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Molecular dynamics simulations of helium clustering and bubble growth under tungsten surfaces
Computational Materials Science 163 (2019) 141–147
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Molecular dynamics simulations of helium clustering and bubble growth under tungsten surfaces
T
Ali Y. Hamida, Jizhong Suna, , Hongyu Zhanga, Arvind S. Jadona, Thomas Stirnerb ⁎
a b
Key Laboratory of Materials Modification (Ministry of Education), School of Physics, Dalian University of Technology, Dalian 116024, China Department of Applied Natural Science, University of Applied Sciences Deggendorf, Dieter-Görlitz-Platz-1, D-94469 Deggendorf, Germany
ARTICLE INFO
ABSTRACT
Keywords: Molecular dynamics Helium bubbles Tungsten surface Plasma-facing material Nuclear fusion
We study the surface response of W{0 0 1} to helium bombardment using molecular dynamics simulations. Simulations have been performed for incident helium of energy 80 eV and surface temperature 2100 K. The saturation of He retention has been observed to be high, a result of the bubbles trapping helium atoms and preventing them from diffusing to the surface and further back into the plasma. On the other hand, we have observe near-surface “cluster rupture” leading to the expulsion of helium atoms towards the vacuum. We have found that bubbles typically grow in a relatively narrow band of He/V ratios (1–3). Besides, it was observed that tungsten atoms migrated from the top surface into the bulk. The coalescence of helium bubbles has also been observed.
1. Introduction Tungsten (W) has been used as plasma facing material (PFM) in nuclear fusion devices [1], owing to its excellent thermomechanical properties [2–5]. A main potential impediment to successful operation of a tungsten divertor is the surface erosion due to the helium exposure and how helium retention might influence the tritium inventory trapped in the divertor. Many researchers have investigated the interactions of helium with tungsten surface for generating important changes in the tungsten surface morphology for different operating conditions, even for energies under the threshold of physical sputtering. The threshold of tungsten is above 100 eV, the ranging (200–300 eV) [6]. At low temperatures (below 900 K) and energy in the range of 0–100 eV, a non-specific damage pattern forms [7–9], leading to probably raised erosion or sputtering, but no specific formation of microstructure. At temperatures above 2000 K, helium seems to create bubbles that burst across the surface which leave holes of the order of 0.1–1 μm in diameter [10]. At low energy (<100 eV) under 2000 k helium species bombardment gives rise to nucleation and growth of helium bubbles and surface modification by forming microscopic features (known as ‘fuzz’) for different plasma devices, such as linear plasma devices [11–15], tokamak plasmas [16,17] and magnetron sputtering devices [18]. This fuzz formation takes place for pure helium-plasmas and deuterium-helium mixing plasmas [14,19], but has not been detected for pure deuterium-plasmas. It reduces near-surface thermal
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conductivity [11] and optical reflectivity [20], and might cause issues for device lifetime and related concerns in the fusion devices. Researchers have invested significant efforts to study the mechanism of fuzz formation in helium-plasma-facing tungsten by performing atomistic simulations of helium interaction with tungsten in recent years. These comprise studies of the growth of over-pressurized bubbles in both tungsten [21–24] and titanium [25]; effects of subsurface bubbles on sputtering yields [26,27]; He interactions with surfaces and grain boundaries [28–30]; He bubble formation and growth, both in the bulk [31–34] and near surfaces [35]; and direct or indirect implantation of He species on tungsten surface to observe its dynamics and others effects [21,36–39]. This growing body of work has proposed that the initial stages of fuzz formation are owing to helium bubble formation and also the subsequent stress and strain related to growing bubbles, with surface features growing by ejection of dislocation loops and/or individual Frenkel pairs that form adatoms. Presence of helium bubbles below the surface does not strongly affect the sputtering yield [26,27], although experimental studies have shown that sputtering is reduced due to the presence of fuzz relative to fuzz-free surfaces [40]. Although many experiments have been performed to analyze the effects of W and He interactions, there are only a few simulation studies which discussing bubble growth with helium/vacancy ratios. Considering the prevalent view that the formation and growth of nanostructures are strongly related to helium bubbles, we focus on the understanding of bubble
Corresponding author. E-mail address: [email protected] (J. Sun).
https://doi.org/10.1016/j.commatsci.2019.03.008 Received 26 September 2018; Received in revised form 22 January 2019; Accepted 2 March 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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growth and their effect on fuzz formation in tungsten surfaces. In the present study, molecular dynamics (MD) simulations have been performed to analyze the bubble growth and fuzz formation for incident energy 80 eV, temperature 2100 K and high flux of He on W. We have to mention that the temperature chosen here is slightly out off the temperature range for commonly recognized finding fuzz [15]. We have calculated the helium atoms for each metal vacancy (He/V) to describe the dynamics of bubbles near the surface and in the depth of the material. Simulations have been performed for an adequately long time to get a proper insight into the above-mentioned phenomena and saturation state. The simulation results demonstrate a better estimate from a statistical point of view of helium retention, the bubble formation and growth, and cluster size distributions, etc. 2. Simulation methods MD simulations of surface evolution owing to helium bombardment on tungsten are performed using LAMMPS [41]. We have utilized an EAM (embedded atom method) potential developed by Bonny for large scale atomistic simulations in the ternary W-H-He system [42]. The size of tungsten sample with body center cubic (bcc) structure is approximately 63.56 Å × 63.56 Å × 95.34 Å consisting of 24,400 atoms, the lattice parameter is 3.178 Å at temperature 2100 k. First, the simulation has been initialized using a Gaussian velocity distribution at the required temperature 2100 K and thermal equilibrium is achieved around 20 ps under the rescaling thermostat. Secondly, the cell is bombarded during an accumulative pattern with the incident direction normal to the (0 0 1) surface after turned off the temperature rescaling. Each helium atom is chosen randomly over the entire x-y plane, while the z-coordinate is taken at a distance larger than the maximum interaction range of the potential above the surface. Periodic boundary conditions have been applied on the lateral four faces (x and y directions) of the simulation cell, while the top and bottom faces in the z-direction are non-periodic. This means the atom is not allowed to move from one side to another side of the box in zdirection. If this happens, the atom will be removed from the simulation domain. The bottom two layers (z direction) of the simulation domain are kept fixed throughout the simulation to avoid mesh drift of the atoms in the vertical direction owing to the escape of helium atoms. During the bombardment, the temperature is controlled on the two layers of the tungsten atoms above the two fixed bottom layers and one layer on lateral sides of tungsten bulk using a Berendsen thermostat. To carry out the proposed study, incident flux and energy are 1.05 × 10 28 m 2s 1 and 80 eV, respectively, and the time step is chosen 0.4 fs. This time step has been checked for it is appropriateness, and the total simulation time is 72 ns.
