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Formation and behaviors of helium bubbles in Li4SiO4: A molecular dynamics simulation
Computational Materials Science 169 (2019) 109104
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Formation and behaviors of helium bubbles in Li4SiO4: A molecular dynamics simulation
T
⁎
Shenggui Maa,d, Tao Gaoa,c, , Xiaojun Chenb, Chengjian Xiaob, Tiecheng Luc, Xia Jiangd a
Institute of Atomic and Molecular Physics, Sichuan University, 610065 Chengdu, China Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China c Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, College of Physical Science and Technology, Sichuan University, Chengdu 610065, China d National Engineering Research Center for Flue Gas Desulfurization, Chengdu 610065, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Li4SiO4 Molecular dynamics Helium bubble
Molecular dynamics simulations were conducted to investigate the formation and behaviors of helium bubbles in Li4SiO4. We found that a single helium atom easily moved to a lithium vacancy with minimal energy, and helium dimers were also observed in Li4SiO4. The temperature directly influenced the formation and diffusion of helium, and helium atoms aggregated and formed helium bubbles at a temperature of 700 K. The release of helium bubbles at several temperatures was simulated to analyze the effects of helium bubble release on the Li4SiO4 surface. The temperature was also important factor influencing the recovery of defects. These results will be useful for establishing a physical model of irradiation-induced microstructure evolution inside tritium breeding material and provide a good reference for understanding the initial stage of helium bubble formation and growth in Li4SiO4.
1. Introduction Nuclear fusion of deuterium and tritium (D-T) is an attractive option for future fusion power production [1–5]. Deuterium can be extracted from seawater; however, there is no natural source of tritium due to its short half-life. Therefore, it is necessary to generate tritium from breeder blankets in fusion reactors. Solid tritium breeding materials (TBM) of lithium ceramics (such as Li2O, γ-LiAlO2, Li2SiO3, Li4SiO4, Li2TiO3, and Li2ZrO3) are used to produce and recover tritium fuel [6–10]. Li4SiO4 is one of the most promising candidates among TBM due to its high lithium density, high melting point, compatibility with structural materials, and excellent tritium release performance [11–13]. Under high-energy neutron irradiation, energetic helium and tritium atoms are produced in TBM of a D-T fusion reactor by (n,α) transmutation reactions via: 6 1 3 4 3Li + 0n → 1T + 2He
+ 4.8 (MeV)
(1)
+ 10n − 2.5 (MeV)
(2)
Or 7 1 3 4 3Li + 0n → 1T + 2He
Due to the extremely low solubility of the materials, helium atoms as a byproduct tend to be trapped at defects that are produced in
⁎
displacement cascades and easily aggregate to form gas bubbles. The formation of helium bubbles in TBM can consequently induce void swelling and produce high temperature embrittlement and surface roughening and blistering that can significantly degrade the mechanical properties and represent major lifetime limiting factors for TBM [14]. Therefore, the formation and behaviors of helium bubbles in Li4SiO4 are the most important issues in nuclear fusion technology and present a significant challenge to material design. Helium diffusion and aggregation in various bulk metals have been widely studied using molecular dynamics (MD). For example, the implantation of helium ions can severely reduce the ductility of vanadium alloys, directly degrading their properties [15]. The effect of the environmental temperature and the depth of helium bubbles on titanium’s volume, pressure, and release progress was studied using a molecular dynamics simulation [16]. Faiza et al. presented molecular dynamics simulations at the initial stage of helium clustering and bubble formation to reveal sub-surface mechanisms in tungsten [17]. The bursting and expansion of helium bubbles near the surface of a tungsten material were investigated by molecular dynamics simulation. The results indicated that a helium bubble with a radius of 1.0 nm needs a high pressure of several tens of GPa to burst near the surface and expand the bubble structure under the surface. The nucleation and growth of
Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan University, 610065 Chengdu, China. E-mail address: [email protected] (T. Gao).
