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The growth and release of helium bubbles near tungsten surface studied with molecular dynamics simulations
Nuclear Inst. and Methods in Physics Research B 455 (2019) 66–73
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
The growth and release of helium bubbles near tungsten surface studied with molecular dynamics simulations
T
Yulu Zhou, Chiwen Yuan, Tao Li, Xiaoma Tao, Yifang Ouyang
⁎
Guangxi Key Laboratory for Relativistic Astrophysics, College of Physical Science and Technology, Guangxi University, Nanning, Guangxi 530004, China
ARTICLE INFO
ABSTRACT
Keywords: Tungsten Helium bubble Surface morphology Self-healing Molecular dynamics simulations
The growth and release processes of helium bubbles near tungsten surface have been investigated by molecular dynamics (MD) simulations. The results indicate that the surface morphologies are dependent on orientation of surfaces. Before bubble rupture occurs, stepped, thin schistose and pyramidal structures are observed on the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. When the angle between the normal direction of surface and the sliding direction (〈1 1 1〉 direction) is larger, flatter surface would be formed and the subsequent release process would be more violent. In the bursting process, the release rate of helium and the degree of surface damage are correlated with the surface stacking height before bubble bursts. Unrepaired crack structures have been observed on the (1 1 0) and (1 0 0) surfaces, while a smaller hole on the (1 1 1) surface. The stacking atoms have a tendency to make the surface restore to the bcc structure. At high temperature, the surface pore with radius ∼1 nm can be self-healed from outer to inner by the diffusion of surface atoms, while no recovery is observed in MD time scale when the ratio of He/V in the bubble is high.
1. Introduction Tungsten is considered one of the best options as a plasma-facingmaterial (PFM) for the diverter in the International Thermonuclear Experimental Reactor (ITER) because of its high temperature capabilities and good sputtering erosion resistance. Experimental work has shown that the bombardment of high-flux helium plasma results in the formation of bubbles in tungsten, this may induce morphological modifications of tungsten surfaces (e.g., pores [1–3], nano-fuzzes [4,5]). Many researchers have performed experimental studies to investigate the factors such as the starting structure of tungsten [4,6], helium ion energy [7], helium flux [3,4], and the surface temperature [1,8] influence the bubble formation and surface modification processes. The theoretical studies of the interaction between helium and tungsten surface have been carried out using first principles calculations [9], molecular dynamics (MD) simulations [10–16], kinetic Monte Carlo (KMC) models [17] and rate theory (RT) [18]. The helium bubble nucleation and growth processes [10,11], the bubble pressure [12,13] and lifetime [14], the surface pore diameter [18] and morphology modifications [13,17] have been concerned. Experimental observations showed that the dependences of surface morphology on the crystal orientations [3,19–22]. Ohno et al. [21] suggested that the surface feature is associated with the angle between
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the slip plane (1 1 0) and the plane of crystal grains. Wavy structures were observed on the (1 1 0), (1 0 0), and (1 1 1) faces. Yamagiwa et al. [22] suggested that the helium bubble formation would be suppressed for some grain orientations such as the (1 1 0) surface. For these orientations, because the diffusion of helium in depth direction is low, the density of helium near the surface is saturated, and thus, some helium atoms will be released from the surface before they form bubbles. Through MD simulations, Sefta et al. [13] suggested that the surface morphology is associated with the angle between the glide and surface normal directions. They also found the pinhole on tungsten (1 1 0) surface can be self-healed for a while, and the similar phenomena were observed by Gong et al. [23] on nickel (1 1 0) surface. However, there is still a lack of understanding of the formation mechanism for different surface morphologies, especially how factors such as temperature and the ratio of helium to vacancy (He/V) in the bubble influence the selfhealing process. In this article, the growth and release of near-surface helium bubbles in tungsten was investigated by MD simulations. The dynamics of surface morphology evolution during the damage and repair processes was studied. The degree of surface damage and release curve of helium were determined to reveal the formation mechanism of different surface morphologies. These simulations indicate that stepped, thin schistose and pyramidal structures appear for different surface orientations. The
Corresponding author. E-mail address: [email protected] (Y. Ouyang).
https://doi.org/10.1016/j.nimb.2019.06.023 Received 14 August 2018; Received in revised form 20 May 2019; Accepted 17 June 2019 Available online 25 June 2019 0168-583X/ © 2019 Elsevier B.V. All rights reserved.