Fig. 1. Surface evolution of a W(001) surface under flux of 1.058 × 10 28 m 2 s 1 for different times. Left column: 12 ns; right column: 48 ns. Up row: simulation cell; middle row: side view; bottom row: cluster size (number of He atoms) vs. Depth. Tungsten atoms above the surface are green, and those below blue. Helium atoms highlighted in red. The number of bubbles which has the same cluster size is indicated by color. Bubbles that form far away from the surface are marked with an oval circle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
by estimating the number of He atoms in one cluster. As the incident fluence increases, surface growth also increases (Figs. 1(a(i)), (a(ii)), 2(a(iii)) and (a(iv))). This happens due to the formation of interstitial tungsten atoms (loop-punching) during the formation of the helium clusters. The rate of such loop-punching is strongly dependent on the rate at which helium atoms arrive at the bubble [46]. These W atoms are constrained around the helium cluster for a long time, leading to movement of these atoms onto the upper surface along the 1 1 1 directions, which ends in stacking the W atoms on the surface. Thus, complicated combinational effects of the helium clusters and interstitial atoms lead to the growth of the surfaces. The growth made in these figures are 8.5, 12.5, 21, 15.5 Å, respectively, in the normal direction to the surface. More details about surface growth as a function of helium fluence can be read in Ref. [38,39]. Fig. 2(a(iii)) shows near-surface events like bubbles-coalescence that could be involved in the early stages of fuzz. Figs. 1(b(i)), (b(ii)), 2(b(iii)) and (b(iv)) show the bubbles with tungsten atoms; the regions of bubbles are highlighted in red. It can be seen from Figs. 1(b(i-ii)), 2(b(iii-iv)) that as the time advances, helium atoms move inside the W surface and dislocate some W atoms which results in movement of these dislocated atoms above the surface. Bubbles form close to each other but not close enough to truly merge with-other bubbles but in several cases, a mix-Burgers-vector dislocation [21] accompanies such a cluster of bubbles as manifested in Fig. 1(b(ii)) (such as dislocation type 1/2 1 1 1 ). Expectedly, we can see a large number of growing bubbles close to the surface. Around 72 ns,
3. Results and discussion 3.1. Bubble evolution on (0 0 1) surface As previous studies indicate [43,44] that surface orientation plays very important role in the depth distribution related to helium plasma exposure. The mean depth at which helium “slows down” to thermal velocities may be a function of surface orientation, such as {1 1 1} surface orientation has the deepest depth distribution. The influence of surface orientation is not restricted to the initial depth distribution. However, it is important to explore what should be the preferred crystal orientation, in a polycrystalline sample. Surface tension of {0 0 1} and {1 1 1} surfaces have been found higher than other surfaces, according to the calculations of Wang and co-researchers [45]. As a first step in determining the number of helium atoms in every cluster bubble, we assign helium atoms to clusters-groups, as long as the separation between any He atoms short of distance rHe = 2 Å with each other, they belong to the same cluster (slightly greater than the half separation between the nearest neighbours of W-W atoms). Now, the cluster size is calculated 142
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Fig. 2. Surface evolution of a W(001) surface under flux of 1.058 × 10 28 m 2s 1 for different times. Left column: 66.6 ns; right column: 72 ns. Up row: simulation cell; middle row: side view; bottom row: cluster size (number of He atoms) vs. Depth. Tungsten atoms above the surface are green, those below blue. Helium atoms highlighted in red. The number of bubbles which has the same cluster size is indicated by color. Bubbles that form far away from the surface are marked with an oval shape. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
helium atoms approach to saturation in terms of implantation, as shown in Fig. 2(biv)). When helium atoms form a cluster, which becomes a trap site for other helium atoms, the diffusion of these helium atoms slowed-down greatly. Clusters form at different depths but the growth is slow below depth of 7 nm. Figs. 1(c(i)), 1(c(ii)), 2(c(iii)) and (c(iv)) show the helium cluster size distribution as a function of depth; the number of clusters of a different size is indicated by different colors. As the time advances, the cluster size increases in the depth up to 6 nm; due to adhesion, fewer clusters exist in depth 7 nm, as shown in oval circles (Figs. 1(c(i-ii)), 2(c(iii-iv))). The bubbles show little or no growth deeper than 8 nm below the original surface. It should be noted that the largest bubble in Fig. 2(c(iii)) was grown through one of the growth processes, namely the coalescence of three non-synchronized bubbles. The largest bubble and its neighbor bubble in the red oval circle in Fig. 2(c(iii)) further merged into a larger bubble in the red oval circle as shown in Fig. 2(c(iv)). There are two clusters highlighted by a red circle in Fig. 2 (c(iii)), but there is only one larger cluster in a red circle in Fig. 2 (c(iv)). The size of the large cluster in Fig. 2 (c(iv)) is the sum of the two small clusters in Fig. 2 (c(iii)). It indicates that the two small clusters have merged and formed the larger cluster during 66.6 and 69.9 ns. This conclusion was in fact confirmed by monitoring their evolution in the simulation. When the two neighbouring helium clusters met together, the interstitial defects diffused away, leading to release the pressure
Fig. 3. Side view of the W atoms with coordination number (Ncor ). Snapshots were all obtained at different times. (a) at t = 60 ns; (b) at t = 62.4 ns; (c) at t = 66.6 ns; (d) at t = 69.6 ns. Red balls: He atoms; green balls: W atoms with Ncor 9 ; gray dots: W atoms with Ncor 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
inside the helium bubbles and which promoted the coalescence of helium bubbles (Fig. 2 (c(iv))). A movie of the simulation cell evolution under He implantation is provided as supplementary material. 143
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Fig. 5. Number of W atoms around each bubble. (i) represented fig.3(a); (ii) represented fig.3(b).
