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Effects of Zr and V additions on the stability and migration of He in bcc W: A first-principles study
Physics Letters A 383 (2019) 2777–2783
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Physics Letters A www.elsevier.com/locate/pla
Effects of Zr and V additions on the stability and migration of He in bcc W: A first-principles study Ningning Zhang a , Yujuan Zhang a,∗ , Yu Yang b , Ping Zhang b , Changchun Ge a,∗ a b
Institute of Nuclear Materials, School of Materials Science and Engineering, University of Science and Technology Beijing (USTB), Beijing 100083, China LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
a r t i c l e
i n f o
Article history: Received 1 January 2019 Received in revised form 12 April 2019 Accepted 19 May 2019 Available online 22 May 2019 Communicated by R. Wu Keywords: Tungsten Helium Zirconium Vanadium Stability Diffusion
a b s t r a c t The effects of zirconium (Zr) and vanadium (V) on the dissolution, diffusion and trapping behaviors of helium (He) in body-centered cubic (bcc) tungsten (W) have been investigated using first-principles simulations. We found that Zr and V atoms usually prefer to disperse into W-rich region rather than aggregate in W host lattice. Energetically, the relatively stable position for an interstitial He remains the tetrahedral interstitial site in W with the presence of Zr/V atom. The solution energy of the He atom is reduced because of the attractive interaction between He and Zr/V atom. Compared to W with Zr, the stronger attractive interaction between V and He results in the lower He solution energy in W with V. Kinetically, the He atom diffusion to Zr/V has a lower energy barrier than that of He diffusion to W along the optimal diffusion path TIS–TIS. In addition, the existing Zr/V atom improves the ability of Zr/VVacancy complex to capture He atom. These results provide incontrovertible evidence that the existing Zr/V atom has great influence on the behavior of He atom in bulk W. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In the past decade, extensive research has been concentrated on the development of renewable energy. Among of them, nuclear fusion energy has been considered as a promising energy due to its clean and economical energy with nearly infinite resource. DEMO, based on the International Thermonuclear Experimental Reactor (ITER) experimental nuclear fusion reactor, is expected to lead to full-scale electricity-producing fusion power stations and future commercial reactors [1]. The plasma-facing components as a fundamental and important component in DEMO are designed to withstand the high energy neutron environment resulting from the fusion reactions. Due to harsh condition, the materials used in plasma-facing components calls for high demands for its property. Thus, the choice of plasma facing materials (PFM) plays a key role in the successful development of DEMO. Tungsten (W), a high-Z material, has been chosen to be the main candidate material for the PFM [2], owing to its high melting point, excellent stability at elevated temperature, good thermal conductivity, low sputtering yield, and excellent anti-plasma sputtering [3–5]. Apparently, the surface of W will be exposed to extremely high fluxes of He ions and the transmutation He, which directly leads to the dis-
*
Corresponding authors. E-mail addresses: [email protected] (Y. Zhang), [email protected] (C. Ge). https://doi.org/10.1016/j.physleta.2019.05.035 0375-9601/© 2019 Elsevier B.V. All rights reserved.
placement damage, bubble formation, and ultimate failure of the material [6–8]. Recent experiments led to the conclusion that large bubbles formed after He exposure can grow and reach the surface, leading to repeated surface exfoliation of about a 1 μm thick layer [6,9]. He-induced damage at the surface of W is one of the most important problems that restrict its application as PFM [10]. In addition, another important problem to hinder the usage of W is its near non-existent ductility at room temperature with a high ductile-to-brittle transition temperature (DBTT). It has been proposed that alloying a small amount of impurities zirconium (Zr) and vanadium (V) have great influence on improving the ductility of W material by improving dislocation mobility, refining microstructure or increasing the recrystallization temperature [11–15]. Undoubtedly, the He ions will inevitably interact with these impurities and studying the interaction between these impurities and He atom in W is very important. The previous results pointed out the relationship between the binding energies of Zr and V additions with He atom [16,17]. However, the effects of both additions on the stability, migration, and trapping behaviors of He in body centered cubic (bcc) W are largely unknown, which are difficult to be observed from experimental studies. In this work, using first-principles calculations, the effects of Zr and V additions on He behavior in bcc W were systemically investigated. The most stable configurations for a single interstitial He atom surrounded by one Zr or V atom are evaluated by solution energy, and it has been explained by the charge-density
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Fig. 1. The configurations for X-X pair (X denotes Zr or V) with different distances: (a) 1nn, (b) 2nn and (c) 3nn; (d) configuration of X-vacancy pair with 1nn. The pink spheres show the bcc W lattice sites; the gray spheres are the sites of X atom; the open square is a vacancy. 1nn/2nn/3nn means the first/second/third nearest neighbor. Note that the small cubic is not the unit cell used in calculation; rather, it displays the local structure of around the defect. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
