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Migration and nucleation of helium atoms at (110) twist grain boundaries in tungsten
Journal of Nuclear Materials 487 (2017) 200e209
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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Migration and nucleation of helium atoms at (110) twist grain boundaries in tungsten Ya-Xin Feng a, Jia-Xiang Shang a, *, Guang-Hong Lu b, c a
School of Materials Science and Engineering, Beihang University, Beijing 100191, China School of Physics and Nuclear Engineering, Beihang University, Beijing 100191, China c Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China b
h i g h l i g h t s The preference sites for the He interstitial on three typical twist grain boundaries (TGBs) plane are obtained. The dislocation network in the LAGB is a good sink for defects, which can attract and bind defects in the grain boundary. The magnitude and dimensionality of He migration in TGBs are reduced and influenced by grain boundary structure. Compared with the bulk, TGBs have higher cluster densities, smaller cluster sizes and more SIAs at high temperature.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 September 2016 Received in revised form 17 January 2017 Accepted 29 January 2017 Available online 15 February 2017
The migration and nucleation of He atoms at three typical (110) twist grain boundaries (TGBs): the lowangle grain boundary (LAGB), the ordinary high-angle grain boundary (HAGB) and the S3 TGB in W are investigated using molecular dynamics simulations. The presence of TGBs can absorb He atoms from bulk and impede the growth of He bubbles. Moreover, different grain boundary (GB) structures behave differently when interacting with He atoms. The LAGB can control the He distribution on the GB plane through its screw dislocation network, suggesting a promising approach for design of radiation tolerant materials. The ordinary HAGB presents a strong trap effect due to its disordered GB structure, which may induce a large He retention at the GB and embrittlement. The S3 TGB can provide a diffusion path for He atoms, although the diffusion rate is not as fast as it in bulk. © 2017 Elsevier B.V. All rights reserved.
Keywords: Helium Migration Nucleation Twist grain boundaries Tungsten
1. Introduction One of the most important challenges for the successful commercialization of fusion power is the development of plasma facing materials (PFMs) that can tolerate the extreme conditions of elevated temperatures and high flux of plasma present in fusion reactors. Tungsten (W) is regarded as a promising candidate for PFMs because of its high melting temperature, high thermal conductivity and low sputtering erosion [1e3]. However, there are still many challenges in its future application. One of the major challenges is its exposure to large fluences of helium (He) plasma generated by ðn; aÞ reactions, which can precipitate into clusters and bubbles [4e9], promote swelling, hardening and
* Corresponding author. E-mail address: [email protected] (J.-X. Shang). http://dx.doi.org/10.1016/j.jnucmat.2017.01.045 0022-3115/© 2017 Elsevier B.V. All rights reserved.
embrittlement [10,11], and eventually degrade mechanical properties and lifetime of structural materials [12,13]. Grain boundaries (GBs), severing as effect sinks for radiationinduced defects, can significantly improve the radiation resistance of materials and heal the crystal [14e17]. To date, extensive researches have covered the interaction between GBs and He atoms [18e22]. Bai et al. [16] investigate the defect-GB interaction mechanism in Cu and find that the S11 tilt GB can absorb interstitials and reemit them to annihilate bulk vacancies, leaving a healed crystal. The self-healing mechanism is also verified through first-principle calculations by Liu et al. [17]. Furthermore, Valles et al. [21] study the influence of a high GB density on the amount, size and distribution of defects produced by pulsed He irradiation in W and reveal that the He retention at GBs increases with the GB density. Among different GBs, twist grain boundaries (TGBs) draw more and more attention for their unique GB structures [23,24]. In our previous work [25], the energy and structure of (110) twist
Y.-X. Feng et al. / Journal of Nuclear Materials 487 (2017) 200e209
grain boundaries in W have been systematically investigated. According to the analysis of dislocation, (110) TGBs can be divided into three types: low-angle grain boundaries (LAGBs), intermediateangle grain boundaries (IAGBs) and high-angle grain boundaries (HAGBs). When the twist angle q 16:10 , a regular dislocation network consisting of 12 ½111, 12 ½1 11 and ½001 screw dislocations exists in LAGBs. And the size and shape of meshes in the network vary with increased twist angles. The regions separated by dislocations are body-centered cubic arrangement regions (referred as normal regions in this work). In IAGBs, with 17:23 q 22:22 , both atomistic structures and dislocations are disordered and dislocations do not form a regular network. The TGBs with q 23:5 are HAGBs, where no dislocation is observed. The HAGBs can be divided into three sub-types further: special boundaries with low S, boundaries in their vicinity with similar structures as the corresponding special boundary in local regions as well as ordinary HAGBs consisting of periodic patterns. Previously, molecular statics, molecular dynamics and experiments have been combined to study the He bubble nucleation at LAGBs in Au and Cu [26,27]. The results indicate that He bubbles preferentially nucleate at screw dislocation nodal points and a He bubble superlattice is formed, which implies a potential approach for the design of radiation tolerant materials. Kumar et al. [28] simulate the shear deformation of {110} LAGB in a-Fe with and without He bubbles and reveal that the presence of He has a predominantly impact on the mechanical response of this particular dislocation structure, inducing hardening and possibly embrittlement. Despite the valuable resources provided by these early studies, we still lack a comprehensive understanding of the behavior of He atoms in different TGBs. In this work, we focus on the He migration and nucleation behaviors at early stages in different TGBs. In the following, we will first describe the simulation method in section 2. The migration and nucleation behaviors of He atoms in different TGBs are presented in section 3, followed by the conclusions given in section 4.
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2. Method In this work, the potential for W-He system proposed by Juslin and Wirth [29] is used. They develop a new pair potential for W-He interaction and modify the Acaland-Thetford W-W potential [30] at short range. For He-He interaction, the Beck potential [31] with the short range fit by Morishita et al. [32] is adopted. Before MD simulations, we calculate the parameters for the W-He interaction using the present potential and compare them with those from experiment, DFT calculations and other potentials (Table 1). The comparison indicates that the present potential provide a good description for the W-He interaction. Besides, the present potential proposed by Juslin and Wirth has been widely used in the researches of the W-He interaction, such as He cluster growth [33], He diffusion on grain boundaries [34] as well as He behaviors near surface [35e37], which further prove its reliability. To investigate the effect of GB structures on He migration and nucleation, three typical TGBs are studied: the LAGB with q ¼ 3 , the ordinary HAGB with q ¼ 34:38 and the S3 TGB with q ¼ 70:53 . The details of methodology used in construction of the simulation models of TGBs have been described elsewhere [25,48]. The upper and lower sections of a single crystal rotate about the ½110 direction by 2q clockwise and counterclockwise respectively. After rotation, the equilibrium GB structures are obtained via the combination of conjugate gradient energy minimization and quasidynamic quenching. Periodic boundary conditions are applied along the x and y directions, while a fixed boundary condition is applied along the z direction. The migration and nucleation of He atoms are investigated respectively through two independent simulations. In the first simulation, the mean square displacement (MSD) is used to analysis the migration of a He interstitial, which is randomly inserted in the TGB plane. MSD calculations are performed from 300 to 1200 K with migration time of 1 ns? For each TGB, five calculations are performed to reduce the statistics effect and their results are averaged. In the LAGB, the MSDs are calculated in the dislocation network and normal regions respectively for the apparent difference between them. In the second simulation, the nucleation process of He atoms in TGBs under different He
Table 1 Parameters of the W-He system determined from the present potential, in comparison with those form experiment, density-functional theory (DFT) calculations, the modified embedded atom method (MEAM) potential and the bond-order potential (BOP). a: the lattice constant (Å); Ec : cohesive energy (eV/atom); Ef : formation energy (eV); v: vacancy: SIA: self-interstitial atom; tet: tetrahedral interstitial; oct: octahedral interstitial; db〈ijk〉: 〈ijk〉 dumbbell interstitial configuration. Present a Ec Ef ;v
DFT
Experimental c
d
h,i
3.165 8.90 3.63 10.31
3.18 7.406i 3.46a,3.56b 11.64a,11.05b
EfSIA ;oct
10.41
11.99a,11.68b
12.05h
EfSIA ;db〈100〉 EfSIA ;db〈110〉 EfSIA ;db〈111〉 EfHe ;subs EfHe ;tet EfHe ;oct
10.29
11.74a,11.49b
12.01h
10.18
10.10a,9.84b
9.51
9.82a,9.55b
4.69
4.70a
4.70h
6.15
6.16
a
6.21h
6.38
a
6.39h
EfSIA ;tet
a b c d e f g h i j
Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref.