Fig. 4. Number of W atoms with Ncor function of He fluence.
method has been used to calculate the vacancy number per cluster: First, we determined the cluster size by using the method described in Section 3.1. To determine the number of vacancies: we transfer all He atoms to the lattice of W atoms in the initial simulation cell (perfect lattice without damage from He bombardment) by assuming that any atom does not occupy any space. If any He atom distances itself from the nearest W atom shorter than rV (rV = 1.05Å, greater than any thermal fluctuation displacement) it is deleted from the lattice. These He atoms are assembled into clusters if their distance shorter than rB = 2 Å . The vacancy number is determined by subtracting the size of this newly created cluster from the previously calculated cluster size. The cutoff distances rHe and rB are kept equal which will ensure that bubbles would be much more easily to be specified continually. Sometimes, the algorithm can produce an error by estimating two helium clusters as a single bubble. We have check it, and fixed it in the simulation. Size of bubbles increases with increasing the number of vacancy for different He/V = (1 9) ratios, as shown in Fig. 6 (a). Here, the vacancy number is not dependent on the time. The bubbles, which are on shallower depth, grow rapidly, and the He/V ratios lie between 2 and 3 for them (as shown in Fig. 6 (b)) as compared with the bubbles located deeper below the surface (black line indicates deepest bubble). During the bubble growth, the ratio He/V is not constant, oscillating between 2 and 3 showing the bubble releases and receives He atoms. Fig. 6 (b) shows growth of bubbles which are near the surface (less than 3 nm below). The bubble size larger, having almost constant growth rate near the surface due to more impacts of He species as compared to the bubbles located at the depth further from the surface. Vacancy number is also more near the surface due to loop-punching. The number of bubbles present in this simulation yield many paths, so we plot all at once as seen in Fig. 6 (c). Hence, Fig. 6 (c) represents bubble growth for overall bubbles below the surface as a function of vacancies for bubbles having >10 He atoms. It can be manifested from Fig. 6(a), (b) and (c) that the He/V ratio for most bubbles lies between 1 and 3. Here, each point represents a bubble with He/V ratio at a particular time for the whole duration of simulation, sampled at a time interval every 2.4 ns. The helium clusters are marked with oval circles as shown in Figs. 1 (c (i-ii)), 2 (c(iii-iv)), which demonstrate the formation and growth along the depth (Fig. 6 (a)). Our findings are different from findings published in Ref [47] for (0 0 1) surface under helium flux of 4 × 10 25 m 2s 1 (ignoring reflections therein). Specifically, we have found very different bubble size profiles than that study. This difference is due to different conditions, for example, the temperature, the potential, etc.
9, pressure of W atoms both as a
3.2. Migration path for self-interstitial-atoms (SIAs) Self-interstitial-atoms (SIAs) can initially remain loosely bound to the cluster or migrate to the surface. In Fig. 3(a,c), a large number of SIAs (highlighted in green) moved toward the surface through helium clusters. Accompanied by the movement, the disordered tungsten atoms around the clusters disappeared (Fig. 3(a,c)) due to the pressure release of helium cluster, and some stacking tungsten atoms that were generated can finally be seen on the top of the surface (Fig. 3(a,c)). Similar results have been reported in Ref [22], in which the bubbles were forced to grow at specific locations, which is not our focus in this paper. We calculated the coordination number (Ncor ) of the tungsten atoms in the substrates shown in Fig. 3(a,c)) and Fig. 4. The coordination number was calculated by defining the bondlength as 2.826 Å for the tungsten crystal. The results are illustrated in Fig. 3(a-d), in which the tungsten atom with is Ncor 9 is represented by a green ball; otherwise, it is represented by a gray dot. In reality, in Figs. 3(b,d), the coordination numbers of most tungsten atoms around helium atoms and clusters are greater than or equal to 9. These Fig. 3(b and d) show the migration of some tungsten atoms from the top surface into the bulk material (Reverse migration). Especially, in Fig. 3(b,d) we can see large clusters of tungsten atoms with Ncor 9, as SIAs were hindered and constrained by helium clusters. Also, Fig. 4 tells us that increase of stress on W atoms around the bubble in Fig. 3(b,d). Once the SIAs moved away from the helium clusters, the clusters of tungsten atoms disappeared as their Ncor became less than or equal to 8 (Fig. 3(a and c)). In the migration path of the SIAs, the coordination numbers of some tungsten atoms may increase, as shown in Fig. 3(b,d). Figs. 3 and 4 show the number of tungsten atoms with Ncor 9 as a function of the helium fluence. When the SIAs were hindered and constrained by the helium clusters (Fig. 3(b) and (d)), the number of tungsten atoms with Ncor 9 was high, fluctuating between 1400 and 1600. Then, with the SIAs moving to and absorbed on the surface, the number of tungsten atoms with Ncor 9 reduced to around 200. Fig. 5 shows the number of tungsten atoms around each bubble. It is clear from Fig. 5(i) that the proportion of tungsten atoms around the bubbles is almost negligible compared to the case in Fig. 5(ii) where the number is approximately six times the number of helium atoms inside the bubble.