simulations and local electronic densities of states (LDOS). The HeZr/He-V interaction as a function of the distance are calculated. The migration barriers of He atom in the presence of Zr or V addition are determined. In addition, the trapping behavior for multiple He atoms inside a vacancy with and without Zr or V are discussed. We hope that those results will not only be quite helpful to understand the interaction of He and Zr/V but also can form the foundation of higher-level models. 2. Computational methods In this study, density functional theory calculations of the effects of Zr and V additions on the stability and migration of He in bcc W were performed using the projector-augmented-wave method [18] as implemented in the Vienna ab initio simulation package (VASP) developed at the Technical University of Vienna [19,20]. All the electron exchange correlation functional was calculated using the Perdew–Burke–Ernzerh of approximation (PBE) described by the generalized gradient approximation (GGA) [21]. A plane-wave cutoff of 350 eV was used in all calculations. Systematic calculations presented here have been performed on 128-atom in a 4 × 4 × 4 supercell with periodic boundary condition. The Brillouin-zone integration was performed within Monkhorst-Pack scheme using a 3 × 3 × 3 mesh for the geometry optimizations and 4 × 4 × 4 mesh for electronic calculations [22]. The diffusion pathways of single He atom in W with/without Zr or V atom were calculated using the climbing-image nudged elastic band (CI-NEB) simulations [23]. Both supercell size and atomic positions are relaxed to equilibrium, and energy minimization is continued until the forces on all atoms are converged to smaller than 10−2 eV/Å. The total energy of each system was relaxed until the difference value is smaller than 10−5 eV. A −A The binding energy of two defects (A1 , A2 ), E b 1 2 , is calculated as follows: A − A2
Eb 1
A2 A1 + A2 A1 bulk = E tot + E tot − E tot − E tot A + A2
where E tot1
(1)
is total energy of the supercell containing both A1 A
bulk and A2 ; E tot is total energy of perfect W in supercell; E tot1 and A E tot2
are total energies of the supercell with A1 and A2 , respectively. With such a scheme a negative binding energy means repulsion between the entities, while a positive binding energy indicates a attraction. All the supercells contain the same number of sites, i.e., have the same size. The solubility of He in W pure containing a X atom (X=Zr, V) can be characterized by the solution energy (E sol He ), which is given as:
E sol He = E 1 X , He − E 1 X − E He ,isolated
(2)
Table 1 Binding energies (eV) of Zr-Zr, V-V, Zr-vacancy and V-vacancy pairs. Configuration
E bZ r − Z r /eV
E bV − V /eV
E bZ r − vac /eV
E bV − vac /eV
1nn 2nn 3nn
−2.923 −2.397 −2.342
−2.749 −0.076 −0.040
−1.0559
−0.430
– –
– –
where E 1 X , He are the energies of the supercell with He atom and a X atom; E 1 X is the energy of the supercell with a X atom; the E He,isolated is the energy of an isolated He atom (a single He in supercell). trap The trapping energy (E X − v , He ) of per He atom sequentially trapped by the X-vacancy (X-v) pair can be obtained by: trap
E X − v , He = E X − v , Hen − E X − v , Hen−1 − ( E W , He( T −site) − E W )
(3)
where E X − v , Hen and E X − V , Hen−1 are the total energies of the X-v complex system with n and n − 1 He atoms, respectively; n is the number of He atoms at the X-v pair; E W , He(T −site) and E W are the energies of the W supercells with and without He atom, retrap spectively. A negative E X − v , He means energy gain when the He atom is trapped by vacancy relative to their being dispersed into different tetrahedral sites. 3. Results and discussion 3.1. He solution energy in presence of Zr and V To estimate the influence of zirconium (Zr) and vanadium (V) on solubility of helium (He) atom in bcc tungsten, we first investigated the existing form of alloying element in intrinsic pure W. The binding energies of Zr-Zr and V-V pairs with different distance in intrinsic pure W were calculated. The previous theoretical results showed that both Zr and V elements prefer to occupy the substitutional site in W [16,17,24]. Thus, we arranged two alloying elements on two different substitutional sites of W to form Zr-Zr or V-V pairs, and the schematic diagram of these configurations are illustrated in Fig. 1. The calculated binding energies of Zr-Zr and V-V pairs are calculated using Eq. (1) and listed in Table 1. In Table 1, all of the Zr-Zr and V-V pairs as 1nn, 2nn, 3nn configurations have negative binding energies, implying that the interaction of two defects is repulsive interaction. It indicates that Zr and V atoms usually prefer to disperse into W-rich region rather than aggregate in W host lattice. A single He atom can occupy either a tetrahedral interstitial site (TIS) or an octahedral interstitial site (OIS) in the intrinsic pure W. In our previous work, we have already studied the relative stability of the various He interstitial sites, and the results show that He atom at TIS (6.41 eV) is more stable than OIS one (6.64 eV) [25, 26]. The He solution energy at different TIS and OIS were calculated to determine the He preferential site in W with presence of
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Fig. 2. Local atomic configurations and calculated solution energies for He at the TIS and OIS near one Zr or V atom in comparison with the data of He in intrinsic pure W. The pink, yellow, green, and blue spheres denote W, Zr, V and He atoms, respectively.
Fig. 3. Total charge densities for He-solute defects in W. (a), (b) and (c) are He-W, He–Zr and He-V in (0 0 1) plane, respectively. The units are eÅ−3 .
Zr/V addition. After full relaxation of these configurations, the solution energy of He are calculated using Eq. (2) and represented in Fig. 2. It can be clearly seen that the solution energy of He atom at TIS is lower than that of at OIS in both W with presence of Zr and W with presence of V systems. Thus, we conclude that He atoms still prefer to occupy a TIS in W with presence of Zr/V addition. However, the solution energy of He atom at both TIS and OIS in W with presence of Zr/V are lower than that in intrinsic pure W. The binding energy between Zr/V and He atoms are calculated using Eq. (1) to explain the reason for it. A positive binding energy means attraction between Zr/V and He atoms. The binding energy between Zr/V and He atoms is 0.68 eV/0.96 eV, which indicates that the attractive interaction plays a dominant role between the Zr/V and He atoms. The result in this calculation agrees with the reported previous work [16,17]. We also find that the binding energy between V and He atoms is larger than that between V and He atoms. Moreover, the solution energy of He atom at interstitial sites in presence of V is lower than that in presence of Zr, and the distance of V-He is smaller than that of Zr-He. These imply that the attractive interaction between V and He atoms is stronger than that between Zr and He atoms. However, the mechanism of these observations is not clear and the correlation of solution energy with the electronic structure was needed to interpret.