[38]. [39]. [40]. [41]. [42]. [43]. [44]. [45]. [46]. [47].
6.30
3.165 8.90e 3.7 ± 0.2f
MEAMj
BOP 3.165 8.906h,8.89i 3.52h,1.68i 10.75h
9.53h 9.06 ± 0.63g
9.33h
3.164 8.66 3.95
8.98
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Table 2 Dimensions (nm) and the number of W atoms and He atoms in each model. Model Type
LAGB ordinary HAGB S3 TGB Bulk
x
y
12.08 14.98 10.96 8.95
17.68 10.58 15.51 12.66
z
17.90 17.90 17.90 17.90
No. of W atoms
233,440 179,520 192,000 128,000
No. of He atoms 0:1%
0:5%
1%
204 157 168 128
1021 785 840 640
2043 1571 1680 1280
concentration is performed at 300 and 1200 K for 2 ns. He atoms are randomly inserted in the tetrahedral positions within the dynamic region of each model, which are the most stable configuration for He atoms in bulk W [38], to produce the He concentration of 0:1%, 0:5% and 1%. After insertion, the model is relaxed at 0 K for 10 ps, followed by rescaling temperature to desired values and keeping constant afterwards. As a comparison, the bulk W model is also simulated under the same conditions, where the axes are x k ½110, y k ½001 and z k ½110 respectively. The dimensions and the numbers of W and He atoms in each model are given in Table 2. The NPT ensemble is employed to keep temperature constant with a timestep of 1 fs. The diffusion coefficient of He in W is calculated using the Einstein relation:
D¼
MSD 6t
where MSD ¼
(1) PN
! ! r i ðtÞ r i ð0Þ2 , r is the position of He and t is
i¼1 ½
the diffusion time. To accurately calculate the diffusion coefficient, we decompose the single trajectory into a set of shorter independent segments with equal duration and apply Eq. (1) to each segment to calculate Di (Di indicates the diffusion coefficient of the ith segment), followed by averaging Di over all segments. The time interval adopted in this work is 100 ps. The diffusion activation energy (Ea) can be determined from the Arrhenius relation:
. D ¼ D0 exp Ea kb T
(2)
where D0 is the prefactor of diffusion and kb is the Boltzmann constant. The nucleation of He atoms is monitored by counting the number and size of He clusters, defined as He atoms within a distance of 0.2 nm to each other. In order to track the distribution of He atoms with time in the GB normal direction (z direction), each simulation model is divided into thin slabs along the z direction with a thickness of 0.5 nm. The He concentration in each slab is defined as the percentage of the number of He atoms vs the number of W atoms in that slab. Besides, the Wigner-Seitz unit cell is used to identify the self-interstitial atoms (SIAs) and vacancies, which is achieved by the voronoi package of lammps. The whole system volume is divided into Wigner-Seitz unit cells based on the W atoms. Ideally, each unit cell contains one W atom. An empty primitive cell (with no W atoms) is taken as a vacancy, and the extra W atoms (more than one) contained in a primitive cell are taken as SIAs. The MD simulation and the visualization of atomic configurations are achieved through the open-source software LAMMPS
Fig. 1. (aec) He formation energies for different interstitial sites in (a) LAGB, (b) ordinary HAGB and (c) S3 TGB. The spots represent the stable positions for a He interstitial and are colored according the formation energy. (d) The average He interstitial formation energy as a function of the distance from the GB plane. The dashed line represents the He formation energy at the tetrahedral site in bulk W, 6.15 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 3 Average binding energy (eV), diffusion activation energies (eV) and prefactor of diffusion (109 m2 =s) for interstitial He to each model. The numbers in the round brackets are the corresponding values for He in the dislocation network of LAGB between 300 and 750 K. LAGB Dislocation network EbHe Ea D0
Ordinary HAGB
S3 special boundary
Bulk
Normal region
2.24
0.08
1.44
0.59
0.284(-0.001) 1.47(0.02)
0.102 8.0
0.012 0.02
0.109 6.67
0.107 31.59
Fig. 2. (a) Mean-square displacement (MSD) of a He atom in each TGB and bulk at 300, 750 and 1200 K. (bef) MSD components along x, y and z directions at 300, 750 and 1200 K in (b) bulk, (c) dislocation network of LAGB, (d) normal region of LAGB, (e) ordinary HAGB and (f) S3 TGB.
[49] and Atomeye [50]. The He interstitial formation energy and binding energy are defined as: He EbHe ¼ EGB EGB EfHe ;bulk Eref ;He
He EfHe ;GB ¼ EGB EGB Eref ;He
and
(3)
(4)
He and E where EGB GB are the energies of the GB with and without He respectively; Eref ;He is the cohesive energy of close packed He, which is 0.0054 eV for the Beck He-He potential; EfHe is the for;bulk mation energy of a He atom in bulk W, which is 6.15 eV for a He atom in the tetrahedral position.
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Fig. 3. The lnD-1/T curve of He in each TGB and bulk over the range 300e1200 K.
3. Results and discussion 3.1. The migration of He atoms in TGBs Fig. 1(aec) show the stable positions for the He interstitial in TGBs together with the corresponding formation energy, where the spots represent the stable positions for a He interstitial and the color of spots indicate the magnitude of the formation energy. As we can see, for the LAGB, the formation energy in the normal region is approximately 6.06 eV, which closes the value in bulk W, while the formation energy in the cores of the dislocation network is about 3.9 eV, indicating the screw dislocations in the LAGB are good sinks for He clusters. Influenced by the GB structure, the stable positions are scattered in the ordinary HAGB and arrange in periodic rows in the S3 TGB with the average formation energies of 4.71 and 5.55 eV (Fig. 1(bec)). Fig. 1(d) shows the average He interstitial formation energy as a function of the distance from the GB plane.
