W. Y. Dinga,
H. Y. He*a and
B. C. Panab
aDepartment of Physics, University of Science and Technology of China, Hefei, Anhui 230026, P.R.China. E-mail: hyhe@ustc.edu.cn
bHefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, P.R.China
First published on 21st November 2013
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.
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.
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
The formation energy of a stacking fault is defined as
Ef = (Etot − nEW)/S, | (1) |
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 Ef(slab) as below.
Ef(slab) = (Eslab − nEW)/S − (Esur1 + Esur2), | (2) |
Esur = (Eslab0 − nEW)/2S0, | (3) |
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.
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.
The binding energy of H atoms in ISF varying with the number of H atoms is defined as
Eb = (Etot − EW−pure − NHEH)/NH, | (4) |
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 NH > 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 (NH = 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 NH = 15 and NH = 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.
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