Nuclear Inst. and Methods in Physics Research B 455 (2019) 66–73
Y. Zhou, et al.
Fig. 1. Side view of the tungsten surface (grey) and helium bubbles (purple) during the bubble growth and release processes for the (1 1 0) surface (He/V = 2:1, T = 1000 K).
Fig. 2. Side view of the tungsten surface (grey) and helium bubbles (purple) during the bubble growth and release processes for the (1 0 0) surface (He/V ratio = 2:1, T = 1000 K).
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Fig. 3. Side view of the tungsten surface (grey) and helium bubbles (purple) during the bubble growth and release processes for the (1 1 1) surface (He/V ratio = 2:1, T = 1000 K).
Fig. 4. Side and top views of the tungsten substrate (grey) and stacking atoms on the surface (color) at t = 350 ps for three different surface orientations (He/V ratio = 2:1, T = 1000 K).
parameters such as the temperature and the ratio of He/V in the bubble influence the size of leaving pore on the (1 1 1) surface.
and W-He interactions, the analytical bond-order potential (BOP) of WH-He system developed by Li et al. [25] was employed. For interactions between helium atoms, we used the pair potential developed by Aziz et al. [26]. The simulation box was a 30a0 × 30a0 × 25a0 bcc supercell, where a0 = 3.165 Å is the lattice constant of tungsten. Periodic boundary conditions were applied in two horizontal directions, while the free surface was in the vertical direction. The (1 1 0), (1 0 0) and
2. Simulation method MD simulations were carried out using the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) [24]. For the W-W 68
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simulation was about 1028 m−2 s−1, while the flux expected at the ITER divertor is 1022–1024 m−2 s−1. It has been tested that 1 ps is long enough to ensure that the system equilibrium is reached. It is believed that the simulation can provide qualitative insight into the mechanisms of bubble growth, release and self-healing. 3. Results and discussion 3.1. Helium bubble growth and release for different surface orientations Simulations were performed for three surfaces at 1000 K with He/V ratio in the bubble equals to 2:1. Figs. 1-3 show the dynamics processes for the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. The size of helium atoms has been enlarged for apparent illustration. For the (1 1 0) surface (Fig. 1), the evolution process can be divided into three stages. Firstly, the bubble pressure increases as helium atoms trapped by the bubble, until the critical point that one layer of substrate atoms drift to the surface along the 〈1 1 1〉 direction (t = 176 ps). Since the high pressure of bubble can be released effectively by emitting 〈1 1 1〉 interstitial dislocation loops to the surface, the substrate crystal around the bubble appear to be nearly perfect. Secondly, when several tungsten layers are stacked on the surface, some helium atoms release to vacuum rapidly as the bubble boundary emerges to the top surface, accompanying by some atoms ejected from the substrate (t = 244 ps). Finally, most of the helium atoms are released, leaving a hole in the surface. The stacking tungsten atoms on the surface rearrange into a bcc-like structure (t = 350 ps). For the (1 0 0) surface (Fig. 2), the bubble pressure can also be released by emitting 〈1 1 1〉 surface defects, but many 〈1 1 1〉 crowdion interstitials still stay in the substrate. Most defects accumulate towards the surface direction because the formation energy of 〈1 1 1〉 crowdion interstitial near surface is smaller than that in the bulk [27,28]. The different phenomena for these two surfaces should be attributed to the mechanism proposed by Sefta et al. [13]. The angle between the 〈1 1 1〉 and 〈1 0 0〉 directions (54.8°) is larger than that between the 〈1 1 1〉 and 〈1 1 0〉 directions (35.4°), therefore,
Fig. 5. The percentage of released helium as a function of evolution time for three different surface orientations (He/V ratio = 2:1, T = 1000 K).