The effect influence distance of TGBs is about 0.5 nm, beyond which the average formation energy approaches a stable value. It should be noted that the stable value for the LAGB is smaller than that formation energy in bulk W, which may be caused by the dislocation structure. The average binding energy to the He interstitial in each TGB is given in Table 3. It is apparent that the disordered structures have a much stronger binding to the He interstitial than those ordered. Fig. 2(a) shows the MSDs of a He atom in each model at 300, 750 and 1200 K. At 300 K, the MSDs in TGBs are apparently smaller than that in the bulk especially for the dislocation network of the LAGB and the ordinary HAGB, where the MSDs are negligible. The increasing temperature raises the MSDs to different extents, but does not change the trend. The MSD components along x, y and z directions for each model are presented in Fig. 2(bef). For the bulk, the He atom migrates mainly along the [001] direction at 300 K, and the migration changes from one dimension to three dimension at higher temperature. According to the researches of Shu et al. [51,52], at the temperature below 300 K, the He atom diffuses directly from one TIS (tetrahedral interstitial site) to another, while the migration is a mixture of the TIS-TIS (〈110〉 direction in bulk W) and the TIS-OIS (octahedral interstitial site)-TIS (〈001〉 direction in bulk W) pathes at higher temperature. Combined with our simulation results, we can find that the He atom prefers the TIS-OIS-TIS path rather than the TIS-TIS path when migrating in bulk at 300 K, because the TIS-OIS-TIS path has a shorter diffusion distance. At higher temperature, the enhanced mobility makes the He interstitial migrate along both pathes equally. Compared with the bulk, the magnitude and dimension of the He migration in TGBs are reduced and influenced by the GB structure. For the LAGB, a strong binding to the He atom is obviously observed in the dislocation network, while the He atom can migrate randomly along three directions in normal regions before being trapped by the dislocation network (Fig. 2(ced)). At high temperature, the enhanced mobility makes it possible for the He atom in the normal region to escape from the GB, which is observed several times in our simulations. For the ordinary HAGB, the MSDs are negligible at all temperatures (Fig. 2(e)), demonstrating that the He atom is pinned where it is allocated, which is consistent with the high binding energy shown in Table 3. For the S3 TGB, although there are some
Fig. 4. He concentration profiles at 2 ns for each TGB and bulk with different He concentration and temperature. The dashed lines represent the TGB plane.
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205
Fig. 5. Atomic configurations of He atoms, SIAs and vacancies under different He concentration and temperature at 2 ns projected onto the LAGB plane, with the thickness of 0.45 nm.
Fig. 6. Atomic configurations of He atoms, SIAs and vacancies under different He concentration and temperature at 2 ns projected onto the ordinary HAGB plane, with the thickness of 0.45 nm.
fluctuations along ½110 direction, the main contributions to MSD come from ½111 and ½112 directions, indicating that the migration is two-dimensional along the TGB plane (Fig. 2(f)). Previously, Gao et al.[53,54,55] report the He diffusion at the S11〈110〉f323g and
S3〈110〉f112g tilt GBs in a-Fe. The single He interstitial diffuses in the S11 tilt GB with one-dimensional migration along the ½113 direction, whereas it migrates two-dimensionally at low temperature (600e800 K), and three-dimensionally in the S3 tilt GB at high
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Fig. 7. Atomic configurations of He atoms, SIAs and vacancies under different He concentration and temperature at 2 ns projected onto the S3 TGB plane, with the thickness of 0.45 nm.
temperature (1200 K). Three-dimensional diffusion behavior of He interstitial is an indicator of the dissociation of the He interstitial form GB at high temperature. In contrast, the migration dimensionality of He interstitial in each TGB remains unchanged at high temperature, suggesting that the binding of TGBs to He interstitial is stronger. The diffusion-temperature (expressed as lnD-1/T) curve of He in W in the temperature range from 300 to 1200 K is shown in Fig. 3. As seen in Fig. 3, the diffusivity of He in TGBs is apparently lower than that in bulk at the same temperature, especially for the dislocation network of the LAGB and the ordinary HAGB. In the dislocation network of LAGB, the He atom hardly moves under the temperature range from 300 to 750 K, owing to the strong binding energy. When the temperature is higher than 750 K, the He atom has enough energy to overcome the barrier and migrates. A stronger trapping effect is observed in the ordinary HAGB, where the He atom is not activated at all temperatures, due to its disordered GB structure. The fitted diffusion activation energies and prefactors are shown in Table 3. The diffusion activation energy of He in bulk is 0.107 eV, which is between the diffusion barrier along the TIS-TIS path (0.023 eV) and that along the TIS-OIS-TIS path (0.174 eV) [51,52], indicating the migration of He in bulk is a mixture of the TIS-TIS and the TIS-OIS-TIS paths. Since the He atom is trapped and hardly moves, the diffusion activation energies of He in the dislocation region of the LAGB between 300 K and 750 K and the ordinary HAGB do not represent the real diffusion barrier. The diffusion activation energy of He in the dislocation region between
750 K and 1200 K is 0.284 eV, which is larger than that in bulk, suggesting He migration is more difficult. In contrast, the diffusion activation energies of He in the normal region of the LAGB and the S3 TGB (0.102 and 0.109 eV respectively) are close to that in bulk. However, the migration of He is influenced by the dislocation network in the normal region of LAGB and limited in the diffusion dimension in the S3 TGB, hence, the He atom has lower prefactors of diffusion compared to the bulk, thus resulting in a lower diffusivity. In this section, the migration behaviors of a He atom in TGBs at different temperatures are presented. Contrary to the paradigm that GBs facilitate the migration of impurities, we find that TGBs inhibit the He migration in both magnitude and dimension. This phenomenon arises from the relative insolubility of He in most materials combined with the size mismatch between He and W, which results in an interstitial diffusion mechanism rather than diffusion that relies on the presence of self-vacancies [34]. Moreover, the migration feature of the He atom in TGBs depends on the GB structure. The dislocation network in the LAGB can effectively attract and bind He atoms, implying a potential way to control the He distribution on the GB plane. Compared with the dislocation network, the ordinary HAGB behaves a stronger trap effect, which may induce a large retention of He atoms at the GB region and embrittlement. Different from the other two TGBs, the S3 TGB can provide a diffusion path for He atoms, despite the diffusion rate is not as fast as it in bulk.
Y.-X. Feng et al. / Journal of Nuclear Materials 487 (2017) 200e209
Fig. 8. (a) He cluster density, (b) average size and (c) number of SIA as a function of He concentration for each TGB and bulk W at 300 and 1200 K.