There is a general consensus that He atom prefers to keep its own electronic structure due to its closed-shell electronic structure. It has been found that He likes to occupy the low charge density regions and its solution energy is directly proportional to electron density [26–28]. To clarify the electron effect on the He solution energy, the total charge densities for He in intrinsic pure W, W with presence of Zr and V additions are calculated, respectively, which are shown in Fig. 3. It is obvious that a broader region of very low charge density around He with the presence of the solute Zr/V, which indicates that the charge density is reduced around the Zr/V. The charge density depletion around the Zr/V leads to the strong attraction between the Zr/V atom and He atom and a decrease in the solution energy of He atom. By comparison of charge densities around Zr (Fig. 3b) and V (Fig. 3c), a lower charge density near V is seen while the charge density around Zr is relatively higher, which gives rise to the stronger attractive interaction between V and He atom and the lower solution energy of He in W with presence of V. The hybridization of He atom in different systems can also be observed from the calculated local electronic densities of states (LDOS). The LDOS for d-states of the neighboring W atom and p-states of the He atom have been investigated and plotted in Fig. 4. It can be seen from Fig. 4 that the impurities Zr and V
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Fig. 4. Local DOS for the substitutional impurities Zr and V compared with that of the system without additions. (a) the d-states for the neighboring W atoms; (b) the p-state for the He atom. The zero energy point indicates the Fermi level of the supercell with the He defect.
Fig. 5. (a) The solution energy He atom and (b) the binding energy between Zr/V and He atoms in W with X (X=Zr, V) atom as a function of the He-X distance. The blue spheres show the sites of single He atom; the pink spheres are the bcc W lattice sites; the gray sphere shows the site of X atom.
produce distortion of the LDOS of the neighboring W atoms and He atoms, which indicates the ongoing hybridization. The p-states near the Fermi energy are particularly unfavorable for He atom due to He is an atom with a completed spherically symmetric s shell [29,30]. The large He p-states at the Fermi energy level is not conducive to the energetically favorable for the corresponding He defect configuration [29]. From Fig. 4(b) one can see that, the p-states at the Fermi energy level of He atom for W with presence of Zr and V are lower than that of He atom for intrinsic pure W, and the p-states at the Fermi energy level of He atom for W with presence of V is the lowest. Therefore, the solution energy of He at ITS in W with Zr/V atom are lower than that of He at ITS in intrinsic pure W, and the solution energy of He at TIS in W with presence of V is the lowest. To investigate the interactions of He-Zr and He-V pairs inside W solid, we computed the solution energies of He atom and the binding energy between Zr/V and He atoms with different He-Zr/V using Eq. (2) and Eq. (1), respectively. According to the stable occupy site for impurity Zr or V atom and He atom in W, we replaced one W atom by one Zr or V atom and then put a single He atom into the TIS surrounding the impurity atom to form a He-Zr or He-V pair. The initial configurations are shown in the Fig. 5(a). All different configurations involving the different distances between He and Zr or V are full relaxed. We find that the He atom is occupied at site A for the initial configuration B including impurity Zr atom, which suggests that there is an attraction interaction between He and Zr atoms in the initial structure. The solution energy of He atom at all TIS in intrinsic pure W is equal and the value is 6.41 eV. In Fig. 5, we can see that the He solution energy in W with impurity Zr or V are lower than that of He at the TIS in pure W and the binding energy between Zr/V and He atoms is positive,
Table 2 The initial and finial distances between Zr/V and He atoms for different configuration. Configuration
A
B
C
D
E
F
initial finial (Zr-He) finial (V-He)
1.772 1.875 1.628
2.857 1.875 2.78
3.633 3.550 3.630
4.267 4.267 4.267
4.820 4.820 4.820
5.760 5.760 5.760
indicating that the attractive interaction plays a dominant role between the He and Zr/V atoms. As revealed by Fig. 5 (a), the He and Zr or V atoms attract with each other with a screening distance of about 5.76 Å, beyond which the He and Zr or V atoms are nearly non-interactive. The trapping radius is the distance beyond which the attraction of He towards impurities is considered negligible [16]. Thus, the trapping radius of Zr/V atom on He is about 5.76 Å. Moreover, according to the initial and finial distances between Zr/V and He atoms as shown in Table 2, He atom spontaneously migrates to Zr/V atom when the initial distance between Zr/V and He atoms is less than 3.633 Å, which suggests that there is a strong attractive interaction between Zr/V and He atoms. It should be noted that the results are in good agreement with the previous theoretical study by Wu [16,17], confirming the accuracy of our work. 3.2. Effects of Zr and V on He diffusion Up to date, much effort has been directed toward the He migration behavior in metals [30–33]. We investigated the He migration barrier by possible paths of He from a sixth nearest-neighbor TIS (6nn TIS as site F) diffusing to a first nearest-neighbor TIS (1nn TIS as site A) near Zr and V using the CI-NEB simulations in order to
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Fig. 6. Diffusion barrier for He moving from a far 6nn (F) TIS to a 1nn (A) TIS near (a) Zr and (b) V in W.
