Interaction of H with stacking fault in W(111) film: A possible formation mechanism of H bubbles

Abstract

The behavior of H atoms near a stacking fault in W(111) surface is extensively studied based on first-principles density functional theory calculations. We find that H near the stacking fault can be captured and trapped in this defect. These trapped H atoms significantly weaken and even break the W–W bonds in the stacking fault, inducing accumulation of more hydrogen atoms in the stacking fault. Our calculations predict the accommodating capacity of the stacking fault for H to be larger than 3.4 × 10¹⁵ cm⁻², consistent with the experimentally observed H blistering in W-based fusion reactor materials.

---

I. Introduction

With the aim to make the long-awaited transition from experimental studies of plasma physics to fusion power plants, the International Thermonuclear Experimental Reactor (ITER) Project¹ was proposed world-wide. In the ITER project, the challenge is to seek or develop plasma facing materials (PFMs), which possess excellent mechanical and thermal properties under the extreme environments including the irradiation of energetic particles and the higher temperatures of about 1000 K. Among several candidates, tungsten (W) is promising for PFM in fusion reactor, due to its special mechanical and thermal properties.^2–4 Experiments have found that W-based PFMs not only suffer strong bombardment from energetic particles, such as neutrons, hydrogen isotopes (H, D and T) and helium (He),^5–10 but are also damaged by the H blistering and He blistering in them as well. Both the H bubbles and He bubbles seriously degrade the mechanical properties of the W-based PFMs,¹¹ and thus influence the lifetime of W-based PFMs.

In recent years, many efforts have been devoted to exploring the formation of H bobbles in the PFM of tungsten.^{5–9,12–17} Experimental studies have shown that the bombardment of high flux of H isotope ions (D) on polycrystalline W can cause H accumulation and H bubbles formation at the surface region in a W film.^6–9 Generally speaking, the formation of a H-bubble in W film is essentially associated with the interaction between H (or its isotopes) and W. In particular, the defects such as atomic vacancies, dislocations and surface defects in W film prefer to accommodate H to form H bubbles. Of these structural defects, a monovacancy, which was mostly regarded as the origin of H bubble, was found to accommodate 10 H atoms.¹²

It is noted that the size of a monovacancy containing 10 H atoms is really small with respect to that of a realistic H bubble in W film. So, such hydrogenated monovacancies are only a kind of prototype of H bubbles in W. To get the size of H bubbles observed in experiments, such a prototype of H bubbles should grow. A possible way for the growth of the prototypes is that the trapped H in a vacancy may break some W–W bonds at the inner wall of the monovacancy, and some W atoms could be stripped from the inner wall of the vacancy. Consequently, the monovacancy becomes a microvoid, and more H atoms may accumulate inside to form a H bubble. If this is the case, each stripped W atom is saturated by H atoms. These hydrogenated W fragments can not diffuse away from the microvoid in W film. Instead, all of the W–H fragments stay inside the microvoid. As a result, these fragments block the accumulation of H atoms in the microvoid, and thus the microvoids can hardly evolute to the realistic H bubbles.

Beside monovacancies, many other kinds of defects, such as grain boundary, dislocations and surface defects, commonly exist in W films. These structural defects are also the possible nucleating sites for H bubbles in W film. In literature, Liu and co-workers investigated the behaviour of H at a grain boundary in W, and found that a H bubble cannot form there yet.¹³

Stacking faults are the kinds of common face defects, which normally present in W materials.¹⁸ Structurally, there exists a large defective region in a stacking fault, where the interaction of W–W is weak with respect to that in a perfect region. Therefore, H atoms may have a good possibility of gathering in this defective region to form H blistering. Unfortunately, the interaction between H atoms and the stacking fault in W film has not been reported so far, to our knowledge.

In this work, based on the first-principles calculations, we investigate the behavior of H atoms in the vicinity of a stacking fault. We find that H atoms near a stacking fault can be trapped by this face defect very easily. More interestingly, the size of the formed H bubbles at the stacking fault in the surface region are much larger than that in the bulk region, indicating a possible formation mechanism of H bubbles in W(111) surface region. In addition, the evolution of the H bubbles at a stacking fault is revealed.