3.2. The nucleation of He atoms in TGBs Fig. 4 shows the He concentration profiles at 2 ns under different He concentration and temperature. A strong precipitation of He atoms in TGBs is observed in Fig. 4, which is enhanced at higher temperature. At the He concentration of 0:1%, most He atoms precipitate at the TGBs; However, some He atoms begin to
207
accumulate beyond the TGBs as the increase of the He concentration, manifesting that there is a limit on the attraction of the TGBs to He atoms. The corresponding distribution of defects (He atoms, SIAs and vacancies) on each TGB plane is presented in Figs. 5e7, with a thickness of about 0.45 nm. As seen in Fig. 5, at the He concentration of 0:1% and 300 K, isolated He atoms distribute loosely along the dislocation network in the LAGB (Fig. 5(a)). As the He concentration increases, some He atoms accumulate and form small He clusters (Fig. 5(bec)). When temperature rises to 1200 K, most He atoms change from isolated He atoms to clustered He atoms and these defects distribute strictly along the dislocation network except the He clusters and SIAs marked in Fig. 5(f), implying the He concentration of 1% may excess the capacity of the dislocation network. Different from the distribution of defects in the LAGB, the defects distribute randomly within the ordinary HAGB (Fig. 6), owing to its relatively disordered GB structure. It is worthy to note that there are abundant isolated He atoms in the ordinary HAGB plane, no matter what the He concentration and temperature are, which further proves the high He binding energy in this boundary. For the S3 TGB, He atoms, mainly in the form of isolated He at 300 K and clustered He ate 1200 K, distribute randomly within the boundary other than several isolated He atoms arranging in a row (Fig. 7). As revealed by Fig. 1(c), the most stable configuration for He atoms in the S3 TGB is in the arrangement of periodic rows, which is distinctly different from the distribution of He atoms shown in Fig. 7. This phenomenon can be explained by the slight formation energy difference and low binding energy for the He atom in the S3 TGB. The maximum formation energy difference in the S3 TGB is 0.67 eV, which is much smaller than that in the LAGB and ordinary HAGB, 2.51 and 1.42 eV respectively, indicating that the He atom is relatively stable even at the position with a high formation energy. And the low binding energy guarantees that the He atom can migrate easily within the boundary, as seen in Fig. 2(f). These two factors lead to the random distribution of He atoms in the S3 TGB. Besides, influenced by the horizontal stripe structure of this TGB, SIAs tend to distribute in a row and its number is fewer than in the other two TGBs, which is clearly shown in Figs. 7e8. Fig. 8 describes the variation of the cluster density, average cluster size and number of SIAs with the He concentration and temperature. As described in Fig. 8, the cluster density increases with He concentration and decreases with temperature, while the average cluster density increases obviously as the rise of temperature and reaches a peak at the He concentration of 0:5%. Under the same condition, the order by size of the cluster density for each model are contrary to that of the average cluster size, which is also observed at S3 and S73b tilt GBs in a-Fe [19]. In contrast to the bulk, TGBs have higher cluster densities and smaller average sizes at 1200 K, which coincides with previous simulations [19,20], while such comparison shows no regularity at 300 K. Recent simulations about the He nucleation at the twist, tilt and twin GBs in Mo [20] reveal that the GB trapping effect helps to stabilize He atoms or clusters as embryos of bubbles and impedes further growth of He clusters by absorption of mobile He atoms, resulting in a higher density and smaller average size of He clusters. Moreover, the change in the dimensionality of diffusion due to the GB trapping in turn affects the distribution of He bubbles. All these are in agreement with our results at 1200 K. At 300 K, the GB trapping effect is unapparent because of the low mobility of He atoms. The number of SIAs behaves diversely at different temperature, which is not sensitive to the He concentration at 300 K, but increases linearly with the He concentration at 1200 K. And it seems that the number of SIAs in ordered structures is smaller than that in disordered ones. In this section, the nucleation behaviors of He atoms in TGBs under different He concentrations and temperatures are presented.
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A strong precipitation of He atoms in TGBs is observed and the growth of He bubbles is impeded, which will relieve void swelling or other modification to the microstructure. Furthermore, in the LAGB, He atoms distribute along the dislocation network especially at high temperature, indicating a effect approach to control He distribution namely forming a dislocation network. 4. Conclusion The migration and nucleation of He atoms in TGBs are studied using MD simulations, and compared with that in bulk W. Three typical TGBs are investigated in this work: the low-angle grain boundary (LAGB) with a dislocation network, the ordinary highangle grain boundary (HAGB) consisting of periodic patterns and the S3 TGB with good symmetry. In bulk W, the He atom migrates dimensionally along the [001] direction at 300 K and three dimensionally at higher temperature. Compared with the migration in bulk W, the magnitude and dimensionality of He migration in TGBs are reduced and influenced by the GB structure. In the LAGB, the He atom is either trapped by the screw dislocations or migrates randomly along three directions in the normal regions. The ordinary HAGB has a similar but stronger trap effect in contrast to the dislocation network of the LAGB. The He atom is pinned where it is allocated and hardly moves. In the S3 TGB, the He atom migrates two dimensionally along the TGB plane, although there are some fluctuations of the MSD along the ½110 direction. As higher temperature, the MSDs rise to different extents, but the migration dimensionality of He in each TGB does not change. The nucleation of He atoms in TGBs depends on temperature, He concentration and GB structure. A strong precipitation of He atoms in TGBs is observed and enhanced at higher temperature, while more and more He atoms accumulate beyond TGBs as the He concentration increases. On the TGB plane, He atoms distribute along the dislocation network in the LAGB and randomly in the other two TGBs. In contrast with bulk W, TGBs have higher cluster densities, smaller average cluster sizes and more emission of SIAs at 1200 K, while such comparison shows no regularity at 300 K. The above presented He migration and nucleation behaviors in TGBs under different conditions will contribute to the design of radiation tolerant materials. Acknowledgements The authors acknowledge the financial support from the National Magnetic Confinement Fusion Program under Grant No. 2013GB109002. The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A). References [1] V. Barabash, G. Federici, R. Matera, A.R. Raffray, ITER Home Teams, Armour materials for the iter plasma facing coments, Phys. Scr. T81 (1999) 74e83. [2] G. Federici, R.A. Anderl, P. Andrew, et al., In-vessel tritium retention and removal in iter, J. Nucl. Mat. 266e269 (1999) 14e29. [3] G. Federici, H. Wuerz, G. Janeschitz, R. Tivey, Erosion of plasma-facing components in iter, Fusion Eng. Des. 61e62 (2002) 81e94. [4] G.J. Thomas, Experimental studies of helium in metals, Radiat. Eff. Defects Solids 78 (1983) 37e51. [5] H. Trinkaus, B.N. Singh, Helium accumulation in metals during irradiation where do we stand? J. Nucl. Mat. 232 (2003) 229e242. [6] H. Iwakiri, K. Yasunaga, K. Morishita, N. Yoshida, Microstructure evolution in tungsten during low-energy helium ion irradiation, J. Nucl. Mat. 283e287 (2000) 1134e1138. [7] M. Miyamoto, D. Nishijima, M.J. Baldwin, R.P. Doerner, Y. Ueda, K. Yasunaga, N. Yoshida, K. Ono, Microscopic damage of tungsten exposed to deuteriumhelium mixture plasma in pisces and its impacts on retention property, J. Nucl. Mat. 415 (2011) S657eS660.