https://doi.org/10.1016/j.commatsci.2019.109104 Received 29 December 2018; Received in revised form 22 June 2019; Accepted 25 June 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 169 (2019) 109104
S. Ma, et al.
Table 1 The formation energies of He atoms in the lithium vacancy. Sample
Supercell
Number of He atoms
Formation energies (eV)
1 2 3
3×6×3 5 × 10 × 5 6 × 12 × 6
54 250 432
4.69 4.66 4.69
helium bubbles in the bulk and grain boundaries of bcc iron were investigated by Yang using molecular dynamics simulations [18]. As previously mentioned, numerous investigations have been carried out to understand the behavior of helium atoms in metal, but there has been less effort to understand the behavior of helium in tritium breeder materials. The behavior of helium release from Li2TiO3 was observed by thermal desorption spectroscopy (TDS), in which the temperature was greater than the operating temperature of a breeder blanket [19]. However, little is known about the helium behavior from the microscopic perspective. Molecular dynamics (MD) simulations are a useful tool for analyzing defect properties and investigating the detailed atomistic dynamic behaviors of various systems over time scales from picoseconds to nanoseconds. MD simulations can provide valuable insight at the atomistic scale, which is not directly accessible from experiments. The aim of this paper is to simulate the formation and behaviors of helium bubbles in Li4SiO4 using a newly developed potential model. First, we simulate the diffusion of a single helium atom and helium dimer. Next, the formation of a helium bubble and the changes in the defects are observed. Then, we simulate the release process of a helium bubble from near the surface and analyze the recovery of the damaged structure, in which the helium atoms are directly released. These results will be useful for establishing a physical model of irradiation-induced microstructure evolution inside TBM and provide a good reference for understanding the initial stage of helium bubble formation and growth in Li4SiO4 under a fusion environment. The rest of this paper is organized as follows. In Section 2, the computational methodology is described. In Section 3, the results and discussion are presented including the diffusion of helium atoms, formation of a helium bubble, and the release process of a helium bubble from near the surface. The conclusions are summarized in Section 4.
Fig. 2. (a) Snapshot of the helium dimer in Li4SiO4. (b) A snapshot at 2 ps and (c) a snapshot at 200 ps.
a large-scale atomic/molecular massively parallel simulator (LAMMPS) [20] and used the classical molecular dynamics simulation. We employed self-developed pair potential for the crystalline Li4SiO4 [21], and the He-Li, He-O, and He-Si interactions were described by the interatomic potentials of Borrmann et al. [22], Grimes et al. [23], and Saadoune et al. [24], respectively. The He-He interaction is chosen as the well-known Lennard-Jones potential [22], which was suggested to be reliable for simulating the behavior of helium in a solid. In the MD simulations, the isothermal-isobaric (NPT) ensemble was applied to reach a constant pressure and temperature. Integration of the equation of motion was performed with a time step of 1 fs. A crystal of 31,500 atoms (5 × 10 × 5 supercell) was used in the simulations to avoid the influence of the periodic boundaries. The initial model was relaxed using the conjugate gradient method to reach a minimum energy state, followed by temperature rescaling to the required annealing temperature of 300 K and maintained for 50 ps. Then, the system of contained helium atoms was simulated with the NPT ensemble at several time steps. All of the results of the simulations were visualized by the Open Visualization Tool (OVITO) software [25].
2. Computational methodology In the present work, all of the MD simulations were performed with
Fig. 1. (a) Typical snapshots of a single helium atom in Li4SiO4. (b) A snapshot at 0.06 ps; (c) a snapshot at 0.8 ps; (d) a snapshot at 0.9 ps; and (e) a snapshot at 1.5 ps. 2
Computational Materials Science 169 (2019) 109104
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Fig. 3. The morphology of helium bubbles with different numbers of atoms.
Fig. 4. The morphology of Li4SiO4 after relaxation with different numbers of helium atoms.
3. Results and discussion
3.2. Diffusion of a single helium atom and helium dimer
3.1. Formation energy of helium atoms
A single helium atom was randomly introduced into a perfect Li4SiO4 supercell. Fig. 1 shows the moving trajectory of the helium atom in 1.5 ps at 300 K. For clarity, a small region with approximately 30 atoms at different times is shown in Fig. 1(b–e). As expected, the single helium atom migrated in the Li4SiO4 matrix for a very short time and was trapped in the lithium vacancy. The helium atom jumped with 1.5 ps from one site to another. The displaced Li4SiO4 atoms restored its lattice position after the helium moved to other sites. With the increasing temperature, the frequency of the helium atom jumping from site to site increased. This was because a lithium vacancy is considered a primary irradiation-induced defect in lithium ceramic breeder materials. Thus, the helium easily moved to the lithium vacancy. A second helium atom was added to the Li4SiO4 approximately 5 Å
The formation energy is calculated by comparing the energy of a crystal containing lithium vacancy and helium substitute with a perfect crystal with the same number of atoms. In this work, three samples tabulated in Table 1 which the concentration of He is equivalent to the Ref. [26] were tested to simulate the formation energies. The formation energy of the helium atoms in the lithium vacancy simulated by the potential models is 4.69 eV, which compares well with the value of 4.78–6.23 eV under O-poor conditions calculated using the DFT method as reported by Shi [26].
