# Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{+}) bombard the first wall material, forming agglomerations and bubbles in the structural material, resulting in hydrogen-induced cracking, surface blistering and swelling [9,10,11]. These damages can seriously lead to the degradation of the mechanical properties of the material and affect the safety of the reactor operation [12,13,14]. It is generally believed that the nature of such damage phenomenon is derived from the interplay between hydrogen and various lattice defect. Therefore, it is necessary to study the behavior of hydrogen and hydrogen bubble nucleation further to slow down degradation and extend the service life of materials, particularly within the context of radiation damaged materials, such as metallic vanadium.

## 2. Computational Details

^{−6}eV. These equilibrium structures were utterly relaxed until the force acting on each atom is less than 0.001 eV/Å. The Brillouin zones were sampled with 3 × 3 × 3 k-points by Monkhorst-Pack scheme for (4 × 4 × 4) supercell [39]. As a reference, the calculated equilibrium lattice parameter of bcc V is 3.00 Å, which is consistent with previous calculations [32,33] and experimental values of 3.03 Å [40].

## 3. Result and Discussion

#### 3.1. H–H Interaction

#### 3.2. Vacancy-H Interaction

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Satou, M.; Abe, K.; Kayano, H. High-temperature deformation of modified V-Ti-Cr-Si type alloys. J. Nucl. Mater.
**1991**, 179, 757–761. [Google Scholar] [CrossRef] - Rowcliffe, A.; Zinkle, S.; Hoelzer, D. Effect of strain rate on the tensile properties of unirradiated and irradiated V–4Cr–4Ti. J. Nucl. Mater.
**2000**, 283, 508–512. [Google Scholar] [CrossRef] - Kurtz, R.J.; Hamilton, M.L. Biaxial thermal creep of V–4Cr–4Ti at 700 C and 800 C. J. Nucl. Mater.
**2000**, 283, 628–632. [Google Scholar] [CrossRef] - Dyomina, E.; Fenici, P.; Kolotov, V.; Zucchetti, M. Low-activation characteristics of V-alloys and SiC composites. J. Nucl. Mater.
**1998**, 258, 1784–1790. [Google Scholar] [CrossRef] - Jones, R.H.; Heinisch, H.L.; McCarthy, K. Low activation materials. J. Nucl. Mater.
**1999**, 271, 518–525. [Google Scholar] [CrossRef] - Taylor, N.; Forty, C.; Petti, D.; McCarthy, K. The impact of materials selection on long-term activation in fusion power plants. J. Nucl. Mater.
**2000**, 283, 28–34. [Google Scholar] [CrossRef] - Bloom, E.; Conn, R.; Davis, J.; Gold, R.; Little, R.; Schultz, K.; Smith, D.; Wiffen, F. Low activation materials for fusion applications. J. Nucl. Mater.
**1984**, 122, 17–26. [Google Scholar] [CrossRef] - Barabash, V.; Peacock, A.; Fabritsiev, S.; Kalinin, G.; Zinkle, S.; Rowcliffe, A.; Rensman, J.W.; Tavassoli, A.A.; Marmy, P.; Karditsas, P.J.; et al. Materials challenges for ITER—Current status and future activities. J. Nucl. Mater.
**2007**, 367–370, 21–32. [Google Scholar] [CrossRef] - Sun, Y.; Peng, Q.; Lu, G. Quantum mechanical modeling of hydrogen assisted cracking in aluminum. Phys. Rev. B
**2013**, 88, 104109. [Google Scholar] [CrossRef] [Green Version] - Jia, Y.Z.; Liu, W.; Xu, B.; Qu, S.L.; Shi, L.Q.; Morgan, T.W. Subsurface deuterium bubble formation in W due to low-energy high flux deuterium plasma exposure. Nucl. Fusion
**2017**, 57, 034003. [Google Scholar] [CrossRef] - Garner, F.A.; Simonen, E.P.; Oliver, B.M.; Greenwood, L.R.; Grossbeck, M.; Wolfer, W.; Scott, P. Retention of hydrogen in fcc metals irradiated at temperatures leading to high densities of bubbles or voids. J. Nucl. Mater.
**2006**, 356, 122–135. [Google Scholar] [CrossRef] - Aoyagi, K.; Torres, E.; Suda, T.; Ohnuki, S. Effect of hydrogen accumulation on mechanical property and microstructure of V–Cr–Ti alloys. J. Nucl. Mater.