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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Migration and nucleation of helium atoms at (110) twist grain boundaries in tungsten Ya-Xin Feng a, Jia-Xiang Shang a, *, Guang-Hong Lu b, c a
School of Materials Science and Engineering, Beihang University, Beijing 100191, China School of Physics and Nuclear Engineering, Beihang University, Beijing 100191, China c Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China b
h i g h l i g h t s The preference sites for the He interstitial on three typical twist grain boundaries (TGBs) plane are obtained. The dislocation network in the LAGB is a good sink for defects, which can attract and bind defects in the grain boundary. The magnitude and dimensionality of He migration in TGBs are reduced and influenced by grain boundary structure. Compared with the bulk, TGBs have higher cluster densities, smaller cluster sizes and more SIAs at high temperature.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 September 2016 Received in revised form 17 January 2017 Accepted 29 January 2017 Available online 15 February 2017
The migration and nucleation of He atoms at three typical (110) twist grain boundaries (TGBs): the lowangle grain boundary (LAGB), the ordinary high-angle grain boundary (HAGB) and the S3 TGB in W are investigated using molecular dynamics simulations. The presence of TGBs can absorb He atoms from bulk and impede the growth of He bubbles. Moreover, different grain boundary (GB) structures behave differently when interacting with He atoms. The LAGB can control the He distribution on the GB plane through its screw dislocation network, suggesting a promising approach for design of radiation tolerant materials. The ordinary HAGB presents a strong trap effect due to its disordered GB structure, which may induce a large He retention at the GB and embrittlement. The S3 TGB can provide a diffusion path for He atoms, although the diffusion rate is not as fast as it in bulk. © 2017 Elsevier B.V. All rights reserved.
Keywords: Helium Migration Nucleation Twist grain boundaries Tungsten
1. Introduction One of the most important challenges for the successful commercialization of fusion power is the development of plasma facing materials (PFMs) that can tolerate the extreme conditions of elevated temperatures and high flux of plasma present in fusion reactors. Tungsten (W) is regarded as a promising candidate for PFMs because of its high melting temperature, high thermal conductivity and low sputtering erosion [1e3]. However, there are still many challenges in its future application. One of the major challenges is its exposure to large fluences of helium (He) plasma generated by ðn; aÞ reactions, which can precipitate into clusters and bubbles [4e9], promote swelling, hardening and
* Corresponding author. E-mail address: [email protected] (J.-X. Shang). http://dx.doi.org/10.1016/j.jnucmat.2017.01.045 0022-3115/© 2017 Elsevier B.V. All rights reserved.
embrittlement [10,11], and eventually degrade mechanical properties and lifetime of structural materials [12,13]. Grain boundaries (GBs), severing as effect sinks for radiationinduced defects, can significantly improve the radiation resistance of materials and heal the crystal [14e17]. To date, extensive researches have covered the interaction between GBs and He atoms [18e22]. Bai et al. [16] investigate the defect-GB interaction mechanism in Cu and find that the S11 tilt GB can absorb interstitials and reemit them to annihilate bulk vacancies, leaving a healed crystal. The self-healing mechanism is also verified through first-principle calculations by Liu et al. [17]. Furthermore, Valles et al. [21] study the influence of a high GB density on the amount, size and distribution of defects produced by pulsed He irradiation in W and reveal that the He retention at GBs increases with the GB density. Among different GBs, twist grain boundaries (TGBs) draw more and more attention for their unique GB structures [23,24]. In our previous work [25], the energy and structure of (110) twist
Y.-X. Feng et al. / Journal of Nuclear Materials 487 (2017) 200e209
grain boundaries in W have been systematically investigated. According to the analysis of dislocation, (110) TGBs can be divided into three types: low-angle grain boundaries (LAGBs), intermediateangle grain boundaries (IAGBs) and high-angle grain boundaries (HAGBs). When the twist angle q 16:10 , a regular dislocation network consisting of 12 ½111, 12 ½1 11 and ½001 screw dislocations exists in LAGBs. And the size and shape of meshes in the network vary with increased twist angles. The regions separated by dislocations are body-centered cubic arrangement regions (referred as normal regions in this work). In IAGBs, with 17:23 q 22:22 , both atomistic structures and dislocations are disordered and dislocations do not form a regular network. The TGBs with q 23:5 are HAGBs, where no dislocation is observed. The HAGBs can be divided into three sub-types further: special boundaries with low S, boundaries in their vicinity with similar structures as the corresponding special boundary in local regions as well as ordinary HAGBs consisting of periodic patterns. Previously, molecular statics, molecular dynamics and experiments have been combined to study the He bubble nucleation at LAGBs in Au and Cu [26,27]. The results indicate that He bubbles preferentially nucleate at screw dislocation nodal points and a He bubble superlattice is formed, which implies a potential approach for the design of radiation tolerant materials. Kumar et al. [28] simulate the shear deformation of {110} LAGB in a-Fe with and without He bubbles and reveal that the presence of He has a predominantly impact on the mechanical response of this particular dislocation structure, inducing hardening and possibly embrittlement. Despite the valuable resources provided by these early studies, we still lack a comprehensive understanding of the behavior of He atoms in different TGBs. In this work, we focus on the He migration and nucleation behaviors at early stages in different TGBs. In the following, we will first describe the simulation method in section 2. The migration and nucleation behaviors of He atoms in different TGBs are presented in section 3, followed by the conclusions given in section 4.
201
2. Method In this work, the potential for W-He system proposed by Juslin and Wirth [29] is used. They develop a new pair potential for W-He interaction and modify the Acaland-Thetford W-W potential [30] at short range. For He-He interaction, the Beck potential [31] with the short range fit by Morishita et al. [32] is adopted. Before MD simulations, we calculate the parameters for the W-He interaction using the present potential and compare them with those from experiment, DFT calculations and other potentials (Table 1). The comparison indicates that the present potential provide a good description for the W-He interaction. Besides, the present potential proposed by Juslin and Wirth has been widely used in the researches of the W-He interaction, such as He cluster growth [33], He diffusion on grain boundaries [34] as well as He behaviors near surface [35e37], which further prove its reliability. To investigate the effect of GB structures on He migration and nucleation, three typical TGBs are studied: the LAGB with q ¼ 3 , the ordinary HAGB with q ¼ 34:38 and the S3 TGB with q ¼ 70:53 . The details of methodology used in construction of the simulation models of TGBs have been described elsewhere [25,48]. The upper and lower sections of a single crystal rotate about the ½110 direction by 2q clockwise and counterclockwise respectively. After rotation, the equilibrium GB structures are obtained via the combination of conjugate gradient energy minimization and quasidynamic quenching. Periodic boundary conditions are applied along the x and y directions, while a fixed boundary condition is applied along the z direction. The migration and nucleation of He atoms are investigated respectively through two independent simulations. In the first simulation, the mean square displacement (MSD) is used to analysis the migration of a He interstitial, which is randomly inserted in the TGB plane. MSD calculations are performed from 300 to 1200 K with migration time of 1 ns? For each TGB, five calculations are performed to reduce the statistics effect and their results are averaged. In the LAGB, the MSDs are calculated in the dislocation network and normal regions respectively for the apparent difference between them. In the second simulation, the nucleation process of He atoms in TGBs under different He
Table 1 Parameters of the W-He system determined from the present potential, in comparison with those form experiment, density-functional theory (DFT) calculations, the modified embedded atom method (MEAM) potential and the bond-order potential (BOP). a: the lattice constant (Å); Ec : cohesive energy (eV/atom); Ef : formation energy (eV); v: vacancy: SIA: self-interstitial atom; tet: tetrahedral interstitial; oct: octahedral interstitial; db〈ijk〉: 〈ijk〉 dumbbell interstitial configuration. Present a Ec Ef ;v
DFT
Experimental c
d
h,i
3.165 8.90 3.63 10.31
3.18 7.406i 3.46a,3.56b 11.64a,11.05b
EfSIA ;oct
10.41
11.99a,11.68b
12.05h
EfSIA ;db〈100〉 EfSIA ;db〈110〉 EfSIA ;db〈111〉 EfHe ;subs EfHe ;tet EfHe ;oct
10.29
11.74a,11.49b
12.01h
10.18
10.10a,9.84b
9.51
9.82a,9.55b
4.69
4.70a
4.70h
6.15
6.16
a
6.21h
6.38
a
6.39h
EfSIA ;tet
a b c d e f g h i j
Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref.