(1 1 1) surfaces were constructed. The two layers of tungsten atoms in the bottom of supercell were fixed to avoid net drift of the simulation cell. The near-surface helium bubble was introduced by removing the tungsten atoms within a spherical of radius R = 3a0, and then filled with helium atoms which were arranged in a bcc lattice. The initial ratio of He/V in the bubble was set as 2:1 or 4:1. The initial central position of the helium bubble was set beneath the surface with the height h = 6a0. Another method that is more similar to the real physical process, is starting from a small cluster and adding helium atoms one by one, but it is too time-consuming for constructing a nanometer-scale bubble. In order to emulate the bubble growth during ion irradiation, one helium atom was inserted into the bubble every 1 ps. The time step was set as 0.1 fs, and the whole evolution time was 350 ps. The simulations were carried out under temperatures of T = 1000 K and 2000 K, respectively. It should be noted that the corresponding flux in our
Fig. 6. Top view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 2:1, T = 1000 K). The surface pore is outlined by dashed lines (blue ellipse). 69
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According to the mechanism that bubble pressure relief through ejecting surface defects along the 〈1 1 1〉 direction, the flat surface structure would be formed when the angle between the surface normal and the 〈1 1 1〉 directions is large [13]. Just as in the experiment, pyramidal, wavy, terraced and smooth structures were observed. However, for the surfaces with the same orientation, different morphologies may be observed. For example, Ohno et al. [21] observed wavy structures forming at (1 0 0) surface while Parish et al. [20] observed pyramidal growth. It should be noted that the implantation factors such as temperature, ion energy and flux can influence the formation of bubbles, and thus the surface morphology, which have not been discussed here. Once the release channel was open, the (1 1 0) and (1 0 0) surfaces were torn and crack structures formed almost instantaneously, while a smaller pinhole formed on the (1 1 1) surface. The surface damage and the helium release curve are displayed in Figs. 4–5. The slope of the line in Fig. 5 represents the helium release rate at the moment. Although the bubble bursting time is stochastic, similar release mechanism and appearance are found for the same initial conditions. Since the stacking height is the greatest before bubble bursts, the (1 1 1) surface undergoes a relatively gentle release process, as shown in Fig. 5. One may notice that many helium atoms still stay beneath the (1 1 1) surface at the end of the simulation. The first bubble bursting occurs at t = 224 ps and becomes gentle after t = 250 ps. Experimental work showed that blister density is the greatest on the grain orientation near (1 1 1) plane, and the smallest on the grain orientation near (1 0 0) plane [19]. The atom binding energy in the crystal plane and the channeling effect of adjacent crystal planes are considered to be responsible for the morphological differences during bubble formation. We infer that another factor, the bursting difficulty determined by the surface stacking height, can also affect the bubble density under the surface. As shown in Fig. 4, the surface stacking atoms have a tendency to rearrange into the bcc structure. However, for the (1 1 0) and (1 0 0) surface, unrepaired wide cracks remain on the surfaces since some substrate atoms are ejected too far away from the cracks to recover. For the (1 1 1) surface, with the decline of bubble pressure after the first
Fig. 7. The surface pore size as a function of evolution time for the (1 1 1) surface (He/V ratio = 2:1, T = 1000 K).
the transmit path for a successful complete sliding event would be longer for the (1 0 0) surface. But the stacking atoms are more diffuse and tend to form only a single layer on the (1 0 0) surface in simulations carried out by Sefta et al. [13]. This mechanism could also be applied to explain the surface morphology before the bubble bursts for the (1 1 1) surface as shown in Fig. 3. Since the surface normal direction is parallel to the 〈1 1 1〉 direction, the tungsten atoms on the bubble top are pushed out and form a pyramid-like structure in which atoms still tend to arrange themselves into a bcc lattice. The structure of stacking atoms can be observed more obviously in Fig. 10 (T = 2000 K) at t = 112 ps. Before bubble rupture occurs, stepped, thin schistose and pyramidal structures are observed on the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. Contrary to the stacking area, the stacking height is the greatest for the (1 1 1) surface, and the smallest for the (1 0 0) surface.