3
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S. Ma, et al.
defects were present around the helium bubble. The volume of the bubble increased rapidly with the helium concentration. The swelling associated with the bubble growth as a function of helium concentration is presented in Fig. 5. The swelling is defined as:
S = (V − V0)/ V0,
(3)
where V0 is the initial volume of the system containing the helium bubble. The swelling followed an approximate linear relationship at low helium concentrations. 3.4. The temperature effects on the helium bubble To research the relationship between the helium bubble and the temperature, we heated the model containing approximately 200 helium atoms to certain temperatures. Temperatures of 300 K, 500 K, 700 K, and 1000 K were the substrate temperatures in our simulations, and the simulated results are shown in Fig. 6. The helium bubble expanded rapidly due to its high internal pressure with the increasing temperature. Meanwhile, many Li4SiO4 atoms were pushed out of the lattice sites and moved outward, forming a void region. When the temperature rose above 700 K, no aggregation of helium bubbles and the of Li4SiO4 defects occurred. Therefore, in our simulations, most of the helium atoms escaped when the temperature was above 700 K.
Fig. 5. The simulated swelling of the Li4SiO4 as a function of the helium concentration.
away from the first atom. The helium dimer was observed followed by evolution for 200 ps, which is presented in Fig. 2. The position of the He and Li atoms at different times is denoted by the black and red spheres and the Si and the O atoms are hidden for clarity. The dimer bestrides the two nearest lithium vacancies and the lithium atoms are ejected from their initial sub-lattices. Then, the helium dimer acts as a trapping site to trap subsequent helium atoms in the adjacent region. Finally, a helium bubble forms as the number of helium atoms increases.
3.5. The release process of a helium bubble from near the surface To understand the mechanism of the release process of a helium bubble from near the surface of Li4SiO4, we constructed a vacuum region and embedded a helium bubble containing approximately 200 helium atoms into the region’s near surface. At first, when the helium bubble is approximately 10 Å near the surface, as shown in Fig. 7, the bubble starts expanding as it gets closer to the surface at 50 ps at 300 K. The helium bubble eventually cracks, and most of the helium atoms are released from the Li4SiO4 surface, causing the formation of a surface protrusion. However, when the helium bubble is approximately 20 Å from the surface, as shown in Fig. 8, the helium atoms remain in the bubble within the matrix, even if the simulation was extended for a much longer time. We also heated the system to 600 K to study the helium bubble release process. Fig. 9 demonstrates that the helium atoms at a depth of 20 Å escaped the Li4SiO4 under 600 K. The results indicate that the helium bubble far away from the surface erupted at a higher temperature than at room temperature. Thus, the temperature and depth
3.3. Swelling associated with helium bubbles To discuss the impact on swelling associated with helium bubbles, we simulated helium bubble formation and observed the changes of the defects. Helium atoms were regularly added to the nearby sites of the former helium dimer to form bubbles. This work adopted a direct and simple method of constructing helium bubbles containing hundreds of helium atoms that has been used for the simulation of helium in metal [27]. The helium atoms were placed in a certain region, and the whole system was relaxed to equilibrium at 300 K. A series of helium bubbles containing several helium atoms were created using this method, as shown in Fig. 3. Meanwhile, Fig. 4 demonstrates that large amounts of
Fig. 6. The morphology of the helium bubble and Li4SiO4 substrate after relaxation at different temperatures. 4
Computational Materials Science 169 (2019) 109104
S. Ma, et al.
Fig. 7. The atomic configurations of the helium bubble at a depth of 10 Å and a temperature of 300 K. (a) Initial model and (b) after relaxation for 50 ps.
Fig. 8. The atomic configurations of the helium bubble at a depth of 20 Å and a temperature of 300 K. (a) Initial model and (b) after relaxation for 50 ps.
Fig. 9. The atomic configurations of the helium bubble at a depth of 20 Å and a temperature of 600 K. (a) Initial model and (b) after relaxation for 50 ps.