Fig. 7. (a) Eight high-symmetric sites for a single He atom in W with Zr/V-Vacancy complex; (b) the most stable configuration for a single He atom in W with Zr/V-Vacancy complex; (c) trapping energies as function of the number of He atoms trapped in W with vacancy and W with Zr/V-Vacancy complex, respectively.
study the effects of Zr or V on He diffusion kinetically. All six sites are stable TISs. The migration barrier barriers and corresponding diffusion paths for He diffusing to a Zr or V atom are explored and presented in Fig. 6. The calculated migration barriers, not only for He diffusing to Zr atom but also for He diffusing to V atom, are lower than that of He along the optimal diffusion path TIS–TIS in intrinsic pure W, which has a diffusion energy barrier of 0.057-0.060 eV [31,32]. It suggests that the Zr or V addition makes He migration much easier comparing with He in intrinsic pure W. Noticing that no diffusion barrier exists as He jumps into 1NN ITS (as site A) from the 2NN TIS (as sit B) for W with V addition, which indicates a downhill “drift” diffusion of He toward the 1NN ITS. On the other hand, if the He interstitial diffuse into the Zr region, He atom needs to overcome a highest energy barrier of 0.053 eV for path D-E, as shown in Fig. 6a. But to enable a real diffuse into the V region, He atom needs to overcome a highest energy barrier of 0.051 eV for path B-C, as shown in Fig. 6b. Based on our calculation results, the trapping radius of Zr/V atom on He is about 5.76 Å (the distance between He at site D and Zr is about 5 Å, and the distance between He at site B and V is 2.78 Å), illustrating that there are attraction and between He at site B and V. Thus, the He atom diffuses into the solute rather than diffusing back to the bulk interstitial site. From the kinetics point of view, the migration of He for W with presence of V is easier than that of He for W with presence of Zr. Because the main difference between two configurations lies in the kinds of additions, variation in the migration barrier of the configurations should be attributed to the presence
of additions. We suppose that the stronger attractive interaction between V and He atom dominate the lower migration barrier. 3.3. Monovacancy trapping for multiple He in presence of Zr and V Vacancy, as a typical defect in metals, plays a significant role in both the structural and mechanical properties of metals. The vacancy has always drawn intense interest owing to its effects on He behaviors such as solution and diffusion and can act as trapping center for He atom [32,33]. The calculations above show that the presence of Zr/V causes a crucial effect on solution behaviors of He in W. To understand the effect of Zr/V on the stability of He Zr/VVacancy complex in dilute Zr-W or V-W systems, a vacancy near Zr or V by removing a W atom was created, as shown in Fig. 1(d). The calculated binding energies of Zr-Vacancy and V-Vacancy pairs in are listed in Table 1. The positive binding energy means the repulsion interaction between Zr/V and vacancy. The possible positions described for a He atom surrounding Zr/V-Vacancy complex in W are described in Fig. 7(a). After the optimization of these systems, we find that the most stable site for He atom in W with existing Zr/V-Vacancy complex is still the exact center of the vacancy, which is shown in Fig. 7(b). It is the same as He atom in W with self-vacancy. Thus, the Zr/V-Vacancy complex can also as trapping center for He atom. To further understand the effect of Zr/V on vacancy trapping for multiple He atoms, the trapping energy which characterize the energy required for moving He atoms into the vacancy space from a remote TIS in sequential way are obtained using Eq. (3). In pre-
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that between Zr and He. Our calculations also reveals that the He atom diffusion to Zr/V has a lower energy barrier than that of He diffusion to W along the optimal diffusion path TIS–TIS. Moreover, the existing Zr/V atom improves the ability of Zr/V-Vacancy complex to capture He atom. The results from this work can shed light on the understanding the influence of existing Zr/V atom on He atom at an atomic level. Acknowledgements This work was supported by Beijing Municipal Natural Science Foundation (Grant No. 2182042) and the National Natural Science Foundation of China (Grant No. 11875004, 11505006, 11604008). References
Fig. 8. Binding energies as function of the number of He atoms between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He in W with vacancy and W with Zr/VVacancy complex, respectively.
vious work, calculation based on density functional theory (DFT) showed that a W vacancy can contain at least nine He atoms [34]. Therefore, the trapping energy of the first to ninth He atom trapped in W with vacancy and W with Zr/V-Vacancy complex in W with vacancy are calculated. The He trapping energy increase as the number of He atoms trapped increasing on the whole, as shown in Fig. 7(c), meaning that the stability of unit cell gradually reduces. The He trapping energy of W with Zr/V-Vacancy complex shows a lower trapping energy than that of Zr/V-free vacancy with the corresponding He number, implying that the Zr/V-Vacancy-Hen complex is more stable in comparison with the Zr/V-free case, and V effect is slightly stronger than Zr. Thus, for the He atom to escape from the Zr/V-Vacancy complex is more hard. The existing Zr/V atom improves the ability of Zr/V-Vacancy complex to capture He atom and this should be attributed to the stronger attractive interaction between Zr/V and He atom. As shown in Fig. 7c, there is no obvious change of trapping energies with and without the solute Zr or V when the number of He is 3, 4 and 9. Therefore, binding energies as function of the number of He atoms between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He in W with vacancy and W with Zr/V-Vacancy complex are calculated to check if Zr/V can promote the binding of the complex. As seen from Fig. 8, binding energies between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He atoms are positive, suggesting that there are mutual attraction between them. The binding energy between Zr/V-Vac-Hen-1 and He is higher than that between Vac-Hen-1 and He atoms for the corresponding He atom. When the number of He is 3, 4 and 9, the trapping energy between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He is 3.15/3.17/3.18 eV, 3.28/3.33/3.36 eV, 2.83/2.85/2.90 eV. Despite the difference in the value is very small, but contribution from Zr/V to promote the binding of the complex can not be neglected. 4. Conclusions We performed the theoretical study of the effects of zirconium (Zr) and vanadium (V) on the dissolution, diffusion and trapping behaviors of helium (He) in tungsten (W) by means of first-principles calculations. The present calculations clearly predict that the tetrahedral interstitial site (TIS) is still the most stable site for an interstitial He in W with the presence Zr/V atom. Meanwhile, the solution energy of the He atom is reduced because of the attractive interaction between He and Zr/V atom. Interestingly, a lower He solution energy in W with V is obtained which results from the stronger attractive interaction between V and He than
