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Density functional study of lithium vacancy in Li4SiO4: Trapping of tritium and helium
Journal of Nuclear Materials 467 (2015) 519e526
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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Density functional study of lithium vacancy in Li4SiO4: Trapping of tritium and helium Yanli Shi a, b, Tiecheng Lu a, b, *, Tao Gao c, **, Xiaogang Xiang a, b, Qinghua Zhang a, b, Xiaohe Yu a, b, Yichao Gong a, b, Mao Yang a, b a b c
Department of Physics and Key Laboratory for Radiation Physics & Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610064, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 March 2015 Received in revised form 9 September 2015 Accepted 10 September 2015 Available online 12 September 2015
Li4SiO4 is a solid breeder material that has important applications in future fusion reactors. The interaction of tritium/helium with lithium vacancy is investigated implementing pseudopotential plane wave method within density functional theory. Models of all types of lithium vacancies and vacancytritium/ helium defect complexes are created. Possible tritium trap sites in lithium vacancies are examined and the formation energies, vacancytritium/helium interaction energies and electronic structures of the defects are calculated. The results indicate that the tritium atom trapped in the lithium vacancy bonds with one of the surrounding oxygen atoms. The formation energies of the vacancytritium complexes are in the range of 0.41e1.28 eV under oxygen-rich condition. The interaction energy calculation shows the lithium vacancy has strong tritium trapping capabilities. Moreover, the vacancyhelium complex formation energies are in the range of 1.97e3.43 eV under O-rich condition. The vacancyhelium interaction is relatively weaker, suggesting the helium atom may escape the lithium vacancy more easily. © 2015 Published by Elsevier B.V.
Keywords: Density functional theory Li4SiO4 Lithium vacancy Tritium Helium
1. Introduction Solid state breeder is one of the most significant designs used in Test Blanket Module (TBM) for future fusion reactors. Potential materials for solid state breeder include many lithium based compounds, such as Li2O, Li2TiO3, L2SiO3 and Li4SiO4. Li4SiO4, known for its excellent lithium density, tritium release capability and material compatibility, has been chosen in both Chinese [1,2] and European [3] TBM designs. Thus, it is vital to understand the tritium release behavior of Li4SiO4. Over the years, extensive out-of-pile and in-pile experiments under various conditions have been conducted to study the tritium release process in Li4SiO4 [4,5]. T. Hanada et al. [6] studied the effect of surface water on the tritium release behavior based on parameters obtained from reactor operation. They also found an optimal
* Corresponding author. Department of Physics and Key Laboratory for Radiation Physics & Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China. Tel.: þ86 13678124898. ** Corresponding author. Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610064, PR China. Tel.: þ86 13688350443. E-mail address: [email protected] (T. Lu). http://dx.doi.org/10.1016/j.jnucmat.2015.09.017 0022-3115/© 2015 Published by Elsevier B.V.