Fig. 10. The morphology of the Li4SiO4 substrate after relaxation at different temperatures. (a) Before relaxation; (b) after relaxation for 500 ps at 300 K; and (c) after relaxation for 500 ps at 700 K.
caused the Li4SiO4 to swell and damaged its structure. However, the helium bubble was released from the Li4SiO4 substrate through the surface and interface, damaging the Li4SiO4 structure. To investigate the recovery of the damaged Li4SiO4 structure, we simulated the structure at different temperatures under which the helium atoms were directly released. Fig. 10 shows a slice of the Li4SiO4 substrate before and after relaxation at different temperatures.
between the free surface of the model and the center point of the helium bubble were two important factors influencing the helium bubble’s release from the Li4SiO4 surface. 3.6. Recovery of the damaged structure Based on the simulation results, the formation of the helium bubble 5
Computational Materials Science 169 (2019) 109104
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Acknowledgment
The damaged structure did not completely recover after relaxation for 500 ps at 300 K, and many vacancies of Li, O, and Si atoms were observed, as shown in Fig. 10(b). However, when the damaged Li4SiO4 structure relaxed at 700 K, the Li, O, and Si atoms recovered to the former crystalline Li4SiO4 structure, as shown in Fig. 10(c). The simulated results suggested that high temperatures can promote the recovery of a damaged structure because high temperatures provide enough kinetic energy to overcome recrystallization barriers. The temperature in nuclear fusion technology should be raised to reduce damage to Li4SiO4 structures.
This work was financially supported by the National Magnetic Confinement Fusion Science Program (No. 2014 GB111001 and No. 2014 GB125002). References [1] K. McGuire, H. Adler, P. Alling, C. Ancher, H. Anderson, J. Anderson, J. Anderson, V. Arunasalam, G. Ascione, D. Ashcroft, Phys. Plasmas 2 (1995) 2176–2188. [2] S.C. Cowley, Nat. Phys. 12 (2016) 384. [3] C. Johnson, J. Nucl. Mater. 270 (1999) 212–220. [4] C.A. Chen, D.L. Luo, Y. Sun, Z.Y. Huang, Y.F. Xiong, Fusion Eng. Des. 83 (2008) 1455–1460. [5] W.E. Lee, M. Gilbert, S.T. Murphy, R.W. Grimes, J. Am. Ceram. Soc. 96 (2013) 2005–2030. [6] C.E. Johnson, Ceram. Int. 17 (1991) 253–258. [7] T. Kinjyo, M. Nishikawa, N. Yamashita, T. Koyama, T. Tanifuji, M. Enoeda, Fusion Eng. Des. 82 (2007) 2147–2151. [8] Y.-H. Park, K.-M. Min, S. Cho, M.-Y. Ahn, Y.-M. Lee, Fusion Eng. Des. 124 (2017) 730–734. [9] W. Lu, J. Wang, W. Pu, K. Li, S. Ma, W. Wang, J. Nucl. Mater. 502 (2018) 349–355. [10] S.-G. Ma, Y.-H. Shen, T. Gao, P.-H. Chen, Int. J. Hydrogen Energy 40 (2015) 3762–3770. [11] Y. Gong, X. Yu, M. Yang, J. Wei, Y. Shi, Z. Huang, T. Lu, W. Huang, Mater. Lett. 159 (2015) 245–248. [12] M. Yang, Y. Gong, G. Ran, H. Wang, R. Chen, Z. Huang, Q. Shi, X. Chen, T. Lu, C. Xiao, J. Nucl. Mater. 514 (2019) 284–289. [13] Y. Shi, T. Lu, T. Gao, X. Xiang, Y. Gong, M. Yang, L. Feng, H. Wang, C. Dang, J. Nucl. Mater. 508 (2018) 257–264. [14] F. Scaffidi-Argentina, M.D. Donne, C. Ferrero, C. Ronchi, Fusion Eng. Des. 27 (1995) 275–282. [15] T. Muroga, J.M. Chen, V.M. Chernov, K. Fukumoto, D.T. Hoelzer, R.J. Kurtz, T. Nagasaka, B.A. Pint, M. Satou, A. Suzuki, H. Watanabe, J. Nucl. Mater. 367–370 (2007) 780–787. [16] L. Liang, M. Ma, W. Xiang, Y. Wang, Y. Cheng, X. Tan, J. Alloys Compd. 645 (2015) S166–S169. [17] S. Faiza, D.H. Karl, J. Niklas, D.W. Brian, Nucl. Fusion 53 (2013) 073015. [18] L. Yang, F. Gao, R.J. Kurtz, X.T. Zu, S.M. Peng, X.G. Long, X.S. Zhou, Acta Mater. 97 (2015) 86–93. [19] T. Kulsartov, I. Tazhibayeva, Y. Gordienko, E. Chikhray, K. Tsuchiya, H. Kawamura, A. Kulsartova, Fusion Sci. Technol. 60 (2011) 1139–1142. [20] S. Plimpton, J. Comput. Phys. 117 (1995) 1–19. [21] S.-G. Ma, X.-G. Kong, S.-C. Li, Y.-H. Shen, X.-J. Chen, C.-J. Xiao, T. Gao, Mater. Chem. Phys. 214 (2018) 548–556. [22] P. Borrmann, E. Hilf, Z. Phys. D: Atoms Mol. Clusters 26 (1993) 350–352. [23] R.W. Grimes, R.H. Miller, C. Catlow, J. Nucl. Mater. 172 (1990) 123–125. [24] I. Saadoune, N.H. De Leeuw, Geochim. Cosmochim. Acta 73 (2009) 3880–3893. [25] S. Alexander, Modell. Simul. Mater. Sci. Eng. 18 (2010) 015012. [26] Y. Shi, T. Lu, T. Gao, X. Xiang, Q. Zhang, X. Yu, Y. Gong, M. Yang, J. Nucl. Mater. 467 (2015) 519–526. [27] B. Zhang, J. Wang, M. Li, Q. Hou, J. Nucl. Mater. 438 (2013) 178–182.
