys. Rev. B

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Nucl. Fusion

Investigating behaviours of hydrogen in a tungsten grain boundary by first principles: from dissolution and diffusion to a trapping mechanism

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J. Vac. Sci. Technol.

Computer simulation of sodium diffusion in β-alumina

Philos. Mag.