3.4. Helium retention The rate of He retention is shown in Fig. 7 as a function of fluence. For initial values of fluence the retention increases until up to 1.5× 10 20m 2 , and subsequently it saturates. Some studies [39] have been carried out to explain the saturation of the helium atom which occurs in absence of the “cluster ruptures”, but is however evidenced for implantation experiments performed at energies below tungsten displacement threshold. Fluence is a strong function of implantation flux
3.3. Bubble growth We also have attempted to trace the size of each single bubble at different depths as a function of vacancy number (likewise the bubble size distributions in Figs. 1(c(i-ii)) and 2(c(iii-iv)). The following 144
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Fig. 7. Rate of helium retention in tungsten (excluding reflection) as a function of fluence. The smaller sudden drops in the curve result from small bubbles bursting.
and therefore the pre-existing tungsten microstructure which causes the formation of the initially immobilized bubbles increases retention through self-trapping. It should be noted the rate of helium retention is the number of helium atoms remaining in the tungsten simulation cell divided by the total number of insertions at a certain point in time as shown in Fig. 7. The lifetime of He bubbles below the surface is concerned, the time point which indicates the starting of He bubble burst from the surface is defined, for-example in Fig. 8. we calculate the volume by the summation of volumes of He atoms that are described by the Voronoi polyhedrons of atoms. When a He atom occurs on above surface, the voronoi polyhedron may fail. During simulation, we compute the symmetric stress tensor [48,49] for each He atom in the cluster, as shown in Fig. 8. The computed stress tensor per atom is actually in units of pressure × volume. In this way we can obtain the negative of total pressure ( P). Around 42 ns, the bursting of small bubble near the surface leads to
Fig. 6. Number of He atoms as a function of the number of vacancies per bubble. (a) Bubbles within 55–80 nm under the original surface (highlightcolored); (b) larger three bubbles in the simulation (colored); (c) Bubbles which contain 10 He atoms or more in the cluster; for the period 0–72 ns. Each point represents a bubble present at a particular instant in time during the simulation, sampled every 2.4 ns for 72 ns; squares correspond to the same bubble at different times. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Bubble pressure of a small bubble moving near the surface as a function of time. Inset shows the surface image at 42.036 ns leading to reduced retention. Tungsten atoms and helium atoms are highlighted in green and red, respectively. 145
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reduced retention as shown in Fig. 7 (one bubble is shown leaving the surface). As the bubbles move toward the surface, bubble pressure decreases as represented in Fig. 8. In our simulations, helium retention increases because of the presence of sub-surface bubbles, which trap He atoms rather than allowing them to diffuse to the surface and back into the plasma. This happens because some helium atoms are far less mobile than those in the bulk as they are bound to the bubbles.
[3] [4] [5] [6]
4. Summary and conclusions
[7]
In the present work, MD simulations have been performed to study the surface response of W {0 0 1} to bombardment of high helium flux of energy 80 eV at temperature 2100 K. Clusters form at different depths but grow slowly below depth of 7 nm, compared with the above. Selfinterstitial-atoms (SIAs) can initially remain loosely bound to the cluster or migrate to the free surface. Tungsten atoms were observed migrating from the top surface into the bulk, SIAs around each bubble become almost six times the number of helium atoms inside each bubble. The saturation of He retention has been observed to be high, a result of the bubbles trapping helium atoms and preventing them from diffusing to the surface and further back into the plasma. On the other hand, we have observed near-surface “cluster rupture” leading to the expulsion of helium atoms towards the vacuum. We also have observed near-surface events of bubbles-coalescence which could be considered involved in the early stages of fuzz. We have found that bubbles typically grow in a relatively narrow band of He/V ratios (1 3) . It has also been observed that the deep-down bubbles release or absorb helium atoms. This study provides data which could be served to understand the behaviour of plasma facing materials at high temperatures. The effects of incident He flux on He cluster sizes will be explored in the future work.
[8]
[9]
[10] [11] [12] [13] [14] [15] [16]
Data availability
[17]
The raw/processed data required to reproduce these findings can be shared if requested.
[18]
CRediT authorship contribution statement
[19]
Ali Y. Hamid: Conceptualization, Methodology, Data curation, Formal analysis, Writing - original draft, Investigation, Writing - review & editing. Jizhong Sun: Conceptualization, Methodology, Formal analysis, Writing - review & editing, Funding acquisition, Project administration. Hongyu Zhang: Data curation, Formal analysis, Visualization. Arvind S. Jadon: Formal analysis, Writing - original draft. Thomas Stirner: Methodology, Writing - review & editing.
[20] [21] [22] [23]
Acknowledgements
[24]
This work is supported by the National Key R&D Program of China under Grant No. 2017YFE0301103 and the National Science Foundation of China under Grant Nos. 11575039 and 51671045. It is also partially supported by the Fundamental Research Funds for the Central Universities (DUT18GF112) and by Supercomputing Center of Dalian University of Technology.