[38]. [39]. [40]. [41]. [42]. [43]. [44]. [45]. [46]. [47].
6.30
3.165 8.90e 3.7 ± 0.2f
MEAMj
BOP 3.165 8.906h,8.89i 3.52h,1.68i 10.75h
9.53h 9.06 ± 0.63g
9.33h
3.164 8.66 3.95
8.98
202
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Table 2 Dimensions (nm) and the number of W atoms and He atoms in each model. Model Type
LAGB ordinary HAGB S3 TGB Bulk
x
y
12.08 14.98 10.96 8.95
17.68 10.58 15.51 12.66
z
17.90 17.90 17.90 17.90
No. of W atoms
233,440 179,520 192,000 128,000
No. of He atoms 0:1%
0:5%
1%
204 157 168 128
1021 785 840 640
2043 1571 1680 1280
concentration is performed at 300 and 1200 K for 2 ns. He atoms are randomly inserted in the tetrahedral positions within the dynamic region of each model, which are the most stable configuration for He atoms in bulk W [38], to produce the He concentration of 0:1%, 0:5% and 1%. After insertion, the model is relaxed at 0 K for 10 ps, followed by rescaling temperature to desired values and keeping constant afterwards. As a comparison, the bulk W model is also simulated under the same conditions, where the axes are x k ½110, y k ½001 and z k ½110 respectively. The dimensions and the numbers of W and He atoms in each model are given in Table 2. The NPT ensemble is employed to keep temperature constant with a timestep of 1 fs. The diffusion coefficient of He in W is calculated using the Einstein relation:
D¼
MSD 6t
where MSD ¼
(1) PN
! ! r i ðtÞ r i ð0Þ2 , r is the position of He and t is
i¼1 ½
the diffusion time. To accurately calculate the diffusion coefficient, we decompose the single trajectory into a set of shorter independent segments with equal duration and apply Eq. (1) to each segment to calculate Di (Di indicates the diffusion coefficient of the ith segment), followed by averaging Di over all segments. The time interval adopted in this work is 100 ps. The diffusion activation energy (Ea) can be determined from the Arrhenius relation:
. D ¼ D0 exp Ea kb T
(2)
where D0 is the prefactor of diffusion and kb is the Boltzmann constant. The nucleation of He atoms is monitored by counting the number and size of He clusters, defined as He atoms within a distance of 0.2 nm to each other. In order to track the distribution of He atoms with time in the GB normal direction (z direction), each simulation model is divided into thin slabs along the z direction with a thickness of 0.5 nm. The He concentration in each slab is defined as the percentage of the number of He atoms vs the number of W atoms in that slab. Besides, the Wigner-Seitz unit cell is used to identify the self-interstitial atoms (SIAs) and vacancies, which is achieved by the voronoi package of lammps. The whole system volume is divided into Wigner-Seitz unit cells based on the W atoms. Ideally, each unit cell contains one W atom. An empty primitive cell (with no W atoms) is taken as a vacancy, and the extra W atoms (more than one) contained in a primitive cell are taken as SIAs. The MD simulation and the visualization of atomic configurations are achieved through the open-source software LAMMPS
Fig. 1. (aec) He formation energies for different interstitial sites in (a) LAGB, (b) ordinary HAGB and (c) S3 TGB. The spots represent the stable positions for a He interstitial and are colored according the formation energy. (d) The average He interstitial formation energy as a function of the distance from the GB plane. The dashed line represents the He formation energy at the tetrahedral site in bulk W, 6.15 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Y.-X. Feng et al. / Journal of Nuclear Materials 487 (2017) 200e209
203
Table 3 Average binding energy (eV), diffusion activation energies (eV) and prefactor of diffusion (109 m2 =s) for interstitial He to each model. The numbers in the round brackets are the corresponding values for He in the dislocation network of LAGB between 300 and 750 K. LAGB Dislocation network EbHe Ea D0
Ordinary HAGB
S3 special boundary
Bulk
Normal region
2.24
0.08
1.44
0.59
0.284(-0.001) 1.47(0.02)
0.102 8.0
0.012 0.02
0.109 6.67
0.107 31.59
Fig. 2. (a) Mean-square displacement (MSD) of a He atom in each TGB and bulk at 300, 750 and 1200 K. (bef) MSD components along x, y and z directions at 300, 750 and 1200 K in (b) bulk, (c) dislocation network of LAGB, (d) normal region of LAGB, (e) ordinary HAGB and (f) S3 TGB.
[49] and Atomeye [50]. The He interstitial formation energy and binding energy are defined as: He EbHe ¼ EGB EGB EfHe ;bulk Eref ;He
He EfHe ;GB ¼ EGB EGB Eref ;He
and
(3)
(4)
He and E where EGB GB are the energies of the GB with and without He respectively; Eref ;He is the cohesive energy of close packed He, which is 0.0054 eV for the Beck He-He potential; EfHe is the for;bulk mation energy of a He atom in bulk W, which is 6.15 eV for a He atom in the tetrahedral position.
204
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Fig. 3. The lnD-1/T curve of He in each TGB and bulk over the range 300e1200 K.
3. Results and discussion 3.1. The migration of He atoms in TGBs Fig. 1(aec) show the stable positions for the He interstitial in TGBs together with the corresponding formation energy, where the spots represent the stable positions for a He interstitial and the color of spots indicate the magnitude of the formation energy. As we can see, for the LAGB, the formation energy in the normal region is approximately 6.06 eV, which closes the value in bulk W, while the formation energy in the cores of the dislocation network is about 3.9 eV, indicating the screw dislocations in the LAGB are good sinks for He clusters. Influenced by the GB structure, the stable positions are scattered in the ordinary HAGB and arrange in periodic rows in the S3 TGB with the average formation energies of 4.71 and 5.55 eV (Fig. 1(bec)). Fig. 1(d) shows the average He interstitial formation energy as a function of the distance from the GB plane.