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Physics Letters A www.elsevier.com/locate/pla
Effects of Zr and V additions on the stability and migration of He in bcc W: A first-principles study Ningning Zhang a , Yujuan Zhang a,∗ , Yu Yang b , Ping Zhang b , Changchun Ge a,∗ a b
Institute of Nuclear Materials, School of Materials Science and Engineering, University of Science and Technology Beijing (USTB), Beijing 100083, China LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
a r t i c l e
i n f o
Article history: Received 1 January 2019 Received in revised form 12 April 2019 Accepted 19 May 2019 Available online 22 May 2019 Communicated by R. Wu Keywords: Tungsten Helium Zirconium Vanadium Stability Diffusion
a b s t r a c t The effects of zirconium (Zr) and vanadium (V) on the dissolution, diffusion and trapping behaviors of helium (He) in body-centered cubic (bcc) tungsten (W) have been investigated using first-principles simulations. We found that Zr and V atoms usually prefer to disperse into W-rich region rather than aggregate in W host lattice. Energetically, the relatively stable position for an interstitial He remains the tetrahedral interstitial site in W with the presence of Zr/V atom. The solution energy of the He atom is reduced because of the attractive interaction between He and Zr/V atom. Compared to W with Zr, the stronger attractive interaction between V and He results in the lower He solution energy in W with V. Kinetically, the He atom diffusion to Zr/V has a lower energy barrier than that of He diffusion to W along the optimal diffusion path TIS–TIS. In addition, the existing Zr/V atom improves the ability of Zr/VVacancy complex to capture He atom. These results provide incontrovertible evidence that the existing Zr/V atom has great influence on the behavior of He atom in bulk W. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In the past decade, extensive research has been concentrated on the development of renewable energy. Among of them, nuclear fusion energy has been considered as a promising energy due to its clean and economical energy with nearly infinite resource. DEMO, based on the International Thermonuclear Experimental Reactor (ITER) experimental nuclear fusion reactor, is expected to lead to full-scale electricity-producing fusion power stations and future commercial reactors [1]. The plasma-facing components as a fundamental and important component in DEMO are designed to withstand the high energy neutron environment resulting from the fusion reactions. Due to harsh condition, the materials used in plasma-facing components calls for high demands for its property. Thus, the choice of plasma facing materials (PFM) plays a key role in the successful development of DEMO. Tungsten (W), a high-Z material, has been chosen to be the main candidate material for the PFM [2], owing to its high melting point, excellent stability at elevated temperature, good thermal conductivity, low sputtering yield, and excellent anti-plasma sputtering [3–5]. Apparently, the surface of W will be exposed to extremely high fluxes of He ions and the transmutation He, which directly leads to the dis-
*
Corresponding authors. E-mail addresses: [email protected] (Y. Zhang), [email protected] (C. Ge). https://doi.org/10.1016/j.physleta.2019.05.035 0375-9601/© 2019 Elsevier B.V. All rights reserved.
placement damage, bubble formation, and ultimate failure of the material [6–8]. Recent experiments led to the conclusion that large bubbles formed after He exposure can grow and reach the surface, leading to repeated surface exfoliation of about a 1 μm thick layer [6,9]. He-induced damage at the surface of W is one of the most important problems that restrict its application as PFM [10]. In addition, another important problem to hinder the usage of W is its near non-existent ductility at room temperature with a high ductile-to-brittle transition temperature (DBTT). It has been proposed that alloying a small amount of impurities zirconium (Zr) and vanadium (V) have great influence on improving the ductility of W material by improving dislocation mobility, refining microstructure or increasing the recrystallization temperature [11–15]. Undoubtedly, the He ions will inevitably interact with these impurities and studying the interaction between these impurities and He atom in W is very important. The previous results pointed out the relationship between the binding energies of Zr and V additions with He atom [16,17]. However, the effects of both additions on the stability, migration, and trapping behaviors of He in body centered cubic (bcc) W are largely unknown, which are difficult to be observed from experimental studies. In this work, using first-principles calculations, the effects of Zr and V additions on He behavior in bcc W were systemically investigated. The most stable configurations for a single interstitial He atom surrounded by one Zr or V atom are evaluated by solution energy, and it has been explained by the charge-density
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Fig. 1. The configurations for X-X pair (X denotes Zr or V) with different distances: (a) 1nn, (b) 2nn and (c) 3nn; (d) configuration of X-vacancy pair with 1nn. The pink spheres show the bcc W lattice sites; the gray spheres are the sites of X atom; the open square is a vacancy. 1nn/2nn/3nn means the first/second/third nearest neighbor. Note that the small cubic is not the unit cell used in calculation; rather, it displays the local structure of around the defect. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