grain size for tritium release. C. Kang et al. [7] performed out-of-pile tritium release experiments with different water contents. They found the portion of gaseous form of tritium decreases with water content whereas the HTO portion increases. C. Xiao et al. [8] performed out-of-pile annealing experiments on Li4SiO4 pebbles, and the diffusion process within crystal grains was found to play a major role in the tritium release process, whereas diffusion in grain boundaries showed little effect. The diffusion coefficients of tritium in the crystal grains were also determined. Theoretical studies of solid state breeder materials have mainly focused on the tritium behavior in crystal grains and on material surfaces. Tritium diffusion in crystal grains has been shown to be an important step of the tritium release process. It is affected by various irradiation induced defects (lithium vacancy, oxygen vacancy and broken bond). Lithium vacancy is considered as a primary irradiation induced defect in lithium based breeder materials, as lithium atoms are constantly knocked out of their positions or consumed to generate tritium under irradiation. Lithium vacancy in Li2O has been studied in detail in previous theoretical works. A. Shluger et al. [9] investigated tritium diffusion in Li2O with a quantum-chemical approach and concluded that the majority of the tritium release from Li2O is determined by the triton ion's
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diffusion via a vacancy mechanism. R. Shah et al. [10] performed ab initio studies on tritium point defects in Li2O and calculated the activation energy for tritium diffusion. Tritium behavior with charged defects in Li2O has also been worked on [11]. Possibly due to its complex crystal structure, studies on Li4SiO4 have been less extensive. K. Munakata et al. [12] studied the crystal structures and electron states of Li4SiO4 using linear combination of atomic orbital and Hartree-Fock (LCAO-HF) ab initio electron calculation. T. Tang et al. [13,14] also reported crystal structures and electronic structures of Li4SiO4 implementing ab initio calculation within density functional theory (DFT). Y. Duan et al. [15] studied the structural, electronic, and thermodynamic properties of Li4SiO4 as a CO2 capture material within DFT. To the best of our knowledge, there has not been any reported work on the tritium behavior in Li4SiO4 so far. Due to the important role of lithium vacancy in tritium release, we believe it is necessary to study the tritium behavior with lithium vacancy in Li4SiO4. On the other hand, as helium bubble formation is a common issue in irradiated materials, and the lithium vacancy is a possible helium nucleation site, the helium behavior with lithium vacancy is also worth looking into. In this study, lithium vacancy and its interaction with tritium/ helium in Li4SiO4 were studied within DFT implementing pseudopotential plane wave method. Models of lithium vacancies and vacancytritium/helium complexes were created based on a Li4SiO4 super cell model. A systematic investigation of all types of lithium vacancies and vacancytritium/helium complexes were conducted. All possible tritium trap sites in the vacancy were analyzed. Formation energies, vacancytritium/helium interaction energies and electronic structures of the defect structures were also calculated. Our study could help towards the understanding of tritium/helium behavior in Li4SiO4 grains. 2. Theoretic methods and model In this study, plane wave DFT calculations were performed within the Vienna Ab initio Simulation Package (VASP) [16]. The generalized gradient approximation (GGA) of Perduw-BurkeErnzerhof (PBE) [17] was implemented. Projector augmentedwave (PAW) [18] potentials generated by G. Kresse [19] were used. The valence states electrons of Li, Si and O atoms include 2s1, 3s23p2 and 2s22p4, respectively. Convergence tests were conducted to determine the energy cutoff of the plane wave basis and the K-point grid. We finally set 400 eV as the energy cutoff. And gamma point centered K-point mesh of 1 1 1 was chosen for geometry optimization and 2 2 2 for energy and electronic structure calculation, respectively. The Gaussian band smearing method with a width of 0.05 eV was utilized. The electronic self-consistent loops were converged to 104 eV/cell and the geometry relaxation was considered to be completed when the total force on the atom is less than 0.02 eV Å1. Both the atom positions and the size/shape of the cell were allowed to change during the geometry relaxation. The crystal structure of Li4SiO4 proposed by Tranqui et al. [20] was used in this study. It is a monoclinic structure with space group P21/m (No. 11). A total of 126 atoms are in this crystal structure, of which 56 are lithium, 14 are silicon and 56 are oxygen. All lithium atoms in this model are full occupied as opposed to an earlier model proposed by Dejong et al. [21], in which 4 types of lithium atoms are partially occupied. In our study, a 1 2 1 super cell of Li4SiO4 was adopted and then its geometry was optimized using DFT calculation, as is shown in Fig. 1a. Crystal parameters of the optimized super cell are as follows: a ¼ 11.443 Å, b ¼ 12.108 Å, c ¼ 16.607 Å, b ¼ 99.408 . They are all in good agreement with previous studies [13e15,20]. The deviations from electron diffraction data [20] are no more than 0.77%.