[25] [26] [27]
Appendix A. Supplementary data
[28] [29]
Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.commatsci.2019.03.008.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Molecular dynamics simulations of helium clustering and bubble growth under tungsten surfaces
T
Ali Y. Hamida, Jizhong Suna, , Hongyu Zhanga, Arvind S. Jadona, Thomas Stirnerb ⁎
a b
Key Laboratory of Materials Modification (Ministry of Education), School of Physics, Dalian University of Technology, Dalian 116024, China Department of Applied Natural Science, University of Applied Sciences Deggendorf, Dieter-Görlitz-Platz-1, D-94469 Deggendorf, Germany
ARTICLE INFO
ABSTRACT
Keywords: Molecular dynamics Helium bubbles Tungsten surface Plasma-facing material Nuclear fusion
We study the surface response of W{0 0 1} to helium bombardment using molecular dynamics simulations. Simulations have been performed for incident helium of energy 80 eV and surface temperature 2100 K. The saturation of He retention has been observed to be high, a result of the bubbles trapping helium atoms and preventing them from diffusing to the surface and further back into the plasma. On the other hand, we have observe near-surface “cluster rupture” leading to the expulsion of helium atoms towards the vacuum. We have found that bubbles typically grow in a relatively narrow band of He/V ratios (1–3). Besides, it was observed that tungsten atoms migrated from the top surface into the bulk. The coalescence of helium bubbles has also been observed.
1. Introduction Tungsten (W) has been used as plasma facing material (PFM) in nuclear fusion devices [1], owing to its excellent thermomechanical properties [2–5]. A main potential impediment to successful operation of a tungsten divertor is the surface erosion due to the helium exposure and how helium retention might influence the tritium inventory trapped in the divertor. Many researchers have investigated the interactions of helium with tungsten surface for generating important changes in the tungsten surface morphology for different operating conditions, even for energies under the threshold of physical sputtering. The threshold of tungsten is above 100 eV, the ranging (200–300 eV) [6]. At low temperatures (below 900 K) and energy in the range of 0–100 eV, a non-specific damage pattern forms [7–9], leading to probably raised erosion or sputtering, but no specific formation of microstructure. At temperatures above 2000 K, helium seems to create bubbles that burst across the surface which leave holes of the order of 0.1–1 μm in diameter [10]. At low energy (<100 eV) under 2000 k helium species bombardment gives rise to nucleation and growth of helium bubbles and surface modification by forming microscopic features (known as ‘fuzz’) for different plasma devices, such as linear plasma devices [11–15], tokamak plasmas [16,17] and magnetron sputtering devices [18]. This fuzz formation takes place for pure helium-plasmas and deuterium-helium mixing plasmas [14,19], but has not been detected for pure deuterium-plasmas. It reduces near-surface thermal
⁎
conductivity [11] and optical reflectivity [20], and might cause issues for device lifetime and related concerns in the fusion devices. Researchers have invested significant efforts to study the mechanism of fuzz formation in helium-plasma-facing tungsten by performing atomistic simulations of helium interaction with tungsten in recent years. These comprise studies of the growth of over-pressurized bubbles in both tungsten [21–24] and titanium [25]; effects of subsurface bubbles on sputtering yields [26,27]; He interactions with surfaces and grain boundaries [28–30]; He bubble formation and growth, both in the bulk [31–34] and near surfaces [35]; and direct or indirect implantation of He species on tungsten surface to observe its dynamics and others effects [21,36–39]. This growing body of work has proposed that the initial stages of fuzz formation are owing to helium bubble formation and also the subsequent stress and strain related to growing bubbles, with surface features growing by ejection of dislocation loops and/or individual Frenkel pairs that form adatoms. Presence of helium bubbles below the surface does not strongly affect the sputtering yield [26,27], although experimental studies have shown that sputtering is reduced due to the presence of fuzz relative to fuzz-free surfaces [40]. Although many experiments have been performed to analyze the effects of W and He interactions, there are only a few simulation studies which discussing bubble growth with helium/vacancy ratios. Considering the prevalent view that the formation and growth of nanostructures are strongly related to helium bubbles, we focus on the understanding of bubble
Corresponding author. E-mail address: [email protected] (J. Sun).
https://doi.org/10.1016/j.commatsci.2019.03.008 Received 26 September 2018; Received in revised form 22 January 2019; Accepted 2 March 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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growth and their effect on fuzz formation in tungsten surfaces. In the present study, molecular dynamics (MD) simulations have been performed to analyze the bubble growth and fuzz formation for incident energy 80 eV, temperature 2100 K and high flux of He on W. We have to mention that the temperature chosen here is slightly out off the temperature range for commonly recognized finding fuzz [15]. We have calculated the helium atoms for each metal vacancy (He/V) to describe the dynamics of bubbles near the surface and in the depth of the material. Simulations have been performed for an adequately long time to get a proper insight into the above-mentioned phenomena and saturation state. The simulation results demonstrate a better estimate from a statistical point of view of helium retention, the bubble formation and growth, and cluster size distributions, etc. 2. Simulation methods MD simulations of surface evolution owing to helium bombardment on tungsten are performed using LAMMPS [41]. We have utilized an EAM (embedded atom method) potential developed by Bonny for large scale atomistic simulations in the ternary W-H-He system [42]. The size of tungsten sample with body center cubic (bcc) structure is approximately 63.56 Å × 63.56 Å × 95.34 Å consisting of 24,400 atoms, the lattice parameter is 3.178 Å at temperature 2100 k. First, the simulation has been initialized using a Gaussian velocity distribution at the required temperature 2100 K and thermal equilibrium is achieved around 20 ps under the rescaling thermostat. Secondly, the cell is bombarded during an accumulative pattern with the incident direction normal to the (0 0 1) surface after turned off the temperature rescaling. Each helium atom is chosen randomly over the entire x-y plane, while the z-coordinate is taken at a distance larger than the maximum interaction range of the potential above the surface. Periodic boundary conditions have been applied on the lateral four faces (x and y directions) of the simulation cell, while the top and bottom faces in the z-direction are non-periodic. This means the atom is not allowed to move from one side to another side of the box in zdirection. If this happens, the atom will be removed from the simulation domain. The bottom two layers (z direction) of the simulation domain are kept fixed throughout the simulation to avoid mesh drift of the atoms in the vertical direction owing to the escape of helium atoms. During the bombardment, the temperature is controlled on the two layers of the tungsten atoms above the two fixed bottom layers and one layer on lateral sides of tungsten bulk using a Berendsen thermostat. To carry out the proposed study, incident flux and energy are 1.05 × 10 28 m 2s 1 and 80 eV, respectively, and the time step is chosen 0.4 fs. This time step has been checked for it is appropriateness, and the total simulation time is 72 ns.