Fig. 8. Top view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 2:1, T = 2000 K). The surface pore is outlined by dashed lines (blue ellipse). 70
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first bursting process lasts several picoseconds, then the surface pore is partially recovered at t = 228 ps. The helium release rate becomes very small after t = 250 ps, although there are still many helium atoms stay inside the bubble. The release channel keeps open but the bubble pressure is not larger enough to trigger the second bursts. In the following evolution, single helium atom escapes from the surface pinhole occasionally. The release and implantation of helium keep almost the same rates, and the surface morphology becomes stable. At temperature of 2000 K, the bubble burst starts earlier (t = 124 ps), as shown in Figs. 8–9. As the bubble pressure is increased at high temperature, the release process becomes more violent, and leads to a larger surface pore. It can be observed in Fig. 10 that the maximum diameter of the pore (t = 127 ps) is almost equal to the initial bubble diameter. During the recovery procedure, the stacking atoms with high kinetic energy can migrate to close the pore from the outer layer to the inner layer (Fig. 10), and make the surface restore to a bcclike structure. At last, a thin circle plate with bcc structure leaves on the surface with height of 5.7 Å, a slight smaller than the height (6.4 Å) for T = 1000 K. The self-healing phenomenon of surface defects has been observed in experiment. Takamura et al. [29] found that tungsten fuzz could be thermally annealed and recovered at elevated temperatures. Johnson et al. [30] observed that the copper surface healed to leave a region almost free of defects after helium bubble bursts. Sefta et al. [13] simulated the self-heal of small pinhole during the release process on W (1 1 0) surface. Here we found some large pore on the (1 1 1) surface produced by violent release process can also be self-healed when the temperature is high enough. When the He/V ratio of the bubble increases to 4:1, a large hole (occasionally two holes at t = 1.75 ps) forms during the bursting process, and shows no recovery in the following evolution, as shown in Figs. 11–12. Ito et al. [12] predicted that the pressure and the He/V
Fig. 9. The surface pore size as a function of evolution time for the (1 1 1) surface (He/V ratio = 2:1, T = 2000 K).
burst, the small surface pore can be partially recovered. In the next part, we will discuss the effect of temperature and He/V ratio in the bubble on the (1 1 1) surface pore healing process. 3.2. Effects of temperature and He/V ratio on the (1 1 1) surface pore As shown in Figs. 3 and 5, for (1 1 1) surface at 1000 K with He/V ratio equals to 2:1, the first bubble bursting starts at t = 224 ps. The morphology and size of the surface pore are displayed in Figs. 6–7. The
Fig. 10. Side view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 2:1, T = 2000 K). 71
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Fig. 11. Top view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 4:1, T = 1000 K). The surface pore is outlined by dashed lines (blue ellipse).
4. Conclusions The growth and release of near-surface helium bubbles in tungsten have been investigated by MD simulations. The surface morphology exhibits apparent dependence of crystal orientation. Before the bubble bursts, stepped, thin schistose and pyramidal structures are observed on the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. Since the pressure of the bubble is released through the ejection of surface defects along the 〈1 1 1〉 direction, flat surface structure would be formed as the angle between the surface normal direction and the 〈1 1 1〉 direction is large. When the bubble bursts, crack structures form on the (1 1 0) and (1 0 0) surfaces, while a smaller hole forms on the (1 1 1) surface. The stacking atoms on the surface tend to rearrange into the bcc structure. For the (1 1 1) surface, large pore forms in the bursting process when the temperature or the He/V ratio in the bubble is high. In the subsequent evolution, the surface pore with radius ∼1 nm can be healed completely from outer to inner layers at high temperature, while no recovery is observed in MD time scale when the He/V ratio in the bubble is high. These results can help to elucidate the morphological modifications of tungsten surfaces after helium irradiation.
Fig. 12. The surface pore size as a function of evolution time for (1 1 1) surface (He/V ratio = 4:1, T = 1000 K).
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 11405034, No. 11865004); the Natural Science Foundation of Guangxi Province (No. 2015GXNSFBA139011, No. 2018GXNSFAA281309).
ratio of the helium bubble follow power law relations. The increasing pressure generated by the larger repulsive forces between the helium atoms increases the amount of tungsten ejected and redeposited. At last the surface exhibits pored pyramid structure, with the stacking height of 14.3 Å. We also simulated the effects of temperature and He/V ratio on the (1 1 0) and (1 0 0) surface evolutions. In the bursting process, high temperature or large He/V ratio would lead to a more violent reaction, as well as a larger surface damage. The surface damage can be partially healed at high temperature. But the surface gaps for these two surfaces are still more difficultly to recovery compared to the (1 1 1) surface.