simulations and local electronic densities of states (LDOS). The HeZr/He-V interaction as a function of the distance are calculated. The migration barriers of He atom in the presence of Zr or V addition are determined. In addition, the trapping behavior for multiple He atoms inside a vacancy with and without Zr or V are discussed. We hope that those results will not only be quite helpful to understand the interaction of He and Zr/V but also can form the foundation of higher-level models. 2. Computational methods In this study, density functional theory calculations of the effects of Zr and V additions on the stability and migration of He in bcc W were performed using the projector-augmented-wave method [18] as implemented in the Vienna ab initio simulation package (VASP) developed at the Technical University of Vienna [19,20]. All the electron exchange correlation functional was calculated using the Perdew–Burke–Ernzerh of approximation (PBE) described by the generalized gradient approximation (GGA) [21]. A plane-wave cutoff of 350 eV was used in all calculations. Systematic calculations presented here have been performed on 128-atom in a 4 × 4 × 4 supercell with periodic boundary condition. The Brillouin-zone integration was performed within Monkhorst-Pack scheme using a 3 × 3 × 3 mesh for the geometry optimizations and 4 × 4 × 4 mesh for electronic calculations [22]. The diffusion pathways of single He atom in W with/without Zr or V atom were calculated using the climbing-image nudged elastic band (CI-NEB) simulations [23]. Both supercell size and atomic positions are relaxed to equilibrium, and energy minimization is continued until the forces on all atoms are converged to smaller than 10−2 eV/Å. The total energy of each system was relaxed until the difference value is smaller than 10−5 eV. A −A The binding energy of two defects (A1 , A2 ), E b 1 2 , is calculated as follows: A − A2
Eb 1
A2 A1 + A2 A1 bulk = E tot + E tot − E tot − E tot A + A2
where E tot1
(1)
is total energy of the supercell containing both A1 A
bulk and A2 ; E tot is total energy of perfect W in supercell; E tot1 and A E tot2
are total energies of the supercell with A1 and A2 , respectively. With such a scheme a negative binding energy means repulsion between the entities, while a positive binding energy indicates a attraction. All the supercells contain the same number of sites, i.e., have the same size. The solubility of He in W pure containing a X atom (X=Zr, V) can be characterized by the solution energy (E sol He ), which is given as:
E sol He = E 1 X , He − E 1 X − E He ,isolated
(2)
Table 1 Binding energies (eV) of Zr-Zr, V-V, Zr-vacancy and V-vacancy pairs. Configuration
E bZ r − Z r /eV
E bV − V /eV
E bZ r − vac /eV
E bV − vac /eV
1nn 2nn 3nn
−2.923 −2.397 −2.342
−2.749 −0.076 −0.040
−1.0559
−0.430
– –
– –
where E 1 X , He are the energies of the supercell with He atom and a X atom; E 1 X is the energy of the supercell with a X atom; the E He,isolated is the energy of an isolated He atom (a single He in supercell). trap The trapping energy (E X − v , He ) of per He atom sequentially trapped by the X-vacancy (X-v) pair can be obtained by: trap
E X − v , He = E X − v , Hen − E X − v , Hen−1 − ( E W , He( T −site) − E W )
(3)
where E X − v , Hen and E X − V , Hen−1 are the total energies of the X-v complex system with n and n − 1 He atoms, respectively; n is the number of He atoms at the X-v pair; E W , He(T −site) and E W are the energies of the W supercells with and without He atom, retrap spectively. A negative E X − v , He means energy gain when the He atom is trapped by vacancy relative to their being dispersed into different tetrahedral sites. 3. Results and discussion 3.1. He solution energy in presence of Zr and V To estimate the influence of zirconium (Zr) and vanadium (V) on solubility of helium (He) atom in bcc tungsten, we first investigated the existing form of alloying element in intrinsic pure W. The binding energies of Zr-Zr and V-V pairs with different distance in intrinsic pure W were calculated. The previous theoretical results showed that both Zr and V elements prefer to occupy the substitutional site in W [16,17,24]. Thus, we arranged two alloying elements on two different substitutional sites of W to form Zr-Zr or V-V pairs, and the schematic diagram of these configurations are illustrated in Fig. 1. The calculated binding energies of Zr-Zr and V-V pairs are calculated using Eq. (1) and listed in Table 1. In Table 1, all of the Zr-Zr and V-V pairs as 1nn, 2nn, 3nn configurations have negative binding energies, implying that the interaction of two defects is repulsive interaction. It indicates that Zr and V atoms usually prefer to disperse into W-rich region rather than aggregate in W host lattice. A single He atom can occupy either a tetrahedral interstitial site (TIS) or an octahedral interstitial site (OIS) in the intrinsic pure W. In our previous work, we have already studied the relative stability of the various He interstitial sites, and the results show that He atom at TIS (6.41 eV) is more stable than OIS one (6.64 eV) [25, 26]. The He solution energy at different TIS and OIS were calculated to determine the He preferential site in W with presence of
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Fig. 2. Local atomic configurations and calculated solution energies for He at the TIS and OIS near one Zr or V atom in comparison with the data of He in intrinsic pure W. The pink, yellow, green, and blue spheres denote W, Zr, V and He atoms, respectively.
Fig. 3. Total charge densities for He-solute defects in W. (a), (b) and (c) are He-W, He–Zr and He-V in (0 0 1) plane, respectively. The units are eÅ−3 .
Zr/V addition. After full relaxation of these configurations, the solution energy of He are calculated using Eq. (2) and represented in Fig. 2. It can be clearly seen that the solution energy of He atom at TIS is lower than that of at OIS in both W with presence of Zr and W with presence of V systems. Thus, we conclude that He atoms still prefer to occupy a TIS in W with presence of Zr/V addition. However, the solution energy of He atom at both TIS and OIS in W with presence of Zr/V are lower than that in intrinsic pure W. The binding energy between Zr/V and He atoms are calculated using Eq. (1) to explain the reason for it. A positive binding energy means attraction between Zr/V and He atoms. The binding energy between Zr/V and He atoms is 0.68 eV/0.96 eV, which indicates that the attractive interaction plays a dominant role between the Zr/V and He atoms. The result in this calculation agrees with the reported previous work [16,17]. We also find that the binding energy between V and He atoms is larger than that between V and He atoms. Moreover, the solution energy of He atom at interstitial sites in presence of V is lower than that in presence of Zr, and the distance of V-He is smaller than that of Zr-He. These imply that the attractive interaction between V and He atoms is stronger than that between Zr and He atoms. However, the mechanism of these observations is not clear and the correlation of solution energy with the electronic structure was needed to interpret.