Fig. 1. Surface evolution of a W(001) surface under flux of 1.058 × 10 28 m 2 s 1 for different times. Left column: 12 ns; right column: 48 ns. Up row: simulation cell; middle row: side view; bottom row: cluster size (number of He atoms) vs. Depth. Tungsten atoms above the surface are green, and those below blue. Helium atoms highlighted in red. The number of bubbles which has the same cluster size is indicated by color. Bubbles that form far away from the surface are marked with an oval circle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
by estimating the number of He atoms in one cluster. As the incident fluence increases, surface growth also increases (Figs. 1(a(i)), (a(ii)), 2(a(iii)) and (a(iv))). This happens due to the formation of interstitial tungsten atoms (loop-punching) during the formation of the helium clusters. The rate of such loop-punching is strongly dependent on the rate at which helium atoms arrive at the bubble [46]. These W atoms are constrained around the helium cluster for a long time, leading to movement of these atoms onto the upper surface along the 1 1 1 directions, which ends in stacking the W atoms on the surface. Thus, complicated combinational effects of the helium clusters and interstitial atoms lead to the growth of the surfaces. The growth made in these figures are 8.5, 12.5, 21, 15.5 Å, respectively, in the normal direction to the surface. More details about surface growth as a function of helium fluence can be read in Ref. [38,39]. Fig. 2(a(iii)) shows near-surface events like bubbles-coalescence that could be involved in the early stages of fuzz. Figs. 1(b(i)), (b(ii)), 2(b(iii)) and (b(iv)) show the bubbles with tungsten atoms; the regions of bubbles are highlighted in red. It can be seen from Figs. 1(b(i-ii)), 2(b(iii-iv)) that as the time advances, helium atoms move inside the W surface and dislocate some W atoms which results in movement of these dislocated atoms above the surface. Bubbles form close to each other but not close enough to truly merge with-other bubbles but in several cases, a mix-Burgers-vector dislocation [21] accompanies such a cluster of bubbles as manifested in Fig. 1(b(ii)) (such as dislocation type 1/2 1 1 1 ). Expectedly, we can see a large number of growing bubbles close to the surface. Around 72 ns,
3. Results and discussion 3.1. Bubble evolution on (0 0 1) surface As previous studies indicate [43,44] that surface orientation plays very important role in the depth distribution related to helium plasma exposure. The mean depth at which helium “slows down” to thermal velocities may be a function of surface orientation, such as {1 1 1} surface orientation has the deepest depth distribution. The influence of surface orientation is not restricted to the initial depth distribution. However, it is important to explore what should be the preferred crystal orientation, in a polycrystalline sample. Surface tension of {0 0 1} and {1 1 1} surfaces have been found higher than other surfaces, according to the calculations of Wang and co-researchers [45]. As a first step in determining the number of helium atoms in every cluster bubble, we assign helium atoms to clusters-groups, as long as the separation between any He atoms short of distance rHe = 2 Å with each other, they belong to the same cluster (slightly greater than the half separation between the nearest neighbours of W-W atoms). Now, the cluster size is calculated 142
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Fig. 2. Surface evolution of a W(001) surface under flux of 1.058 × 10 28 m 2s 1 for different times. Left column: 66.6 ns; right column: 72 ns. Up row: simulation cell; middle row: side view; bottom row: cluster size (number of He atoms) vs. Depth. Tungsten atoms above the surface are green, those below blue. Helium atoms highlighted in red. The number of bubbles which has the same cluster size is indicated by color. Bubbles that form far away from the surface are marked with an oval shape. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
helium atoms approach to saturation in terms of implantation, as shown in Fig. 2(biv)). When helium atoms form a cluster, which becomes a trap site for other helium atoms, the diffusion of these helium atoms slowed-down greatly. Clusters form at different depths but the growth is slow below depth of 7 nm. Figs. 1(c(i)), 1(c(ii)), 2(c(iii)) and (c(iv)) show the helium cluster size distribution as a function of depth; the number of clusters of a different size is indicated by different colors. As the time advances, the cluster size increases in the depth up to 6 nm; due to adhesion, fewer clusters exist in depth 7 nm, as shown in oval circles (Figs. 1(c(i-ii)), 2(c(iii-iv))). The bubbles show little or no growth deeper than 8 nm below the original surface. It should be noted that the largest bubble in Fig. 2(c(iii)) was grown through one of the growth processes, namely the coalescence of three non-synchronized bubbles. The largest bubble and its neighbor bubble in the red oval circle in Fig. 2(c(iii)) further merged into a larger bubble in the red oval circle as shown in Fig. 2(c(iv)). There are two clusters highlighted by a red circle in Fig. 2 (c(iii)), but there is only one larger cluster in a red circle in Fig. 2 (c(iv)). The size of the large cluster in Fig. 2 (c(iv)) is the sum of the two small clusters in Fig. 2 (c(iii)). It indicates that the two small clusters have merged and formed the larger cluster during 66.6 and 69.9 ns. This conclusion was in fact confirmed by monitoring their evolution in the simulation. When the two neighbouring helium clusters met together, the interstitial defects diffused away, leading to release the pressure
Fig. 3. Side view of the W atoms with coordination number (Ncor ). Snapshots were all obtained at different times. (a) at t = 60 ns; (b) at t = 62.4 ns; (c) at t = 66.6 ns; (d) at t = 69.6 ns. Red balls: He atoms; green balls: W atoms with Ncor 9 ; gray dots: W atoms with Ncor 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
inside the helium bubbles and which promoted the coalescence of helium bubbles (Fig. 2 (c(iv))). A movie of the simulation cell evolution under He implantation is provided as supplementary material. 143
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Fig. 5. Number of W atoms around each bubble. (i) represented fig.3(a); (ii) represented fig.3(b).