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Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
The growth and release of helium bubbles near tungsten surface studied with molecular dynamics simulations
T
Yulu Zhou, Chiwen Yuan, Tao Li, Xiaoma Tao, Yifang Ouyang
⁎
Guangxi Key Laboratory for Relativistic Astrophysics, College of Physical Science and Technology, Guangxi University, Nanning, Guangxi 530004, China
ARTICLE INFO
ABSTRACT
Keywords: Tungsten Helium bubble Surface morphology Self-healing Molecular dynamics simulations
The growth and release processes of helium bubbles near tungsten surface have been investigated by molecular dynamics (MD) simulations. The results indicate that the surface morphologies are dependent on orientation of surfaces. Before bubble rupture occurs, stepped, thin schistose and pyramidal structures are observed on the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. When the angle between the normal direction of surface and the sliding direction (〈1 1 1〉 direction) is larger, flatter surface would be formed and the subsequent release process would be more violent. In the bursting process, the release rate of helium and the degree of surface damage are correlated with the surface stacking height before bubble bursts. Unrepaired crack structures have been observed on the (1 1 0) and (1 0 0) surfaces, while a smaller hole on the (1 1 1) surface. The stacking atoms have a tendency to make the surface restore to the bcc structure. At high temperature, the surface pore with radius ∼1 nm can be self-healed from outer to inner by the diffusion of surface atoms, while no recovery is observed in MD time scale when the ratio of He/V in the bubble is high.
1. Introduction Tungsten is considered one of the best options as a plasma-facingmaterial (PFM) for the diverter in the International Thermonuclear Experimental Reactor (ITER) because of its high temperature capabilities and good sputtering erosion resistance. Experimental work has shown that the bombardment of high-flux helium plasma results in the formation of bubbles in tungsten, this may induce morphological modifications of tungsten surfaces (e.g., pores [1–3], nano-fuzzes [4,5]). Many researchers have performed experimental studies to investigate the factors such as the starting structure of tungsten [4,6], helium ion energy [7], helium flux [3,4], and the surface temperature [1,8] influence the bubble formation and surface modification processes. The theoretical studies of the interaction between helium and tungsten surface have been carried out using first principles calculations [9], molecular dynamics (MD) simulations [10–16], kinetic Monte Carlo (KMC) models [17] and rate theory (RT) [18]. The helium bubble nucleation and growth processes [10,11], the bubble pressure [12,13] and lifetime [14], the surface pore diameter [18] and morphology modifications [13,17] have been concerned. Experimental observations showed that the dependences of surface morphology on the crystal orientations [3,19–22]. Ohno et al. [21] suggested that the surface feature is associated with the angle between
⁎
the slip plane (1 1 0) and the plane of crystal grains. Wavy structures were observed on the (1 1 0), (1 0 0), and (1 1 1) faces. Yamagiwa et al. [22] suggested that the helium bubble formation would be suppressed for some grain orientations such as the (1 1 0) surface. For these orientations, because the diffusion of helium in depth direction is low, the density of helium near the surface is saturated, and thus, some helium atoms will be released from the surface before they form bubbles. Through MD simulations, Sefta et al. [13] suggested that the surface morphology is associated with the angle between the glide and surface normal directions. They also found the pinhole on tungsten (1 1 0) surface can be self-healed for a while, and the similar phenomena were observed by Gong et al. [23] on nickel (1 1 0) surface. However, there is still a lack of understanding of the formation mechanism for different surface morphologies, especially how factors such as temperature and the ratio of helium to vacancy (He/V) in the bubble influence the selfhealing process. In this article, the growth and release of near-surface helium bubbles in tungsten was investigated by MD simulations. The dynamics of surface morphology evolution during the damage and repair processes was studied. The degree of surface damage and release curve of helium were determined to reveal the formation mechanism of different surface morphologies. These simulations indicate that stepped, thin schistose and pyramidal structures appear for different surface orientations. The
Corresponding author. E-mail address: [email protected] (Y. Ouyang).
https://doi.org/10.1016/j.nimb.2019.06.023 Received 14 August 2018; Received in revised form 20 May 2019; Accepted 17 June 2019 Available online 25 June 2019 0168-583X/ © 2019 Elsevier B.V. All rights reserved.