II. Methodology

The density functional theory (DFT) implanted in SIESTA package^19–21 is employed for the structural optimization and total energy calculations. The norm conserving pseudopotentials generated by using the Troullier–Martins scheme²² are employed to describe the interaction between valence electrons, which are expressed in a fully separable form developed by Kleiman and Bylander.^23,24 Double-ζ basis sets are used for W and H atoms, and a mesh cutoff of 200 Ry is adopted. For the volumetric and ionic relaxation of a system the conjugate gradient algorithm is chosen and the relaxation is stopped when a convergence criterion of 0.02 eV Å⁻¹ is reached.

In our calculations, the stacking faults in both W bulk and W(111) film are considered. A supercell of 3 × 3 × 6 unit cell is used to simulate bulk W; a slab with 3 × 3 unit cell in the surface, together with a 18-layer thickness separated by a vacuum region of about 20 Å is selected to model the W(111) film. In our calculations, the six atomic layers at bottom of the slab are kept frozen. Based on the Monkhorst–Pack mesh k-points scheme,²⁵ the Brillouin zones of the bulk W and the slab are respectively sampled by 5 × 5 × 3 and 5 × 5 × 1.

Both generalized gradient approximation (GGA)²⁶ and local density approximation (LDA)²⁷ are tested for the description of exchange and correlation interactions among electrons in the body-centered cubic W. The lattice constant of W bulk from GGA is predicted to be 3.16 Å, and that from LDA to be 3.14 Å. The calculated lattice constant from GGA is in excellent agreement with the experimental value,²⁸ thus we perform all our calculations at the GGA level.

The calculations for exploring the diffusion behaviors of H near the stacking fault are carried out with using the climbing image nudged elastic band (CI-NEB) scheme.²⁹ We implemented it in SIESTA package as a post-processing code, and successfully predicted the diffusion behaviors of H in ZnO.^30–32

III. Results and discussion

A. The stability of stacking fault in tungsten film

We firstly concern the formation energies of stacking faults along the typical directions in W bulk. For body-centered cubic (BCC) lattice of W bulk, the normal stacking sequence along the 〈111〉 (z axis) direction is ABCABCABC… and that along the 〈110〉 or 〈100〉 is ABABAB…. Usually, such a perfect stacking sequence does not always keep. Instead, the stacking sequence is in mis-order, forming the so-called stacking faults. In this work, we consider two kinds of stacking faults: the intrinsic stacking faults (ISF) and the extrinsic stacking faults (ESF). For the 〈111〉 direction, the former is obtained by removing an atomic layer from the perfect stacking sequence to form the stacking sequence of ABCBCABC…, while the latter is achieved by adding an additional atomic layer in the perfect crystal to have the stacking sequence of ABACABCABC…. For both 〈110〉 and 〈100〉 directions, the ISF and the ESF are the same.

The formation energy of a stacking fault is defined as

E_f = (E_tot − nE_W)/S, (1)

where the E_tot refers to the total energy of the concerned n-atom bulk system containing a stacking fault, E_W indicates the energy of a W atom in the perfect crystal, and S is the cross-sectional area of the stacking fault. According to this definition, the formation energies of ISF and ESF along the 〈111〉 direction are predicted to be 0.16 eV Å⁻² and 0.29 eV Å⁻² respectively. Meanwhile, the ISF (ESF) along 〈110〉 and 〈100〉 directions are predicted to be 0.18 eV Å⁻² and 0.26 eV Å⁻², respectively. Comparably, the formation energy of ISF along the 〈111〉 direction is lower than those of others, implying that the ISF along the 〈111〉 direction is energetically preferred. Thus, we only take the ISF along the 〈111〉 direction as the typical case to investigate the interaction of H with this kind of stacking faults in W film.

Fig. 1(a and b) shows the geometry of bulk tungsten stacking sequence along 〈111〉, from which W(111) film can be formed. By removing an atomic layer in different depth, W(111) with ISFs at different locations from the surface are obtained. We then explore the energetic stability of the ISF locating at different atomic layers of the W(111) film. It is noted that one surface in our slab is used to mimic the realistic surface of W film, and the other surface in our slab is fixed. So, to evaluate the formation energy of ISF in slab, the energies of both the relaxed and the unrelaxed surfaces should be taken into account in the definition of the ISF formation energy E_f(slab) as below.