Fig. 4. Number of W atoms with Ncor function of He fluence.
method has been used to calculate the vacancy number per cluster: First, we determined the cluster size by using the method described in Section 3.1. To determine the number of vacancies: we transfer all He atoms to the lattice of W atoms in the initial simulation cell (perfect lattice without damage from He bombardment) by assuming that any atom does not occupy any space. If any He atom distances itself from the nearest W atom shorter than rV (rV = 1.05Å, greater than any thermal fluctuation displacement) it is deleted from the lattice. These He atoms are assembled into clusters if their distance shorter than rB = 2 Å . The vacancy number is determined by subtracting the size of this newly created cluster from the previously calculated cluster size. The cutoff distances rHe and rB are kept equal which will ensure that bubbles would be much more easily to be specified continually. Sometimes, the algorithm can produce an error by estimating two helium clusters as a single bubble. We have check it, and fixed it in the simulation. Size of bubbles increases with increasing the number of vacancy for different He/V = (1 9) ratios, as shown in Fig. 6 (a). Here, the vacancy number is not dependent on the time. The bubbles, which are on shallower depth, grow rapidly, and the He/V ratios lie between 2 and 3 for them (as shown in Fig. 6 (b)) as compared with the bubbles located deeper below the surface (black line indicates deepest bubble). During the bubble growth, the ratio He/V is not constant, oscillating between 2 and 3 showing the bubble releases and receives He atoms. Fig. 6 (b) shows growth of bubbles which are near the surface (less than 3 nm below). The bubble size larger, having almost constant growth rate near the surface due to more impacts of He species as compared to the bubbles located at the depth further from the surface. Vacancy number is also more near the surface due to loop-punching. The number of bubbles present in this simulation yield many paths, so we plot all at once as seen in Fig. 6 (c). Hence, Fig. 6 (c) represents bubble growth for overall bubbles below the surface as a function of vacancies for bubbles having >10 He atoms. It can be manifested from Fig. 6(a), (b) and (c) that the He/V ratio for most bubbles lies between 1 and 3. Here, each point represents a bubble with He/V ratio at a particular time for the whole duration of simulation, sampled at a time interval every 2.4 ns. The helium clusters are marked with oval circles as shown in Figs. 1 (c (i-ii)), 2 (c(iii-iv)), which demonstrate the formation and growth along the depth (Fig. 6 (a)). Our findings are different from findings published in Ref [47] for (0 0 1) surface under helium flux of 4 × 10 25 m 2s 1 (ignoring reflections therein). Specifically, we have found very different bubble size profiles than that study. This difference is due to different conditions, for example, the temperature, the potential, etc.
9, pressure of W atoms both as a
3.2. Migration path for self-interstitial-atoms (SIAs) Self-interstitial-atoms (SIAs) can initially remain loosely bound to the cluster or migrate to the surface. In Fig. 3(a,c), a large number of SIAs (highlighted in green) moved toward the surface through helium clusters. Accompanied by the movement, the disordered tungsten atoms around the clusters disappeared (Fig. 3(a,c)) due to the pressure release of helium cluster, and some stacking tungsten atoms that were generated can finally be seen on the top of the surface (Fig. 3(a,c)). Similar results have been reported in Ref [22], in which the bubbles were forced to grow at specific locations, which is not our focus in this paper. We calculated the coordination number (Ncor ) of the tungsten atoms in the substrates shown in Fig. 3(a,c)) and Fig. 4. The coordination number was calculated by defining the bondlength as 2.826 Å for the tungsten crystal. The results are illustrated in Fig. 3(a-d), in which the tungsten atom with is Ncor 9 is represented by a green ball; otherwise, it is represented by a gray dot. In reality, in Figs. 3(b,d), the coordination numbers of most tungsten atoms around helium atoms and clusters are greater than or equal to 9. These Fig. 3(b and d) show the migration of some tungsten atoms from the top surface into the bulk material (Reverse migration). Especially, in Fig. 3(b,d) we can see large clusters of tungsten atoms with Ncor 9, as SIAs were hindered and constrained by helium clusters. Also, Fig. 4 tells us that increase of stress on W atoms around the bubble in Fig. 3(b,d). Once the SIAs moved away from the helium clusters, the clusters of tungsten atoms disappeared as their Ncor became less than or equal to 8 (Fig. 3(a and c)). In the migration path of the SIAs, the coordination numbers of some tungsten atoms may increase, as shown in Fig. 3(b,d). Figs. 3 and 4 show the number of tungsten atoms with Ncor 9 as a function of the helium fluence. When the SIAs were hindered and constrained by the helium clusters (Fig. 3(b) and (d)), the number of tungsten atoms with Ncor 9 was high, fluctuating between 1400 and 1600. Then, with the SIAs moving to and absorbed on the surface, the number of tungsten atoms with Ncor 9 reduced to around 200. Fig. 5 shows the number of tungsten atoms around each bubble. It is clear from Fig. 5(i) that the proportion of tungsten atoms around the bubbles is almost negligible compared to the case in Fig. 5(ii) where the number is approximately six times the number of helium atoms inside the bubble.