Nuclear Inst. and Methods in Physics Research B 455 (2019) 66–73
Y. Zhou, et al.
Fig. 1. Side view of the tungsten surface (grey) and helium bubbles (purple) during the bubble growth and release processes for the (1 1 0) surface (He/V = 2:1, T = 1000 K).
Fig. 2. Side view of the tungsten surface (grey) and helium bubbles (purple) during the bubble growth and release processes for the (1 0 0) surface (He/V ratio = 2:1, T = 1000 K).
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Fig. 3. Side view of the tungsten surface (grey) and helium bubbles (purple) during the bubble growth and release processes for the (1 1 1) surface (He/V ratio = 2:1, T = 1000 K).
Fig. 4. Side and top views of the tungsten substrate (grey) and stacking atoms on the surface (color) at t = 350 ps for three different surface orientations (He/V ratio = 2:1, T = 1000 K).
parameters such as the temperature and the ratio of He/V in the bubble influence the size of leaving pore on the (1 1 1) surface.
and W-He interactions, the analytical bond-order potential (BOP) of WH-He system developed by Li et al. [25] was employed. For interactions between helium atoms, we used the pair potential developed by Aziz et al. [26]. The simulation box was a 30a0 × 30a0 × 25a0 bcc supercell, where a0 = 3.165 Å is the lattice constant of tungsten. Periodic boundary conditions were applied in two horizontal directions, while the free surface was in the vertical direction. The (1 1 0), (1 0 0) and
2. Simulation method MD simulations were carried out using the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) [24]. For the W-W 68
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simulation was about 1028 m−2 s−1, while the flux expected at the ITER divertor is 1022–1024 m−2 s−1. It has been tested that 1 ps is long enough to ensure that the system equilibrium is reached. It is believed that the simulation can provide qualitative insight into the mechanisms of bubble growth, release and self-healing. 3. Results and discussion 3.1. Helium bubble growth and release for different surface orientations Simulations were performed for three surfaces at 1000 K with He/V ratio in the bubble equals to 2:1. Figs. 1-3 show the dynamics processes for the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. The size of helium atoms has been enlarged for apparent illustration. For the (1 1 0) surface (Fig. 1), the evolution process can be divided into three stages. Firstly, the bubble pressure increases as helium atoms trapped by the bubble, until the critical point that one layer of substrate atoms drift to the surface along the 〈1 1 1〉 direction (t = 176 ps). Since the high pressure of bubble can be released effectively by emitting 〈1 1 1〉 interstitial dislocation loops to the surface, the substrate crystal around the bubble appear to be nearly perfect. Secondly, when several tungsten layers are stacked on the surface, some helium atoms release to vacuum rapidly as the bubble boundary emerges to the top surface, accompanying by some atoms ejected from the substrate (t = 244 ps). Finally, most of the helium atoms are released, leaving a hole in the surface. The stacking tungsten atoms on the surface rearrange into a bcc-like structure (t = 350 ps). For the (1 0 0) surface (Fig. 2), the bubble pressure can also be released by emitting 〈1 1 1〉 surface defects, but many 〈1 1 1〉 crowdion interstitials still stay in the substrate. Most defects accumulate towards the surface direction because the formation energy of 〈1 1 1〉 crowdion interstitial near surface is smaller than that in the bulk [27,28]. The different phenomena for these two surfaces should be attributed to the mechanism proposed by Sefta et al. [13]. The angle between the 〈1 1 1〉 and 〈1 0 0〉 directions (54.8°) is larger than that between the 〈1 1 1〉 and 〈1 1 0〉 directions (35.4°), therefore,
Fig. 5. The percentage of released helium as a function of evolution time for three different surface orientations (He/V ratio = 2:1, T = 1000 K).