**2000**, 283, 876–879. [Google Scholar] [CrossRef] - Mukouda, I.; Shimomura, Y.; Yamaki, D.; Nakazawa, T.; Aruga, T.; Jitsukawa, S. Microstructure in vanadium irradiated by simultaneous multi-ion beam of hydrogen, helium and nickel ions. J. Nucl. Mater.
**2002**, 307, 412–415. [Google Scholar] [CrossRef] - Myers, S.; Richards, P.; Wampler, W.; Besenbacher, F. Ion-beam studies of hydrogen-metal interactions. J. Nucl. Mater.
**1989**, 165, 9–64. [Google Scholar] [CrossRef] - Zibrov, M.; Ryabtsev, S.; Gasparyan, Y.; Pisarev, A. Experimental determination of the deuterium binding energy with vacancies in tungsten. J. Nucl. Mater.
**2016**, 477, 292–297. [Google Scholar] [CrossRef] [Green Version] - Zhu, X.-L.; Zhang, Y.; Cheng, L.; Yuan, Y.; De Temmerman, G.; Wang, B.-Y.; Cao, X.-Z.; Lu, G.-H. Deuterium occupation of vacancy-type defects in argon-damaged tungsten exposed to high flux and low energy deuterium plasma. Nucl. Fusion
**2016**, 56, 036010. [Google Scholar] [CrossRef] - Troev, T.; Markovski, A.; Petrova, M.; Peneva, S.; Yoshiie, T. Positron lifetime calculations of defects in vanadium containing hydrogen. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At.
**2006**, 248, 297–304. [Google Scholar] [CrossRef] - Xie, D.G.; Wang, Z.J.; Sun, J.; Li, J.; Ma, E.; Shan, Z.W. In situ study of the initiation of hydrogen bubbles at the aluminium metal/oxide interface. Nat. Mater.
**2015**, 14, 899–903. [Google Scholar] [CrossRef] - Dudarev, S.L. Density Functional Theory Models for Radiation Damage. Annu. Rev. Mater. Res.
**2013**, 43, 35–61. [Google Scholar] [CrossRef] - Fu, C.-C.; Torre, J.D.; Willaime, F.; Bocquet, J.-L.; Barbu, A. Multiscale modelling of defect kinetics in irradiated iron. Nat. Mater.
**2004**, 4, 68–74. [Google Scholar] [CrossRef] - Domain, C.; Becquart, C.S.; Foct, J. Ab initiostudy of foreign interstitial atom (C, N) interactions with intrinsic point defects in α-Fe. Phys. Rev. B
**2004**, 69, 144112. [Google Scholar] [CrossRef] - Liu, Y.-L.; Zhang, Y.; Zhou, H.-B.; Lu, G.-H.; Liu, F.; Luo, G.N. Vacancy trapping mechanism for hydrogen bubble formation in metal. Phys. Rev. B
**2009**, 79, 172103. [Google Scholar] [CrossRef] [Green Version] - Lu, G.; Kaxiras, E. Hydrogen embrittlement of aluminum: The crucial role of vacancies. Phys. Rev. Lett.
**2005**, 94, 155501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zepeda-Ruiz, L.A.; Rottler, J.; Wirth, B.D.; Car, R.; Srolovitz, D.J. Self-interstitial transport in vanadium. Acta Mater.
**2005**, 53, 1985–1994. [Google Scholar] [CrossRef] [Green Version] - Heinola, K.; Ahlgren, T.; Nordlund, K.; Keinonen, J. Hydrogen interaction with point defects in tungsten. Phys. Rev. B
**2010**, 82, 094102. [Google Scholar] [CrossRef] [Green Version] - Monasterio, P.R.; Lau, T.T.; Yip, S.; Van Vliet, K.J. Hydrogen-vacancy interactions in Fe-C alloys. Phys. Rev. Lett.
**2009**, 103, 085501. [Google Scholar] [CrossRef] - Ueda, Y.; Shimada, T.; Nishikawa, M. Impacts of carbon impurities in hydrogen plasmas on tungsten blistering. Nucl. Fusion
**2003**, 44, 62. [Google Scholar] [CrossRef] - Kong, X.-S.; You, Y.-W.; Fang, Q.F.; Liu, C.S.; Chen, J.-L.; Luo, G.N.; Pan, B.C.; Wang, Z. The role of impurity oxygen in hydrogen bubble nucleation in tungsten. J. Nucl. Mater.
**2013**, 433, 357–363. [Google Scholar] [CrossRef] - Zhou, X.; Marchand, D.; McDowell, D.L.; Zhu, T.; Song, J. Chemomechanical Origin of Hydrogen Trapping at Grain Boundaries in fcc Metals. Phys. Rev. Lett.
**2016**, 116, 075502. [Google Scholar] [CrossRef] [Green Version] - Valles, G.; Panizo-Laiz, M.; González, C.; Martin-Bragado, I.; González-Arrabal, R.; Gordillo, N.; Iglesias, R.; Guerrero, C.L.; Perlado, J.M.; Rivera, A. Influence of grain boundaries on the radiation-induced defects and hydrogen in nanostructured and coarse-grained tungsten. Acta Mater.