3.4. Helium retention The rate of He retention is shown in Fig. 7 as a function of fluence. For initial values of fluence the retention increases until up to 1.5× 10 20m 2 , and subsequently it saturates. Some studies [39] have been carried out to explain the saturation of the helium atom which occurs in absence of the “cluster ruptures”, but is however evidenced for implantation experiments performed at energies below tungsten displacement threshold. Fluence is a strong function of implantation flux
3.3. Bubble growth We also have attempted to trace the size of each single bubble at different depths as a function of vacancy number (likewise the bubble size distributions in Figs. 1(c(i-ii)) and 2(c(iii-iv)). The following 144
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Fig. 7. Rate of helium retention in tungsten (excluding reflection) as a function of fluence. The smaller sudden drops in the curve result from small bubbles bursting.
and therefore the pre-existing tungsten microstructure which causes the formation of the initially immobilized bubbles increases retention through self-trapping. It should be noted the rate of helium retention is the number of helium atoms remaining in the tungsten simulation cell divided by the total number of insertions at a certain point in time as shown in Fig. 7. The lifetime of He bubbles below the surface is concerned, the time point which indicates the starting of He bubble burst from the surface is defined, for-example in Fig. 8. we calculate the volume by the summation of volumes of He atoms that are described by the Voronoi polyhedrons of atoms. When a He atom occurs on above surface, the voronoi polyhedron may fail. During simulation, we compute the symmetric stress tensor [48,49] for each He atom in the cluster, as shown in Fig. 8. The computed stress tensor per atom is actually in units of pressure × volume. In this way we can obtain the negative of total pressure ( P). Around 42 ns, the bursting of small bubble near the surface leads to
Fig. 6. Number of He atoms as a function of the number of vacancies per bubble. (a) Bubbles within 55–80 nm under the original surface (highlightcolored); (b) larger three bubbles in the simulation (colored); (c) Bubbles which contain 10 He atoms or more in the cluster; for the period 0–72 ns. Each point represents a bubble present at a particular instant in time during the simulation, sampled every 2.4 ns for 72 ns; squares correspond to the same bubble at different times. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Bubble pressure of a small bubble moving near the surface as a function of time. Inset shows the surface image at 42.036 ns leading to reduced retention. Tungsten atoms and helium atoms are highlighted in green and red, respectively. 145
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reduced retention as shown in Fig. 7 (one bubble is shown leaving the surface). As the bubbles move toward the surface, bubble pressure decreases as represented in Fig. 8. In our simulations, helium retention increases because of the presence of sub-surface bubbles, which trap He atoms rather than allowing them to diffuse to the surface and back into the plasma. This happens because some helium atoms are far less mobile than those in the bulk as they are bound to the bubbles.
[3] [4] [5] [6]
4. Summary and conclusions
[7]
In the present work, MD simulations have been performed to study the surface response of W {0 0 1} to bombardment of high helium flux of energy 80 eV at temperature 2100 K. Clusters form at different depths but grow slowly below depth of 7 nm, compared with the above. Selfinterstitial-atoms (SIAs) can initially remain loosely bound to the cluster or migrate to the free surface. Tungsten atoms were observed migrating from the top surface into the bulk, SIAs around each bubble become almost six times the number of helium atoms inside each bubble. The saturation of He retention has been observed to be high, a result of the bubbles trapping helium atoms and preventing them from diffusing to the surface and further back into the plasma. On the other hand, we have observed near-surface “cluster rupture” leading to the expulsion of helium atoms towards the vacuum. We also have observed near-surface events of bubbles-coalescence which could be considered involved in the early stages of fuzz. We have found that bubbles typically grow in a relatively narrow band of He/V ratios (1 3) . It has also been observed that the deep-down bubbles release or absorb helium atoms. This study provides data which could be served to understand the behaviour of plasma facing materials at high temperatures. The effects of incident He flux on He cluster sizes will be explored in the future work.
[8]
[9]
[10] [11] [12] [13] [14] [15] [16]
Data availability
[17]
The raw/processed data required to reproduce these findings can be shared if requested.
[18]
CRediT authorship contribution statement
[19]
Ali Y. Hamid: Conceptualization, Methodology, Data curation, Formal analysis, Writing - original draft, Investigation, Writing - review & editing. Jizhong Sun: Conceptualization, Methodology, Formal analysis, Writing - review & editing, Funding acquisition, Project administration. Hongyu Zhang: Data curation, Formal analysis, Visualization. Arvind S. Jadon: Formal analysis, Writing - original draft. Thomas Stirner: Methodology, Writing - review & editing.
[20] [21] [22] [23]
Acknowledgements
[24]
This work is supported by the National Key R&D Program of China under Grant No. 2017YFE0301103 and the National Science Foundation of China under Grant Nos. 11575039 and 51671045. It is also partially supported by the Fundamental Research Funds for the Central Universities (DUT18GF112) and by Supercomputing Center of Dalian University of Technology.
[25] [26] [27]
Appendix A. Supplementary data
[28] [29]
Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.commatsci.2019.03.008.
[30]
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