The neutral defect formation energy in this study was calculated by
Ef ¼ EðdÞ EðpÞ
X
ni mi
(1)
i
where E(d) is the total energy of the defect model, and E(p) is the total energy of the perfect 1 2 1 super cell. ni is the number of the species added to the perfect unit cell, of which positive number means atoms added to the unit, while negative number means atoms removed from the unit. mi is the chemical potential of the specie. We considered two conditions for the selection of reference materials for chemical potential calculation. For the O-rich condition, we chose H2O for tritium, Li2O for lithium and O2 for oxygen. For the O-poor condition, we chose H2 for tritium and Li metal for lithium. In this case, the formation energy of the lithium vacancy can be written as:
1 Ef ðVLi Þ ¼ EðLi4 SiO4 ; VLi Þ EðLi4 SiO4 Þ þ EðLi2 OÞ 2 1 EðO2 ÞðO richÞ 4
(2)
Ef ðVLi Þ ¼ EðLi4 SiO4 ; VLi Þ EðLi4 SiO4 Þ þ EðLimetal ÞðO poorÞ (3) The formation of tritium trapped in lithium vacancy can be written as:
1 Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; TÞ EðLi4 SiO4 Þ þ EðLi2 OÞ 2 1 EðH2 OÞðO richÞ 2
(4)
Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; TÞ EðLi4 SiO4 Þ þ EðLimetal Þ 1 EðH2 ÞðO poorÞ 2
(5)
For helium trapped in lithium vacancy, the formation energy was calculated by:
1 Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; HeÞ EðLi4 SiO4 Þ þ EðLi2 OÞ EðHeÞ 2 1 EðO2 ÞðO richÞ 4 (6) Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; HeÞ EðLi4 SiO4 Þ þ EðLimetal Þ EðHeÞðO poorÞ
(7)
The vacancytritium/helium interaction energy was also calculated. The interaction energy Ei is written by:
Ei ðVLi ; T=HeÞ ¼ EðLi4 SiO4 ; VLi ; T=HeÞ þ EðLi4 SiO4 Þ EðLi4 SiO4 ; T=HeÞ EðLi4 SiO4 ; VLi Þ
(8)
EðLi4 SiO4 ; VLi ; T=HeÞ is the energy of the Li4SiO4 model containing both the lithium vacancy and tritium/helium. EðLi4 SiO4 Þ is the energy of the perfect Li4SiO4 super cell. EðLi4 SiO4 ; T=HeÞ is the energy of the model with a tritium/helium interstitial atom. EðLi4 SiO4 ; VLi Þ is the energy of the model with a lithium vacancy.
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Fig. 1. (a) Super cell model of Li4SiO4. (b) Li4SiO4 model viewed from [0 1 0], with numbered lithium atom positions. Lithium atoms are represented by purple balls. Silicon atoms are represented by yellow balls. Oxygen atoms are represented by red balls. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Lithium vacancy 3.1. Defect structure A systematic analysis was performed to study the various lithium vacancies in Li4SiO4. A 126-atom Li4SiO4 single cell is composed of two centrosymmetric sets of 63 atoms. Each set has 19 unique lithium atoms (28 in total) floating around 7 groups of isolated SiO4 units. Thus, there are 19 unique lithium atoms. The lithium atoms are numbered accordingly as shown in Fig. 1b. The oxygen atoms are positioned as the first nearest neighbor around lithium atoms and the coordination number varies between the different lithium atoms. Thus, according to their coordination number with oxygen atoms and the relative positions of these oxygen atoms, the 19 unique lithium atoms can be categorized into three groups (Configuration A, B and C), as shown in Fig. 2. The lithium atom of Configuration A has 4 nearest oxygen atoms which constitute a tetrahedral configuration (Fig. 2a). There are thirteen unique lithium atoms in Configuration A, which are No. 1, 2, 3, 5, 6, 8, 9, 10, 13, 15, 16, 17 and 18. Each lithium atom has a slightly different tetrahedral structure. LieO distances are in the range of 1.881e2.054 Å, which is in agreement with that reported by Tranqui et al. [20].