4. Conclusions In summary, we conducted MD simulations to investigate the formation and behaviors of helium bubbles in Li4SiO4. The significant contributions of this work are summarized as follows: 1) A single helium atom easily moved to a lithium vacancy with minimal energy, and a helium dimer was also present in the Li4SiO4. 2) The temperature directly influenced the formation and diffusion of the helium. The helium atoms aggregated to form a helium bubble at a temperature of 700 K. When a helium bubble was present in the Li4SiO4, many defects were induced as the bubble coalesced and extended outward. The impact on the swelling associated with the helium bubble was also discussed. 3) The release process of the helium bubble from near the surface was simulated. The results indicated that the temperature and the depth between the free surface and the center point of the helium bubble were two important factors influencing the recovery from the damage caused by the helium bubble’s release from the Li4SiO4 surface. CRediT authorship contribution statement Shenggui Ma: Conceptualization, Investigation, Methodology, Software, Writing - original draft, Writing - review & editing. Tao Gao: Conceptualization, Formal Analysis, Funding acquisition, Methodology, Validation. Xiaojun Chen: Conceptualization, Supervision. Chengjian Xiao: Project administration, Resources. Tiecheng Lu: Project administration, Resources. Xia Jiang: Formal Analysis, Writing - review & editing.
6
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Formation and behaviors of helium bubbles in Li4SiO4: A molecular dynamics simulation
T
⁎
Shenggui Maa,d, Tao Gaoa,c, , Xiaojun Chenb, Chengjian Xiaob, Tiecheng Luc, Xia Jiangd a
Institute of Atomic and Molecular Physics, Sichuan University, 610065 Chengdu, China Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China c Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, College of Physical Science and Technology, Sichuan University, Chengdu 610065, China d National Engineering Research Center for Flue Gas Desulfurization, Chengdu 610065, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Li4SiO4 Molecular dynamics Helium bubble
Molecular dynamics simulations were conducted to investigate the formation and behaviors of helium bubbles in Li4SiO4. We found that a single helium atom easily moved to a lithium vacancy with minimal energy, and helium dimers were also observed in Li4SiO4. The temperature directly influenced the formation and diffusion of helium, and helium atoms aggregated and formed helium bubbles at a temperature of 700 K. The release of helium bubbles at several temperatures was simulated to analyze the effects of helium bubble release on the Li4SiO4 surface. The temperature was also important factor influencing the recovery of defects. These results will be useful for establishing a physical model of irradiation-induced microstructure evolution inside tritium breeding material and provide a good reference for understanding the initial stage of helium bubble formation and growth in Li4SiO4.