(1 1 1) surfaces were constructed. The two layers of tungsten atoms in the bottom of supercell were fixed to avoid net drift of the simulation cell. The near-surface helium bubble was introduced by removing the tungsten atoms within a spherical of radius R = 3a0, and then filled with helium atoms which were arranged in a bcc lattice. The initial ratio of He/V in the bubble was set as 2:1 or 4:1. The initial central position of the helium bubble was set beneath the surface with the height h = 6a0. Another method that is more similar to the real physical process, is starting from a small cluster and adding helium atoms one by one, but it is too time-consuming for constructing a nanometer-scale bubble. In order to emulate the bubble growth during ion irradiation, one helium atom was inserted into the bubble every 1 ps. The time step was set as 0.1 fs, and the whole evolution time was 350 ps. The simulations were carried out under temperatures of T = 1000 K and 2000 K, respectively. It should be noted that the corresponding flux in our
Fig. 6. Top view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 2:1, T = 1000 K). The surface pore is outlined by dashed lines (blue ellipse). 69
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According to the mechanism that bubble pressure relief through ejecting surface defects along the 〈1 1 1〉 direction, the flat surface structure would be formed when the angle between the surface normal and the 〈1 1 1〉 directions is large [13]. Just as in the experiment, pyramidal, wavy, terraced and smooth structures were observed. However, for the surfaces with the same orientation, different morphologies may be observed. For example, Ohno et al. [21] observed wavy structures forming at (1 0 0) surface while Parish et al. [20] observed pyramidal growth. It should be noted that the implantation factors such as temperature, ion energy and flux can influence the formation of bubbles, and thus the surface morphology, which have not been discussed here. Once the release channel was open, the (1 1 0) and (1 0 0) surfaces were torn and crack structures formed almost instantaneously, while a smaller pinhole formed on the (1 1 1) surface. The surface damage and the helium release curve are displayed in Figs. 4–5. The slope of the line in Fig. 5 represents the helium release rate at the moment. Although the bubble bursting time is stochastic, similar release mechanism and appearance are found for the same initial conditions. Since the stacking height is the greatest before bubble bursts, the (1 1 1) surface undergoes a relatively gentle release process, as shown in Fig. 5. One may notice that many helium atoms still stay beneath the (1 1 1) surface at the end of the simulation. The first bubble bursting occurs at t = 224 ps and becomes gentle after t = 250 ps. Experimental work showed that blister density is the greatest on the grain orientation near (1 1 1) plane, and the smallest on the grain orientation near (1 0 0) plane [19]. The atom binding energy in the crystal plane and the channeling effect of adjacent crystal planes are considered to be responsible for the morphological differences during bubble formation. We infer that another factor, the bursting difficulty determined by the surface stacking height, can also affect the bubble density under the surface. As shown in Fig. 4, the surface stacking atoms have a tendency to rearrange into the bcc structure. However, for the (1 1 0) and (1 0 0) surface, unrepaired wide cracks remain on the surfaces since some substrate atoms are ejected too far away from the cracks to recover. For the (1 1 1) surface, with the decline of bubble pressure after the first
Fig. 7. The surface pore size as a function of evolution time for the (1 1 1) surface (He/V ratio = 2:1, T = 1000 K).
the transmit path for a successful complete sliding event would be longer for the (1 0 0) surface. But the stacking atoms are more diffuse and tend to form only a single layer on the (1 0 0) surface in simulations carried out by Sefta et al. [13]. This mechanism could also be applied to explain the surface morphology before the bubble bursts for the (1 1 1) surface as shown in Fig. 3. Since the surface normal direction is parallel to the 〈1 1 1〉 direction, the tungsten atoms on the bubble top are pushed out and form a pyramid-like structure in which atoms still tend to arrange themselves into a bcc lattice. The structure of stacking atoms can be observed more obviously in Fig. 10 (T = 2000 K) at t = 112 ps. Before bubble rupture occurs, stepped, thin schistose and pyramidal structures are observed on the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. Contrary to the stacking area, the stacking height is the greatest for the (1 1 1) surface, and the smallest for the (1 0 0) surface.