E_f(slab) = (E_slab − nE_W)/S − (E_sur1 + E_sur2), (2)

where the E_slab refers to the total energy of the n-atom slab containing a stacking fault, E_W means the energy of a W atom in the perfect bulk, E_sur1 is the surface formation energy of the relaxed W(111) surface, E_sur2 is the surface formation energy of the unrelaxed W(111) surface, and S stands for the area of the surface in the slab. The surface formation energies E_sur1 and E_sur2 are obtained by

E_sur = (E_slab0 − nE_W)/2S₀, (3)

in which the E_slab0 indicates the total energy of the n-atom slab for a perfect surface, and S₀ denotes the corresponding area of the surface. If both surfaces of the slab are relaxed, we have E_sur1 = E_sur, and if unrelaxed, we have E_sur2 = E_sur.

Fig. 1 The side view (a), top view (b) of bulk tungsten stacking sequence along 〈111〉 (z) direction and the formation energies E_f (c) of ISF in W(111) film as a function of the depth from the surface.

Fig. 1(c) displays the formation energies of the ISF locating in different atomic layers in the slab, from which one can see that the formation energy of the ISF at the third atomic layer is the smallest. As the location of the ISF becomes deep from the surface, the formation energy of the ISF increases by about 0.06 eV Å⁻² from the second layer to the fifth layer, and then converges to the bulk value of 0.16 eV Å⁻². This means that the influence of the surface effect on the formation of the ISF is not in long-range, but within several atomic layers at the surface region. In the present work, we choose the case of ISF located at the sixth atomic layer as a typical case to investigate the interaction of H with the ISF near the film surface.

B. The trapping process of a diffusive H atom by an ISF in W(111) film

We now investigate the diffusion behavior of H near an ISF, including the diffusion of a H atom from the vicinity region to the ISF and the diffusive event in the ISF. For the first case, our calculations identify that, in the region near the ISF, a H atom preferably locates at the tetrahedral site, as shown by the mark A in Fig. 2(a); and in the region of the ISF, a H atom favours positioning at the site of C in Fig. 2(a). Our calculations show that the energy of H at site C is lower than that at A site by about 1.1 eV. Such a large energy difference implies that ISF acts as a potential well for H atoms.

Fig. 2 The diffusion path (a) and the energy profiles (b) of H from perfect region to the ISF. The reaction coordinates in (b) refer to (a).

Although an ISF in W(111) acts as a deep well for H atoms as mentioned above, the trap of H by the well is critically dependent on the diffusion behavior of the H atom from the site A to the site C. To explore the concerned diffusion behavior of H, the energy profile regarding to the migration of a H atom from site A to site C is computed by using the CI-NEB scheme.²⁹ As plotted in Fig. 2(b), there is an energy barrier of less than 0.14 eV in the diffusion path, which indicates H near an ISF can easily migrate to the defective region of the ISF. This energy barrier is a little smaller than our calculated value of 0.22 eV and the previously reported ones (0.20 eV,¹² 0.21 (0.26) eV (ref. 33)) for a H atom diffusing from a tetrahedral site to a nearby tetrahedral site in perfect bulk W. We emphasize that such a very small energy barrier demonstrates that the H atom at site A near the ISF can easily migrate to site C in the ISF region even at low temperatures. In contrast, the energy barrier for H diffusing from site C in the ISF to site A requires about 1.24 eV. Such a high energy barrier implies that it is hard for H to migrate away from the ISF region.

Since a H atom in vicinity can be captured and tightly trapped by an ISF, we wonder whether or not it can diffuse within the region of the ISF. To check this concern, we examine the diffusion behavior of a H atom within the ISF region. As shown in Fig. 3(c), the calculated diffusion barriers of H in ISF are less than 0.26 eV, indicating that H can move in the stacking fault with ease. Structurally, the barrier of 0.26 eV corresponds to the configuration of H near the center of a rhombus (as plotted with gray atoms in Fig. 3(b)).

Fig. 3 The side view (a), top view (b) of the diffusion path, and the energy profiles (c) of H in the ISF. The reaction coordinates in (c) refer to (a) or (b).

From above, we obtain a clear picture about the diffusion behavior of a H atom near ISF: H atoms near the stacking fault can easily migrate into this face defect, and the H atoms in the ISF region hardly migrate away from the ISF, but they are diffusive within the ISF region.

C. The formation of H bubble at ISF

In terms of the calculated diffusion energies of H near the stacking fault above, we believe that H atoms have large possibility gathering in the stacking fault through diffusion. Nevertheless, accumulating H atoms in the ISF should weaken the interaction of W–W at the stacking fault, and further cause H blistering at this defect. To uncover the formation process of the H blistering, we pay our attention to the gathering behaviors of H atoms and the corresponding structural changes at the ISF.