1. Introduction Nuclear fusion of deuterium and tritium (D-T) is an attractive option for future fusion power production [1–5]. Deuterium can be extracted from seawater; however, there is no natural source of tritium due to its short half-life. Therefore, it is necessary to generate tritium from breeder blankets in fusion reactors. Solid tritium breeding materials (TBM) of lithium ceramics (such as Li2O, γ-LiAlO2, Li2SiO3, Li4SiO4, Li2TiO3, and Li2ZrO3) are used to produce and recover tritium fuel [6–10]. Li4SiO4 is one of the most promising candidates among TBM due to its high lithium density, high melting point, compatibility with structural materials, and excellent tritium release performance [11–13]. Under high-energy neutron irradiation, energetic helium and tritium atoms are produced in TBM of a D-T fusion reactor by (n,α) transmutation reactions via: 6 1 3 4 3Li + 0n → 1T + 2He
+ 4.8 (MeV)
(1)
+ 10n − 2.5 (MeV)
(2)
Or 7 1 3 4 3Li + 0n → 1T + 2He
Due to the extremely low solubility of the materials, helium atoms as a byproduct tend to be trapped at defects that are produced in
⁎
displacement cascades and easily aggregate to form gas bubbles. The formation of helium bubbles in TBM can consequently induce void swelling and produce high temperature embrittlement and surface roughening and blistering that can significantly degrade the mechanical properties and represent major lifetime limiting factors for TBM [14]. Therefore, the formation and behaviors of helium bubbles in Li4SiO4 are the most important issues in nuclear fusion technology and present a significant challenge to material design. Helium diffusion and aggregation in various bulk metals have been widely studied using molecular dynamics (MD). For example, the implantation of helium ions can severely reduce the ductility of vanadium alloys, directly degrading their properties [15]. The effect of the environmental temperature and the depth of helium bubbles on titanium’s volume, pressure, and release progress was studied using a molecular dynamics simulation [16]. Faiza et al. presented molecular dynamics simulations at the initial stage of helium clustering and bubble formation to reveal sub-surface mechanisms in tungsten [17]. The bursting and expansion of helium bubbles near the surface of a tungsten material were investigated by molecular dynamics simulation. The results indicated that a helium bubble with a radius of 1.0 nm needs a high pressure of several tens of GPa to burst near the surface and expand the bubble structure under the surface. The nucleation and growth of
Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan University, 610065 Chengdu, China. E-mail address: [email protected] (T. Gao).
https://doi.org/10.1016/j.commatsci.2019.109104 Received 29 December 2018; Received in revised form 22 June 2019; Accepted 25 June 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 169 (2019) 109104
S. Ma, et al.
Table 1 The formation energies of He atoms in the lithium vacancy. Sample
Supercell
Number of He atoms
Formation energies (eV)
1 2 3
3×6×3 5 × 10 × 5 6 × 12 × 6
54 250 432
4.69 4.66 4.69
helium bubbles in the bulk and grain boundaries of bcc iron were investigated by Yang using molecular dynamics simulations [18]. As previously mentioned, numerous investigations have been carried out to understand the behavior of helium atoms in metal, but there has been less effort to understand the behavior of helium in tritium breeder materials. The behavior of helium release from Li2TiO3 was observed by thermal desorption spectroscopy (TDS), in which the temperature was greater than the operating temperature of a breeder blanket [19]. However, little is known about the helium behavior from the microscopic perspective. Molecular dynamics (MD) simulations are a useful tool for analyzing defect properties and investigating the detailed atomistic dynamic behaviors of various systems over time scales from picoseconds to nanoseconds. MD simulations can provide valuable insight at the atomistic scale, which is not directly accessible from experiments. The aim of this paper is to simulate the formation and behaviors of helium bubbles in Li4SiO4 using a newly developed potential model. First, we simulate the diffusion of a single helium atom and helium dimer. Next, the formation of a helium bubble and the changes in the defects are observed. Then, we simulate the release process of a helium bubble from near the surface and analyze the recovery of the damaged structure, in which the helium atoms are directly released. These results will be useful for establishing a physical model of irradiation-induced microstructure evolution inside TBM and provide a good reference for understanding the initial stage of helium bubble formation and growth in Li4SiO4 under a fusion environment. The rest of this paper is organized as follows. In Section 2, the computational methodology is described. In Section 3, the results and discussion are presented including the diffusion of helium atoms, formation of a helium bubble, and the release process of a helium bubble from near the surface. The conclusions are summarized in Section 4.
Fig. 2. (a) Snapshot of the helium dimer in Li4SiO4. (b) A snapshot at 2 ps and (c) a snapshot at 200 ps.
a large-scale atomic/molecular massively parallel simulator (LAMMPS) [20] and used the classical molecular dynamics simulation. We employed self-developed pair potential for the crystalline Li4SiO4 [21], and the He-Li, He-O, and He-Si interactions were described by the interatomic potentials of Borrmann et al. [22], Grimes et al. [23], and Saadoune et al. [24], respectively. The He-He interaction is chosen as the well-known Lennard-Jones potential [22], which was suggested to be reliable for simulating the behavior of helium in a solid. In the MD simulations, the isothermal-isobaric (NPT) ensemble was applied to reach a constant pressure and temperature. Integration of the equation of motion was performed with a time step of 1 fs. A crystal of 31,500 atoms (5 × 10 × 5 supercell) was used in the simulations to avoid the influence of the periodic boundaries. The initial model was relaxed using the conjugate gradient method to reach a minimum energy state, followed by temperature rescaling to the required annealing temperature of 300 K and maintained for 50 ps. Then, the system of contained helium atoms was simulated with the NPT ensemble at several time steps. All of the results of the simulations were visualized by the Open Visualization Tool (OVITO) software [25].