Fig. 8. Top view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 2:1, T = 2000 K). The surface pore is outlined by dashed lines (blue ellipse). 70
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first bursting process lasts several picoseconds, then the surface pore is partially recovered at t = 228 ps. The helium release rate becomes very small after t = 250 ps, although there are still many helium atoms stay inside the bubble. The release channel keeps open but the bubble pressure is not larger enough to trigger the second bursts. In the following evolution, single helium atom escapes from the surface pinhole occasionally. The release and implantation of helium keep almost the same rates, and the surface morphology becomes stable. At temperature of 2000 K, the bubble burst starts earlier (t = 124 ps), as shown in Figs. 8–9. As the bubble pressure is increased at high temperature, the release process becomes more violent, and leads to a larger surface pore. It can be observed in Fig. 10 that the maximum diameter of the pore (t = 127 ps) is almost equal to the initial bubble diameter. During the recovery procedure, the stacking atoms with high kinetic energy can migrate to close the pore from the outer layer to the inner layer (Fig. 10), and make the surface restore to a bcclike structure. At last, a thin circle plate with bcc structure leaves on the surface with height of 5.7 Å, a slight smaller than the height (6.4 Å) for T = 1000 K. The self-healing phenomenon of surface defects has been observed in experiment. Takamura et al. [29] found that tungsten fuzz could be thermally annealed and recovered at elevated temperatures. Johnson et al. [30] observed that the copper surface healed to leave a region almost free of defects after helium bubble bursts. Sefta et al. [13] simulated the self-heal of small pinhole during the release process on W (1 1 0) surface. Here we found some large pore on the (1 1 1) surface produced by violent release process can also be self-healed when the temperature is high enough. When the He/V ratio of the bubble increases to 4:1, a large hole (occasionally two holes at t = 1.75 ps) forms during the bursting process, and shows no recovery in the following evolution, as shown in Figs. 11–12. Ito et al. [12] predicted that the pressure and the He/V
Fig. 9. The surface pore size as a function of evolution time for the (1 1 1) surface (He/V ratio = 2:1, T = 2000 K).
burst, the small surface pore can be partially recovered. In the next part, we will discuss the effect of temperature and He/V ratio in the bubble on the (1 1 1) surface pore healing process. 3.2. Effects of temperature and He/V ratio on the (1 1 1) surface pore As shown in Figs. 3 and 5, for (1 1 1) surface at 1000 K with He/V ratio equals to 2:1, the first bubble bursting starts at t = 224 ps. The morphology and size of the surface pore are displayed in Figs. 6–7. The
Fig. 10. Side view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 2:1, T = 2000 K). 71
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Fig. 11. Top view of the tungsten substrate (grey) and stacking atoms on the surface (color) for the (1 1 1) surface (He/V ratio = 4:1, T = 1000 K). The surface pore is outlined by dashed lines (blue ellipse).
4. Conclusions The growth and release of near-surface helium bubbles in tungsten have been investigated by MD simulations. The surface morphology exhibits apparent dependence of crystal orientation. Before the bubble bursts, stepped, thin schistose and pyramidal structures are observed on the (1 1 0), (1 0 0) and (1 1 1) surfaces, respectively. Since the pressure of the bubble is released through the ejection of surface defects along the 〈1 1 1〉 direction, flat surface structure would be formed as the angle between the surface normal direction and the 〈1 1 1〉 direction is large. When the bubble bursts, crack structures form on the (1 1 0) and (1 0 0) surfaces, while a smaller hole forms on the (1 1 1) surface. The stacking atoms on the surface tend to rearrange into the bcc structure. For the (1 1 1) surface, large pore forms in the bursting process when the temperature or the He/V ratio in the bubble is high. In the subsequent evolution, the surface pore with radius ∼1 nm can be healed completely from outer to inner layers at high temperature, while no recovery is observed in MD time scale when the He/V ratio in the bubble is high. These results can help to elucidate the morphological modifications of tungsten surfaces after helium irradiation.
Fig. 12. The surface pore size as a function of evolution time for (1 1 1) surface (He/V ratio = 4:1, T = 1000 K).
Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 11405034, No. 11865004); the Natural Science Foundation of Guangxi Province (No. 2015GXNSFBA139011, No. 2018GXNSFAA281309).
ratio of the helium bubble follow power law relations. The increasing pressure generated by the larger repulsive forces between the helium atoms increases the amount of tungsten ejected and redeposited. At last the surface exhibits pored pyramid structure, with the stacking height of 14.3 Å. We also simulated the effects of temperature and He/V ratio on the (1 1 0) and (1 0 0) surface evolutions. In the bursting process, high temperature or large He/V ratio would lead to a more violent reaction, as well as a larger surface damage. The surface damage can be partially healed at high temperature. But the surface gaps for these two surfaces are still more difficultly to recovery compared to the (1 1 1) surface.
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