**2017**, 122, 277–286. [Google Scholar] [CrossRef] - Hayashi, E.; Kurokawa, Y.; Fukai, Y. Hydrogen-induced enhancement of interdiffusion in Cu-Ni diffusion couples. Phys. Rev. Lett.
**1998**, 80, 5588. [Google Scholar] [CrossRef] - Gui, L.-J.; Liu, Y.-L.; Wang, W.-T.; Jin, S.; Zhang, Y.; Lu, G.-H.; Yao, J.-E. First-principles investigation on vacancy trapping behaviors of hydrogen in vanadium. J. Nucl. Mater.
**2013**, 442, S688–S693. [Google Scholar] [CrossRef] - Ouyang, C.; Lee, Y.-S. Hydrogen-induced interactions in vanadium from first-principles calculations. Phys. Rev. B
**2011**, 83, 045111. [Google Scholar] [CrossRef] - Zhang, P.; Zhao, J.; Wen, B. Trapping of multiple hydrogen atoms in a vanadium monovacancy: A first-principles study. J. Nucl. Mater.
**2012**, 429, 216–220. [Google Scholar] [CrossRef] - Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B
**1996**, 54, 11169. [Google Scholar] [CrossRef] [PubMed] - Kresse, G.; Hafner, J. Ab initiomolecular dynamics for open-shell transition metals. Phys. Rev. B
**1993**, 48, 13115–13118. [Google Scholar] [CrossRef] [PubMed] - Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B
**1994**, 50, 17953–17979. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865. [Google Scholar] [CrossRef] [Green Version] - Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188–5192. [Google Scholar] [CrossRef] - Han, S.; Zepeda-Ruiz, L.A.; Ackland, G.J.; Car, R.; Srolovitz, D.J. Self-interstitials in V and Mo. Phys. Rev. B
**2002**, 66, 220101. [Google Scholar] [CrossRef] [Green Version] - Van de Walle, C.G.; Neugebauer, J. First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys.
**2004**, 95, 3851–3879. [Google Scholar] [CrossRef] - Ohsawa, K.; Eguchi, K.; Watanabe, H.; Yamaguchi, M.; Yagi, M. Configuration and binding energy of multiple hydrogen atoms trapped in monovacancy in bcc transition metals. Phys. Rev. B
**2012**, 85, 094102. [Google Scholar] [CrossRef] - Hou, J.; Kong, X.; Sun, J.; You, Y.; Wu, X.; Liu, C.; Song, J. Hydrogen bubble nucleation by self-clustering: Density Functional Theory and statistical models studies using tungsten as a model system. Nucl. Fusion
**2018**, 58, 096021. [Google Scholar] [CrossRef] [Green Version] - Takagi, I.; Matsubara, N.; Akiyoshi, M.; Moritani, K.; Sasaki, T.; Moriyama, H. Deuterium trapping near vanadium surface bombarded with hydrogen ions. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At.
**2005**, 232, 327–332. [Google Scholar] [CrossRef] - Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C.G. First-principles calculations for point defects in solids. Rev. Mod. Phys.
**2014**, 86, 253–305. [Google Scholar] [CrossRef] - Hayward, E.; Fu, C.-C. Interplay between hydrogen and vacancies in α-Fe. Phys. Rev. B
**2013**, 87, 174103. [Google Scholar] [CrossRef] - Arbuzov, V.; Vykhodets, V.; Raspopova, G. The trapping of hydrogen ions in vanadium and titanium. J. Nucl. Mater.
**1996**, 233, 442–446. [Google Scholar] [CrossRef] - Geng, W.T.; Wan, L.; Du, J.-P.; Ishii, A.; Ishikawa, N.; Kimizuka, H.; Ogata, S. Hydrogen bubble nucleation in α-iron. Scr. Mater.
**2017**, 134, 105–109. [Google Scholar] [CrossRef] - Ferrin, P.; Kandoi, S.; Nilekar, A.U.; Mavrikakis, M. Hydrogen adsorption, absorption and diffusion on and in transition metal surfaces: A DFT study. Surf. Sci.
**2012**, 606, 679–689. [Google Scholar] [CrossRef] - Dag, S.; Ozturk, Y.; Ciraci, S.; Yildirim, T. Adsorption and dissociation of hydrogen molecules on bare and functionalized carbon nanotubes. Phys. Rev. B
**2005**, 72, 155404. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**a**) Initial and final distances between H–H pairs of atoms. The unit cell in the lower right and upper left represents the schematic of the H–H initial distance of 1.061 Å and the final distance of 1.708 Å after optimization, respectively. (