The effect influence distance of TGBs is about 0.5 nm, beyond which the average formation energy approaches a stable value. It should be noted that the stable value for the LAGB is smaller than that formation energy in bulk W, which may be caused by the dislocation structure. The average binding energy to the He interstitial in each TGB is given in Table 3. It is apparent that the disordered structures have a much stronger binding to the He interstitial than those ordered. Fig. 2(a) shows the MSDs of a He atom in each model at 300, 750 and 1200 K. At 300 K, the MSDs in TGBs are apparently smaller than that in the bulk especially for the dislocation network of the LAGB and the ordinary HAGB, where the MSDs are negligible. The increasing temperature raises the MSDs to different extents, but does not change the trend. The MSD components along x, y and z directions for each model are presented in Fig. 2(bef). For the bulk, the He atom migrates mainly along the [001] direction at 300 K, and the migration changes from one dimension to three dimension at higher temperature. According to the researches of Shu et al. [51,52], at the temperature below 300 K, the He atom diffuses directly from one TIS (tetrahedral interstitial site) to another, while the migration is a mixture of the TIS-TIS (〈110〉 direction in bulk W) and the TIS-OIS (octahedral interstitial site)-TIS (〈001〉 direction in bulk W) pathes at higher temperature. Combined with our simulation results, we can find that the He atom prefers the TIS-OIS-TIS path rather than the TIS-TIS path when migrating in bulk at 300 K, because the TIS-OIS-TIS path has a shorter diffusion distance. At higher temperature, the enhanced mobility makes the He interstitial migrate along both pathes equally. Compared with the bulk, the magnitude and dimension of the He migration in TGBs are reduced and influenced by the GB structure. For the LAGB, a strong binding to the He atom is obviously observed in the dislocation network, while the He atom can migrate randomly along three directions in normal regions before being trapped by the dislocation network (Fig. 2(ced)). At high temperature, the enhanced mobility makes it possible for the He atom in the normal region to escape from the GB, which is observed several times in our simulations. For the ordinary HAGB, the MSDs are negligible at all temperatures (Fig. 2(e)), demonstrating that the He atom is pinned where it is allocated, which is consistent with the high binding energy shown in Table 3. For the S3 TGB, although there are some
Fig. 4. He concentration profiles at 2 ns for each TGB and bulk with different He concentration and temperature. The dashed lines represent the TGB plane.
Y.-X. Feng et al. / Journal of Nuclear Materials 487 (2017) 200e209
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Fig. 5. Atomic configurations of He atoms, SIAs and vacancies under different He concentration and temperature at 2 ns projected onto the LAGB plane, with the thickness of 0.45 nm.
Fig. 6. Atomic configurations of He atoms, SIAs and vacancies under different He concentration and temperature at 2 ns projected onto the ordinary HAGB plane, with the thickness of 0.45 nm.
fluctuations along ½110 direction, the main contributions to MSD come from ½111 and ½112 directions, indicating that the migration is two-dimensional along the TGB plane (Fig. 2(f)). Previously, Gao et al.[53,54,55] report the He diffusion at the S11〈110〉f323g and
S3〈110〉f112g tilt GBs in a-Fe. The single He interstitial diffuses in the S11 tilt GB with one-dimensional migration along the ½113 direction, whereas it migrates two-dimensionally at low temperature (600e800 K), and three-dimensionally in the S3 tilt GB at high
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Fig. 7. Atomic configurations of He atoms, SIAs and vacancies under different He concentration and temperature at 2 ns projected onto the S3 TGB plane, with the thickness of 0.45 nm.
temperature (1200 K). Three-dimensional diffusion behavior of He interstitial is an indicator of the dissociation of the He interstitial form GB at high temperature. In contrast, the migration dimensionality of He interstitial in each TGB remains unchanged at high temperature, suggesting that the binding of TGBs to He interstitial is stronger. The diffusion-temperature (expressed as lnD-1/T) curve of He in W in the temperature range from 300 to 1200 K is shown in Fig. 3. As seen in Fig. 3, the diffusivity of He in TGBs is apparently lower than that in bulk at the same temperature, especially for the dislocation network of the LAGB and the ordinary HAGB. In the dislocation network of LAGB, the He atom hardly moves under the temperature range from 300 to 750 K, owing to the strong binding energy. When the temperature is higher than 750 K, the He atom has enough energy to overcome the barrier and migrates. A stronger trapping effect is observed in the ordinary HAGB, where the He atom is not activated at all temperatures, due to its disordered GB structure. The fitted diffusion activation energies and prefactors are shown in Table 3. The diffusion activation energy of He in bulk is 0.107 eV, which is between the diffusion barrier along the TIS-TIS path (0.023 eV) and that along the TIS-OIS-TIS path (0.174 eV) [51,52], indicating the migration of He in bulk is a mixture of the TIS-TIS and the TIS-OIS-TIS paths. Since the He atom is trapped and hardly moves, the diffusion activation energies of He in the dislocation region of the LAGB between 300 K and 750 K and the ordinary HAGB do not represent the real diffusion barrier. The diffusion activation energy of He in the dislocation region between
750 K and 1200 K is 0.284 eV, which is larger than that in bulk, suggesting He migration is more difficult. In contrast, the diffusion activation energies of He in the normal region of the LAGB and the S3 TGB (0.102 and 0.109 eV respectively) are close to that in bulk. However, the migration of He is influenced by the dislocation network in the normal region of LAGB and limited in the diffusion dimension in the S3 TGB, hence, the He atom has lower prefactors of diffusion compared to the bulk, thus resulting in a lower diffusivity. In this section, the migration behaviors of a He atom in TGBs at different temperatures are presented. Contrary to the paradigm that GBs facilitate the migration of impurities, we find that TGBs inhibit the He migration in both magnitude and dimension. This phenomenon arises from the relative insolubility of He in most materials combined with the size mismatch between He and W, which results in an interstitial diffusion mechanism rather than diffusion that relies on the presence of self-vacancies [34]. Moreover, the migration feature of the He atom in TGBs depends on the GB structure. The dislocation network in the LAGB can effectively attract and bind He atoms, implying a potential way to control the He distribution on the GB plane. Compared with the dislocation network, the ordinary HAGB behaves a stronger trap effect, which may induce a large retention of He atoms at the GB region and embrittlement. Different from the other two TGBs, the S3 TGB can provide a diffusion path for He atoms, despite the diffusion rate is not as fast as it in bulk.
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Fig. 8. (a) He cluster density, (b) average size and (c) number of SIA as a function of He concentration for each TGB and bulk W at 300 and 1200 K.