2. Computational methodology In the present work, all of the MD simulations were performed with
Fig. 1. (a) Typical snapshots of a single helium atom in Li4SiO4. (b) A snapshot at 0.06 ps; (c) a snapshot at 0.8 ps; (d) a snapshot at 0.9 ps; and (e) a snapshot at 1.5 ps. 2
Computational Materials Science 169 (2019) 109104
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Fig. 3. The morphology of helium bubbles with different numbers of atoms.
Fig. 4. The morphology of Li4SiO4 after relaxation with different numbers of helium atoms.
3. Results and discussion
3.2. Diffusion of a single helium atom and helium dimer
3.1. Formation energy of helium atoms
A single helium atom was randomly introduced into a perfect Li4SiO4 supercell. Fig. 1 shows the moving trajectory of the helium atom in 1.5 ps at 300 K. For clarity, a small region with approximately 30 atoms at different times is shown in Fig. 1(b–e). As expected, the single helium atom migrated in the Li4SiO4 matrix for a very short time and was trapped in the lithium vacancy. The helium atom jumped with 1.5 ps from one site to another. The displaced Li4SiO4 atoms restored its lattice position after the helium moved to other sites. With the increasing temperature, the frequency of the helium atom jumping from site to site increased. This was because a lithium vacancy is considered a primary irradiation-induced defect in lithium ceramic breeder materials. Thus, the helium easily moved to the lithium vacancy. A second helium atom was added to the Li4SiO4 approximately 5 Å
The formation energy is calculated by comparing the energy of a crystal containing lithium vacancy and helium substitute with a perfect crystal with the same number of atoms. In this work, three samples tabulated in Table 1 which the concentration of He is equivalent to the Ref. [26] were tested to simulate the formation energies. The formation energy of the helium atoms in the lithium vacancy simulated by the potential models is 4.69 eV, which compares well with the value of 4.78–6.23 eV under O-poor conditions calculated using the DFT method as reported by Shi [26].
3
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S. Ma, et al.
defects were present around the helium bubble. The volume of the bubble increased rapidly with the helium concentration. The swelling associated with the bubble growth as a function of helium concentration is presented in Fig. 5. The swelling is defined as:
S = (V − V0)/ V0,
(3)
where V0 is the initial volume of the system containing the helium bubble. The swelling followed an approximate linear relationship at low helium concentrations. 3.4. The temperature effects on the helium bubble To research the relationship between the helium bubble and the temperature, we heated the model containing approximately 200 helium atoms to certain temperatures. Temperatures of 300 K, 500 K, 700 K, and 1000 K were the substrate temperatures in our simulations, and the simulated results are shown in Fig. 6. The helium bubble expanded rapidly due to its high internal pressure with the increasing temperature. Meanwhile, many Li4SiO4 atoms were pushed out of the lattice sites and moved outward, forming a void region. When the temperature rose above 700 K, no aggregation of helium bubbles and the of Li4SiO4 defects occurred. Therefore, in our simulations, most of the helium atoms escaped when the temperature was above 700 K.
Fig. 5. The simulated swelling of the Li4SiO4 as a function of the helium concentration.
away from the first atom. The helium dimer was observed followed by evolution for 200 ps, which is presented in Fig. 2. The position of the He and Li atoms at different times is denoted by the black and red spheres and the Si and the O atoms are hidden for clarity. The dimer bestrides the two nearest lithium vacancies and the lithium atoms are ejected from their initial sub-lattices. Then, the helium dimer acts as a trapping site to trap subsequent helium atoms in the adjacent region. Finally, a helium bubble forms as the number of helium atoms increases.