**b**) The interaction energies of H–H pairs as a function of the H–H distance in bcc V. The unit cell represents a schematic of the strongest bonding energy in H–H configuration.

**Figure 2.**The projected density of states (PDOS) of the hydrogen atoms in different distances of H–H pairs in vanadium. The numbers in the legend represent the distance of H–H pairs after relaxation. In order to see more clearly the changes in each curve, each line is separated from top to bottom.

**Figure 3.**(

**a**) The PDOS curves and structures of multiple hydrogen atoms in the monovacancy in bcc vanadium. (

**b**) The two types of hydrogen atoms are in blue and in red, respectively, corresponding to the color of the PDOS curves in the above.

**Figure 4.**There are two types of schematic H-saturated vacancy cluster structure: (

**a**) The 9-vacancy cluster of 24H-saturated in a (4 × 4 × 4) supercell vanadium (

**b**) The 27-vacancy cluster of 54H-saturated in (5 × 5 × 5) supercell vanadium. Vanadium atoms are in blue, saturated H in pink and molecular H in yellow. Only the V atoms on the surface of the vacancy cluster are displayed. The PDOS for hydrogen on the inner surface and in the molecule, and neighboring vanadium corresponding to the two types of structures with hydrogen molecule are shown on (

**c**,

**d**), respectively.

**Table 1.**The binding energy for the nth hydrogen atom by the most stable $vac+(n-1)H$ structure in bcc vanadium.

Configuration | ${\mathit{E}}_{\mathit{H}}^{\mathit{b}\mathit{i}\mathit{n}\mathit{d}}\text{}\left(\mathbf{eV}\right)$ | Ref. [34] (eV) |
---|---|---|

$vac+H$ | −0.34 | −0.31 |

$vac+2H$ | −0.43 | −0.40 |

$vac+3H$ | −0.27 | −0.25 |

$vac+4H$ | −0.28 | −0.25 |

$vac+5H$ | −0.24 | −0.24 |

$vac+6H$ | −0.16 | −0.12 |

$vac+7H$ | 0.65 | 0.69 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Su, Z.; Wang, S.; Lu, C.; Peng, Q.
Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium. *Materials* **2020**, *13*, 322.
https://doi.org/10.3390/ma13020322

**AMA Style**

Su Z, Wang S, Lu C, Peng Q.
Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium. *Materials*. 2020; 13(2):322.
https://doi.org/10.3390/ma13020322

**Chicago/Turabian Style**

Su, Zhengxiong, Sheng Wang, Chenyang Lu, and Qing Peng.
2020. "Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium" *Materials* 13, no. 2: 322.
https://doi.org/10.3390/ma13020322