3.2. The nucleation of He atoms in TGBs Fig. 4 shows the He concentration profiles at 2 ns under different He concentration and temperature. A strong precipitation of He atoms in TGBs is observed in Fig. 4, which is enhanced at higher temperature. At the He concentration of 0:1%, most He atoms precipitate at the TGBs; However, some He atoms begin to
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accumulate beyond the TGBs as the increase of the He concentration, manifesting that there is a limit on the attraction of the TGBs to He atoms. The corresponding distribution of defects (He atoms, SIAs and vacancies) on each TGB plane is presented in Figs. 5e7, with a thickness of about 0.45 nm. As seen in Fig. 5, at the He concentration of 0:1% and 300 K, isolated He atoms distribute loosely along the dislocation network in the LAGB (Fig. 5(a)). As the He concentration increases, some He atoms accumulate and form small He clusters (Fig. 5(bec)). When temperature rises to 1200 K, most He atoms change from isolated He atoms to clustered He atoms and these defects distribute strictly along the dislocation network except the He clusters and SIAs marked in Fig. 5(f), implying the He concentration of 1% may excess the capacity of the dislocation network. Different from the distribution of defects in the LAGB, the defects distribute randomly within the ordinary HAGB (Fig. 6), owing to its relatively disordered GB structure. It is worthy to note that there are abundant isolated He atoms in the ordinary HAGB plane, no matter what the He concentration and temperature are, which further proves the high He binding energy in this boundary. For the S3 TGB, He atoms, mainly in the form of isolated He at 300 K and clustered He ate 1200 K, distribute randomly within the boundary other than several isolated He atoms arranging in a row (Fig. 7). As revealed by Fig. 1(c), the most stable configuration for He atoms in the S3 TGB is in the arrangement of periodic rows, which is distinctly different from the distribution of He atoms shown in Fig. 7. This phenomenon can be explained by the slight formation energy difference and low binding energy for the He atom in the S3 TGB. The maximum formation energy difference in the S3 TGB is 0.67 eV, which is much smaller than that in the LAGB and ordinary HAGB, 2.51 and 1.42 eV respectively, indicating that the He atom is relatively stable even at the position with a high formation energy. And the low binding energy guarantees that the He atom can migrate easily within the boundary, as seen in Fig. 2(f). These two factors lead to the random distribution of He atoms in the S3 TGB. Besides, influenced by the horizontal stripe structure of this TGB, SIAs tend to distribute in a row and its number is fewer than in the other two TGBs, which is clearly shown in Figs. 7e8. Fig. 8 describes the variation of the cluster density, average cluster size and number of SIAs with the He concentration and temperature. As described in Fig. 8, the cluster density increases with He concentration and decreases with temperature, while the average cluster density increases obviously as the rise of temperature and reaches a peak at the He concentration of 0:5%. Under the same condition, the order by size of the cluster density for each model are contrary to that of the average cluster size, which is also observed at S3 and S73b tilt GBs in a-Fe [19]. In contrast to the bulk, TGBs have higher cluster densities and smaller average sizes at 1200 K, which coincides with previous simulations [19,20], while such comparison shows no regularity at 300 K. Recent simulations about the He nucleation at the twist, tilt and twin GBs in Mo [20] reveal that the GB trapping effect helps to stabilize He atoms or clusters as embryos of bubbles and impedes further growth of He clusters by absorption of mobile He atoms, resulting in a higher density and smaller average size of He clusters. Moreover, the change in the dimensionality of diffusion due to the GB trapping in turn affects the distribution of He bubbles. All these are in agreement with our results at 1200 K. At 300 K, the GB trapping effect is unapparent because of the low mobility of He atoms. The number of SIAs behaves diversely at different temperature, which is not sensitive to the He concentration at 300 K, but increases linearly with the He concentration at 1200 K. And it seems that the number of SIAs in ordered structures is smaller than that in disordered ones. In this section, the nucleation behaviors of He atoms in TGBs under different He concentrations and temperatures are presented.
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A strong precipitation of He atoms in TGBs is observed and the growth of He bubbles is impeded, which will relieve void swelling or other modification to the microstructure. Furthermore, in the LAGB, He atoms distribute along the dislocation network especially at high temperature, indicating a effect approach to control He distribution namely forming a dislocation network. 4. Conclusion The migration and nucleation of He atoms in TGBs are studied using MD simulations, and compared with that in bulk W. Three typical TGBs are investigated in this work: the low-angle grain boundary (LAGB) with a dislocation network, the ordinary highangle grain boundary (HAGB) consisting of periodic patterns and the S3 TGB with good symmetry. In bulk W, the He atom migrates dimensionally along the [001] direction at 300 K and three dimensionally at higher temperature. Compared with the migration in bulk W, the magnitude and dimensionality of He migration in TGBs are reduced and influenced by the GB structure. In the LAGB, the He atom is either trapped by the screw dislocations or migrates randomly along three directions in the normal regions. The ordinary HAGB has a similar but stronger trap effect in contrast to the dislocation network of the LAGB. The He atom is pinned where it is allocated and hardly moves. In the S3 TGB, the He atom migrates two dimensionally along the TGB plane, although there are some fluctuations of the MSD along the ½110 direction. As higher temperature, the MSDs rise to different extents, but the migration dimensionality of He in each TGB does not change. The nucleation of He atoms in TGBs depends on temperature, He concentration and GB structure. A strong precipitation of He atoms in TGBs is observed and enhanced at higher temperature, while more and more He atoms accumulate beyond TGBs as the He concentration increases. On the TGB plane, He atoms distribute along the dislocation network in the LAGB and randomly in the other two TGBs. In contrast with bulk W, TGBs have higher cluster densities, smaller average cluster sizes and more emission of SIAs at 1200 K, while such comparison shows no regularity at 300 K. The above presented He migration and nucleation behaviors in TGBs under different conditions will contribute to the design of radiation tolerant materials. Acknowledgements The authors acknowledge the financial support from the National Magnetic Confinement Fusion Program under Grant No. 2013GB109002. The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A). References [1] V. Barabash, G. Federici, R. Matera, A.R. Raffray, ITER Home Teams, Armour materials for the iter plasma facing coments, Phys. Scr. T81 (1999) 74e83. [2] G. Federici, R.A. Anderl, P. Andrew, et al., In-vessel tritium retention and removal in iter, J. Nucl. Mat. 266e269 (1999) 14e29. [3] G. Federici, H. Wuerz, G. Janeschitz, R. Tivey, Erosion of plasma-facing components in iter, Fusion Eng. Des. 61e62 (2002) 81e94. [4] G.J. Thomas, Experimental studies of helium in metals, Radiat. Eff. Defects Solids 78 (1983) 37e51. [5] H. Trinkaus, B.N. Singh, Helium accumulation in metals during irradiation where do we stand? J. Nucl. Mat. 232 (2003) 229e242. [6] H. Iwakiri, K. Yasunaga, K. Morishita, N. Yoshida, Microstructure evolution in tungsten during low-energy helium ion irradiation, J. Nucl. Mat. 283e287 (2000) 1134e1138. [7] M. Miyamoto, D. Nishijima, M.J. Baldwin, R.P. Doerner, Y. Ueda, K. Yasunaga, N. Yoshida, K. Ono, Microscopic damage of tungsten exposed to deuteriumhelium mixture plasma in pisces and its impacts on retention property, J. Nucl. Mat. 415 (2011) S657eS660.
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