The binding energy of H atoms in ISF varying with the number of H atoms is defined as

E_b = (E_tot − E_W−pure − N_HE_H)/N_H, (4)

in which E_tot is the total energy of the system containing N_H H atoms locating at the ISF, E_W−pure indicates the energy of the related W system without H, and E_H stands for the half value of a hydrogen molecule energy. According to this definition, the binding energies of H atoms in the ISF are obtained, as plotted in Fig. 4. As a comparison, the corresponding binding energies of H at ISF in W bulk are also taken into account. We note that for each case with a certain number of H, different configurations for H atoms locating in ISF are concerned. As shown in Fig. 4, with more H atoms gathering in ISF, the binding energy goes up for the case of ISF either in the surface region or in bulk. More importantly, there are two aspects exhibited in the energy curves. One is that, for a given number of H atoms, the binding energy in the case of surface is systematically lower than that in the bulk. This demonstrates that H bubbles are easier to form in the ISF in the surface region than that in the bulk region. The second aspect is that in the bulk case the binding energy is negative until the number of the accommodated H atoms are more than 35. This corresponds to the H coverage of about 2.2 × 10¹⁵ cm⁻². In contrast, for the surface case, the binding energies are always negative in all of the considered number of H atoms. So, the ISF in the surface region has great capacity to accommodate H atoms, in which a bigger H bubble is easier to form than that in bulk.

Fig. 4 Formation energy of H atom in ISF in W(111) film and that in the W bulk, and the averaged W–W bond length of ISF in W(111) film. The dashed line denotes the W–W bond length in bulk. The inserts are the geometries of W(111) film with 15 and 54 H atoms in ISF.

Basically, the accumulating H atoms have significant influence on the local structure of the ISF, which is reflected in the changes of the averaged bond length of W–W in ISF. Therefore, we survey the averaged bond length of W–W in the ISF with and without containing H atoms, respectively. It is found that the averaged bond length of W–W in ISF without H is about 2.61 Å, being short by about five percent with respect to that (2.74 Å) in perfect W crystalline. With H atoms gathering in the ISF, the strengths of W–W bonds become weak, and the lengths of the W–W bonds are elongated accordingly. Fig. 4 displays the averaged bond length of W–W in ISF as the function of the number of H atoms. In this figure, the W–W bond length in bulk is taken for comparison. From Fig. 4, we can see that as the number of H in ISF increases, the average bond length of W–W increases slowly, featuring a linear trend almost. However, when N_H > 35, the average bond length of W–W increases abruptly, where the averaged W–W bond length is elongated to be about 3.0 Å. In this case, many W–W bonds at ISF are very weak. Further increasing H atoms in ISF induces the average W–W bond length to be 3.3 Å. This implies that many W–W bonds in ISF are broken completely, and the cavity presents in local structure of the ISF. Correspondingly, the accommodating capacity of the stacking fault for H increases to be 3.4 × 10¹⁵ cm⁻² (N_H = 54).

Compared to the strikingly elongated W–W bond, the W–H bond length changes slightly, being about 1.93 Å with ±0.01 Å for different H capacity. The distance between two H atoms is larger than 1.8 Å even for the case with H capacity of 3.4 × 10¹⁵ cm⁻², implying no H₂ is formed in these cases. The typical configurations for the ISF containing H with N_H = 15 and N_H = 54 are inserted in Fig. 4. Clearly, for an ISF locating at the surface region, it traps many diffusive H atoms nearby. When the density of H in ISF increases, the ISF is gradually torn off, offering a large interspace available for the accommodation of more H atoms. This just corresponds to the formation of a H bubble, whose size is comparable to that observed in experiments.

Before closing this paper, we stress that the atomic layers in the surface region can adjust their position along the direction perpendicular to the surface more easily than in the bulk region. Therefore, many big H bubbles may easily form at ISF in surface region rather than in bulk region. So, many big H bubbles may easily form at the stacking fault in the surface region rather than in the bulk region, being consistent with the observation in experiments.

IV. Summary

We investigate the interactions of H atoms with the stacking fault in W(111) film, based on the first-principles calculations. Our calculations reveal that H atoms in the vicinity can easily migrate to the stacking fault and be trapped there, with energy cost of less than 0.14 eV. With more H atoms gathering, the strength of W–W bonds at the stacking fault is weakened, and the W–W bonds are elongated to some extent. Consequently, accumulation of H atoms tears up local structures of the stacking fault with breaking of W–W bonds. This offers larger space for the accommodation of more H atoms, forming large H bubbles in the W surface region.