3.5. The release process of a helium bubble from near the surface To understand the mechanism of the release process of a helium bubble from near the surface of Li4SiO4, we constructed a vacuum region and embedded a helium bubble containing approximately 200 helium atoms into the region’s near surface. At first, when the helium bubble is approximately 10 Å near the surface, as shown in Fig. 7, the bubble starts expanding as it gets closer to the surface at 50 ps at 300 K. The helium bubble eventually cracks, and most of the helium atoms are released from the Li4SiO4 surface, causing the formation of a surface protrusion. However, when the helium bubble is approximately 20 Å from the surface, as shown in Fig. 8, the helium atoms remain in the bubble within the matrix, even if the simulation was extended for a much longer time. We also heated the system to 600 K to study the helium bubble release process. Fig. 9 demonstrates that the helium atoms at a depth of 20 Å escaped the Li4SiO4 under 600 K. The results indicate that the helium bubble far away from the surface erupted at a higher temperature than at room temperature. Thus, the temperature and depth
3.3. Swelling associated with helium bubbles To discuss the impact on swelling associated with helium bubbles, we simulated helium bubble formation and observed the changes of the defects. Helium atoms were regularly added to the nearby sites of the former helium dimer to form bubbles. This work adopted a direct and simple method of constructing helium bubbles containing hundreds of helium atoms that has been used for the simulation of helium in metal [27]. The helium atoms were placed in a certain region, and the whole system was relaxed to equilibrium at 300 K. A series of helium bubbles containing several helium atoms were created using this method, as shown in Fig. 3. Meanwhile, Fig. 4 demonstrates that large amounts of
Fig. 6. The morphology of the helium bubble and Li4SiO4 substrate after relaxation at different temperatures. 4
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Fig. 7. The atomic configurations of the helium bubble at a depth of 10 Å and a temperature of 300 K. (a) Initial model and (b) after relaxation for 50 ps.
Fig. 8. The atomic configurations of the helium bubble at a depth of 20 Å and a temperature of 300 K. (a) Initial model and (b) after relaxation for 50 ps.
Fig. 9. The atomic configurations of the helium bubble at a depth of 20 Å and a temperature of 600 K. (a) Initial model and (b) after relaxation for 50 ps.
Fig. 10. The morphology of the Li4SiO4 substrate after relaxation at different temperatures. (a) Before relaxation; (b) after relaxation for 500 ps at 300 K; and (c) after relaxation for 500 ps at 700 K.
caused the Li4SiO4 to swell and damaged its structure. However, the helium bubble was released from the Li4SiO4 substrate through the surface and interface, damaging the Li4SiO4 structure. To investigate the recovery of the damaged Li4SiO4 structure, we simulated the structure at different temperatures under which the helium atoms were directly released. Fig. 10 shows a slice of the Li4SiO4 substrate before and after relaxation at different temperatures.
between the free surface of the model and the center point of the helium bubble were two important factors influencing the helium bubble’s release from the Li4SiO4 surface. 3.6. Recovery of the damaged structure Based on the simulation results, the formation of the helium bubble 5
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Acknowledgment
The damaged structure did not completely recover after relaxation for 500 ps at 300 K, and many vacancies of Li, O, and Si atoms were observed, as shown in Fig. 10(b). However, when the damaged Li4SiO4 structure relaxed at 700 K, the Li, O, and Si atoms recovered to the former crystalline Li4SiO4 structure, as shown in Fig. 10(c). The simulated results suggested that high temperatures can promote the recovery of a damaged structure because high temperatures provide enough kinetic energy to overcome recrystallization barriers. The temperature in nuclear fusion technology should be raised to reduce damage to Li4SiO4 structures.
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4. Conclusions In summary, we conducted MD simulations to investigate the formation and behaviors of helium bubbles in Li4SiO4. The significant contributions of this work are summarized as follows: 1) A single helium atom easily moved to a lithium vacancy with minimal energy, and a helium dimer was also present in the Li4SiO4. 2) The temperature directly influenced the formation and diffusion of the helium. The helium atoms aggregated to form a helium bubble at a temperature of 700 K. When a helium bubble was present in the Li4SiO4, many defects were induced as the bubble coalesced and extended outward. The impact on the swelling associated with the helium bubble was also discussed. 3) The release process of the helium bubble from near the surface was simulated. The results indicated that the temperature and the depth between the free surface and the center point of the helium bubble were two important factors influencing the recovery from the damage caused by the helium bubble’s release from the Li4SiO4 surface. CRediT authorship contribution statement Shenggui Ma: Conceptualization, Investigation, Methodology, Software, Writing - original draft, Writing - review & editing. Tao Gao: Conceptualization, Formal Analysis, Funding acquisition, Methodology, Validation. Xiaojun Chen: Conceptualization, Supervision. Chengjian Xiao: Project administration, Resources. Tiecheng Lu: Project administration, Resources. Xia Jiang: Formal Analysis, Writing - review & editing.
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