There is a general consensus that He atom prefers to keep its own electronic structure due to its closed-shell electronic structure. It has been found that He likes to occupy the low charge density regions and its solution energy is directly proportional to electron density [26–28]. To clarify the electron effect on the He solution energy, the total charge densities for He in intrinsic pure W, W with presence of Zr and V additions are calculated, respectively, which are shown in Fig. 3. It is obvious that a broader region of very low charge density around He with the presence of the solute Zr/V, which indicates that the charge density is reduced around the Zr/V. The charge density depletion around the Zr/V leads to the strong attraction between the Zr/V atom and He atom and a decrease in the solution energy of He atom. By comparison of charge densities around Zr (Fig. 3b) and V (Fig. 3c), a lower charge density near V is seen while the charge density around Zr is relatively higher, which gives rise to the stronger attractive interaction between V and He atom and the lower solution energy of He in W with presence of V. The hybridization of He atom in different systems can also be observed from the calculated local electronic densities of states (LDOS). The LDOS for d-states of the neighboring W atom and p-states of the He atom have been investigated and plotted in Fig. 4. It can be seen from Fig. 4 that the impurities Zr and V
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Fig. 4. Local DOS for the substitutional impurities Zr and V compared with that of the system without additions. (a) the d-states for the neighboring W atoms; (b) the p-state for the He atom. The zero energy point indicates the Fermi level of the supercell with the He defect.
Fig. 5. (a) The solution energy He atom and (b) the binding energy between Zr/V and He atoms in W with X (X=Zr, V) atom as a function of the He-X distance. The blue spheres show the sites of single He atom; the pink spheres are the bcc W lattice sites; the gray sphere shows the site of X atom.
produce distortion of the LDOS of the neighboring W atoms and He atoms, which indicates the ongoing hybridization. The p-states near the Fermi energy are particularly unfavorable for He atom due to He is an atom with a completed spherically symmetric s shell [29,30]. The large He p-states at the Fermi energy level is not conducive to the energetically favorable for the corresponding He defect configuration [29]. From Fig. 4(b) one can see that, the p-states at the Fermi energy level of He atom for W with presence of Zr and V are lower than that of He atom for intrinsic pure W, and the p-states at the Fermi energy level of He atom for W with presence of V is the lowest. Therefore, the solution energy of He at ITS in W with Zr/V atom are lower than that of He at ITS in intrinsic pure W, and the solution energy of He at TIS in W with presence of V is the lowest. To investigate the interactions of He-Zr and He-V pairs inside W solid, we computed the solution energies of He atom and the binding energy between Zr/V and He atoms with different He-Zr/V using Eq. (2) and Eq. (1), respectively. According to the stable occupy site for impurity Zr or V atom and He atom in W, we replaced one W atom by one Zr or V atom and then put a single He atom into the TIS surrounding the impurity atom to form a He-Zr or He-V pair. The initial configurations are shown in the Fig. 5(a). All different configurations involving the different distances between He and Zr or V are full relaxed. We find that the He atom is occupied at site A for the initial configuration B including impurity Zr atom, which suggests that there is an attraction interaction between He and Zr atoms in the initial structure. The solution energy of He atom at all TIS in intrinsic pure W is equal and the value is 6.41 eV. In Fig. 5, we can see that the He solution energy in W with impurity Zr or V are lower than that of He at the TIS in pure W and the binding energy between Zr/V and He atoms is positive,
Table 2 The initial and finial distances between Zr/V and He atoms for different configuration. Configuration
A
B
C
D
E
F
initial finial (Zr-He) finial (V-He)
1.772 1.875 1.628
2.857 1.875 2.78
3.633 3.550 3.630
4.267 4.267 4.267
4.820 4.820 4.820
5.760 5.760 5.760
indicating that the attractive interaction plays a dominant role between the He and Zr/V atoms. As revealed by Fig. 5 (a), the He and Zr or V atoms attract with each other with a screening distance of about 5.76 Å, beyond which the He and Zr or V atoms are nearly non-interactive. The trapping radius is the distance beyond which the attraction of He towards impurities is considered negligible [16]. Thus, the trapping radius of Zr/V atom on He is about 5.76 Å. Moreover, according to the initial and finial distances between Zr/V and He atoms as shown in Table 2, He atom spontaneously migrates to Zr/V atom when the initial distance between Zr/V and He atoms is less than 3.633 Å, which suggests that there is a strong attractive interaction between Zr/V and He atoms. It should be noted that the results are in good agreement with the previous theoretical study by Wu [16,17], confirming the accuracy of our work. 3.2. Effects of Zr and V on He diffusion Up to date, much effort has been directed toward the He migration behavior in metals [30–33]. We investigated the He migration barrier by possible paths of He from a sixth nearest-neighbor TIS (6nn TIS as site F) diffusing to a first nearest-neighbor TIS (1nn TIS as site A) near Zr and V using the CI-NEB simulations in order to
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Fig. 6. Diffusion barrier for He moving from a far 6nn (F) TIS to a 1nn (A) TIS near (a) Zr and (b) V in W.