Acknowledgements

This work is supported by the National Science Foundation of China (Grant no. NSFC11105140, 11275191), National Magnetic Confinement Fusion Science Program (no. 2013GB107004), Anhui Provincial Natural Science Foundation (no. 11040606M17), the Chinese academy of Science, National Science Foundation of China (Grant nos NSFC10574115 and NSFC50721091). The HP-LHPC of USTC is acknowledged for computational support.

References

1. A. Loarte, et al., Nucl. Fusion, 2007, 47, S203 , and references therein.
2. C. H. Wu and U. Mszanowski, J. Nucl. Mater., 1995, 218, 293.
3. R. A. Causey, C. L. Kunz and D. F. Cowgill, J. Nucl. Mater., 2005, 337–339, 600.
4. J. P. Sharpe, R. D. Kolasinski, M. Shimada, P. Calderoni and R. A. Causey, J. Nucl. Mater., 2009, 390–391, 709.
5. R. Sakamoto, T. Muroga and N. Yoshida, J. Nucl. Mater., 1995, 220–222, 819–822.
6. A. A. Haasz, M. Poon and J. W. Davia, J. Nucl. Mater., 2009, 266–269, 520.
7. T. Venhaus, R. Causey, R. Doerner and T. Abeln, J. Nucl. Mater., 2001, 290–293, 505.
8. T. Shimada and H. Kikuchi, et al., J. Nucl. Mater., 2003, 313–316, 204.
9. Y. Ueda, T. Funabiki, T. Shimada, K. Fukumoto, H. Kurishita and M. Nishikawa, J. Nucl. Mater., 2005, 337–339, 1010.
10. H. Iwakiri, K. Yasunaga, K. Morishita and N. Yoshida, J. Nucl. Mater., 2000, 283–287, 1134.
11. J. B. Condon and T. J. Schober, J. Nucl. Mater., 1993, 207, 1.
12. Y. L. Liu, Y. Zhang, H. B. Zhou, G. H. Lu, F. Liu and G. N. Luo, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 172103.
13. H. B. Zhou, Y. L. Liu, S. Jin, Y. Zhang, G. N. Luo and G. H. Lu, Nucl. Fusion, 2010, 50, 025016.
14. B. Jiang, F. R. Wan and W. T. Geng, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 134112.
15. K. Heinola, T. Ahlgren, K. Nordlund and J. Keinonen, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 094102.
16. K. Heinola and T. Ahlgren, J. Appl. Phys., 2010, 107, 113531.
17. H. B. Zhou, Y. L. Liu, S. Jin, Y. Zhang, G. N. Luo and G. H. Lu, Nucl. Fusion, 2010, 50, 115010.
18. D. A. Smith and K. M. Bowkett, Philos. Mag., 1968, 156, 1219.
19. P. Ordejon, E. Artacho and J. M. Soler, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 53, R10441.
20. D. Sanchez-Portal, P. Ordejon, E. Artacho and J. M. Soler, Int. J. Quantum Chem., 1997, 65, 453.
21. J. M. Soler and E. Artacho, et al., J. Phys.: Condens. Matter, 2002, 14, 2745.
22. N. Troullier and J. L. Martins, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 43, 1991.
23. L. Kleinman and D. M. Bylander, Phys. Rev. Lett., 1982, 48, 1425.
24. D. M. Bylander and L. Kleinman, Phys. Rev. B: Condens. Matter Mater. Phys., 1990, 41, 907.
25. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188.
26. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
27. J. P. Perdew and A. Zunger, Phys. Rev. B: Solid State, 1981, 23, 5048.
28. C. Kittel, Introduction to Solid State Physics, Wiley, New York, 8th edn, 2005.
29. G. Henkelman, B. P. Uberuaga and H. Jónsson, J. Chem. Phys., 2000, 113, 9901.
30. J. Hu, H. Y. He and B. C. Pan, J. Appl. Phys., 2008, 103, 113706.
31. J. Hu, H. Y. He and B. C. Pan, J. Phys. Chem. C, 2009, 113, 11381.
32. H. Y. He, J. Hu and B. C. Pan, J. Chem. Phys., 2009, 130, 204516.
33. K. Heinola and T. Ahlgren, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 073409.

---