Fig. 7. (a) Eight high-symmetric sites for a single He atom in W with Zr/V-Vacancy complex; (b) the most stable configuration for a single He atom in W with Zr/V-Vacancy complex; (c) trapping energies as function of the number of He atoms trapped in W with vacancy and W with Zr/V-Vacancy complex, respectively.
study the effects of Zr or V on He diffusion kinetically. All six sites are stable TISs. The migration barrier barriers and corresponding diffusion paths for He diffusing to a Zr or V atom are explored and presented in Fig. 6. The calculated migration barriers, not only for He diffusing to Zr atom but also for He diffusing to V atom, are lower than that of He along the optimal diffusion path TIS–TIS in intrinsic pure W, which has a diffusion energy barrier of 0.057-0.060 eV [31,32]. It suggests that the Zr or V addition makes He migration much easier comparing with He in intrinsic pure W. Noticing that no diffusion barrier exists as He jumps into 1NN ITS (as site A) from the 2NN TIS (as sit B) for W with V addition, which indicates a downhill “drift” diffusion of He toward the 1NN ITS. On the other hand, if the He interstitial diffuse into the Zr region, He atom needs to overcome a highest energy barrier of 0.053 eV for path D-E, as shown in Fig. 6a. But to enable a real diffuse into the V region, He atom needs to overcome a highest energy barrier of 0.051 eV for path B-C, as shown in Fig. 6b. Based on our calculation results, the trapping radius of Zr/V atom on He is about 5.76 Å (the distance between He at site D and Zr is about 5 Å, and the distance between He at site B and V is 2.78 Å), illustrating that there are attraction and between He at site B and V. Thus, the He atom diffuses into the solute rather than diffusing back to the bulk interstitial site. From the kinetics point of view, the migration of He for W with presence of V is easier than that of He for W with presence of Zr. Because the main difference between two configurations lies in the kinds of additions, variation in the migration barrier of the configurations should be attributed to the presence
of additions. We suppose that the stronger attractive interaction between V and He atom dominate the lower migration barrier. 3.3. Monovacancy trapping for multiple He in presence of Zr and V Vacancy, as a typical defect in metals, plays a significant role in both the structural and mechanical properties of metals. The vacancy has always drawn intense interest owing to its effects on He behaviors such as solution and diffusion and can act as trapping center for He atom [32,33]. The calculations above show that the presence of Zr/V causes a crucial effect on solution behaviors of He in W. To understand the effect of Zr/V on the stability of He Zr/VVacancy complex in dilute Zr-W or V-W systems, a vacancy near Zr or V by removing a W atom was created, as shown in Fig. 1(d). The calculated binding energies of Zr-Vacancy and V-Vacancy pairs in are listed in Table 1. The positive binding energy means the repulsion interaction between Zr/V and vacancy. The possible positions described for a He atom surrounding Zr/V-Vacancy complex in W are described in Fig. 7(a). After the optimization of these systems, we find that the most stable site for He atom in W with existing Zr/V-Vacancy complex is still the exact center of the vacancy, which is shown in Fig. 7(b). It is the same as He atom in W with self-vacancy. Thus, the Zr/V-Vacancy complex can also as trapping center for He atom. To further understand the effect of Zr/V on vacancy trapping for multiple He atoms, the trapping energy which characterize the energy required for moving He atoms into the vacancy space from a remote TIS in sequential way are obtained using Eq. (3). In pre-
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that between Zr and He. Our calculations also reveals that the He atom diffusion to Zr/V has a lower energy barrier than that of He diffusion to W along the optimal diffusion path TIS–TIS. Moreover, the existing Zr/V atom improves the ability of Zr/V-Vacancy complex to capture He atom. The results from this work can shed light on the understanding the influence of existing Zr/V atom on He atom at an atomic level. Acknowledgements This work was supported by Beijing Municipal Natural Science Foundation (Grant No. 2182042) and the National Natural Science Foundation of China (Grant No. 11875004, 11505006, 11604008). References
Fig. 8. Binding energies as function of the number of He atoms between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He in W with vacancy and W with Zr/VVacancy complex, respectively.
vious work, calculation based on density functional theory (DFT) showed that a W vacancy can contain at least nine He atoms [34]. Therefore, the trapping energy of the first to ninth He atom trapped in W with vacancy and W with Zr/V-Vacancy complex in W with vacancy are calculated. The He trapping energy increase as the number of He atoms trapped increasing on the whole, as shown in Fig. 7(c), meaning that the stability of unit cell gradually reduces. The He trapping energy of W with Zr/V-Vacancy complex shows a lower trapping energy than that of Zr/V-free vacancy with the corresponding He number, implying that the Zr/V-Vacancy-Hen complex is more stable in comparison with the Zr/V-free case, and V effect is slightly stronger than Zr. Thus, for the He atom to escape from the Zr/V-Vacancy complex is more hard. The existing Zr/V atom improves the ability of Zr/V-Vacancy complex to capture He atom and this should be attributed to the stronger attractive interaction between Zr/V and He atom. As shown in Fig. 7c, there is no obvious change of trapping energies with and without the solute Zr or V when the number of He is 3, 4 and 9. Therefore, binding energies as function of the number of He atoms between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He in W with vacancy and W with Zr/V-Vacancy complex are calculated to check if Zr/V can promote the binding of the complex. As seen from Fig. 8, binding energies between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He atoms are positive, suggesting that there are mutual attraction between them. The binding energy between Zr/V-Vac-Hen-1 and He is higher than that between Vac-Hen-1 and He atoms for the corresponding He atom. When the number of He is 3, 4 and 9, the trapping energy between Vac-Hen-1 /Zr-Vac-Hen-1 /V-Vac-Hen-1 and He is 3.15/3.17/3.18 eV, 3.28/3.33/3.36 eV, 2.83/2.85/2.90 eV. Despite the difference in the value is very small, but contribution from Zr/V to promote the binding of the complex can not be neglected. 4. Conclusions We performed the theoretical study of the effects of zirconium (Zr) and vanadium (V) on the dissolution, diffusion and trapping behaviors of helium (He) in tungsten (W) by means of first-principles calculations. The present calculations clearly predict that the tetrahedral interstitial site (TIS) is still the most stable site for an interstitial He in W with the presence Zr/V atom. Meanwhile, the solution energy of the He atom is reduced because of the attractive interaction between He and Zr/V atom. Interestingly, a lower He solution energy in W with V is obtained which results from the stronger attractive interaction between V and He than
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