The lithium atom of Configuration B is 5-fold coordinated with the nearest oxygen atoms (Fig. 2b). Lithium atom No. 4 is in Configuration B. Spatial structure of Configuration B is a triangular bipyramid with the lithium atom in the center. Tranqui et al. [20] excluded the oxygen atom at the bottom of the structure shown in Fig. 2b from the configuration and classified it as a tetrahedron. However, this study showed that the LieO distances of the bottom oxygen atom and top oxygen atom shown in Fig. 2b are 2.573 Å and 2.675 Å, respectively. As a result, it is more reasonable to include the bottom oxygen atom in the space configuration. The remaining 3 LieO distances are smaller and in the range of 1.893e2.000 Å. Spatial structure of Configuration C is an octahedron with 6 oxygen atoms at vertex positions and lithium atom in the center (Fig. 2c). The five lithium atoms of Configuration C are No. 7, 11, 12, 14 and 19. Five of the six LieO distances are in a narrow distribution less than 0.13 Å. However, the sixth LieO distance is significantly larger. In the work of Tranqui et al. [20], No. 7 and 19 lithium atoms are excluded from this group possibly for the larger sixth LieO distances. However, the differences between the smallest and the largest LieO distances are 0.98 Å, 0.23 Å, 0.52 Å, 0.12 Å and 0.46 Å for lithium atom No. 7, 11, 12, 14 and 19, respectively. Therefore, it is more reasonable to include No. 7 and 19 in Configuration C. The real Li vacancies are expected to be charged. The work of
Fig. 2. Spatial configurations of three groups of lithium atoms. Lithium atoms are represented by purple balls. Oxygen atoms are represented by red balls. (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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Murphy et al. [22] indicates that 1 charged Li vacancies have lower formation energies than neutral ones in Li2TiO3, thus have better chances to exist in Li2TiO3. Our calculation showed that neutral Li vacancies have lower formation energies when the Fermi level is located near the edge of the valence band in the band gap, however, charged defects are beyond the scope of this investigation and would be discussed in future works. In this study, only neutral defects were investigated. By removing lithium atoms from the structure, a total of 19 lithium vacancy models categorized in 3 configurations were created. These models were subsequently relaxed by DFT calculation, and afterwards used in formation energy calculations and tritium/helium defect study.
either VLi 0 þT0 or VLi 1 þTþ. It was observed that the oxygen dangling bonds created by the removal of lithium atom would be the most probable sites for tritium atom. Configuration A, B and C each has 4, 5 and 6 such oxygen dangling bond, respectively. As there are 19 types of lithium vacancy, it would not be possible to study all these sites within our resources. Thus, we first created 19 VLiT models by positioning tritium atoms at the original positions of Li before their removal and then subjecting these models through geometry relaxation. A general picture of how the 19 types of lithium vacancies affect tritium behavior can be achieved through this approach. Secondly, one lithium vacancy from each configuration was selected to study all the possible sites of tritium.
3.2. Formation energy
4.1. Defect structure
The formation energies of 19 lithium vacancies were calculated and summarized in Table 1. For O-rich condition, formation energies are in the range of 1.31e2.50 eV. For O-poor condition, formation energies are in the range of 4.11e5.30 eV. It is clear that formation energies of lithium vacancies in Li4SiO4 are much higher under O-poor condition. It indicates that lithium vacancies are easy to form in O-rich condition but difficult to form in O-poor condition. There appears to be no correlation between the structure configuration and its formation energy, as no obvious energy difference was found among the three configurations. Lithium vacancies of Configuration A have a wide distribution of formation energies covering the minimum and maximum of 19 formation energies, while formation energies of Configuration C are in the range of 1.31e1.54 eV. The difference in formation energies seems to be dependent on the comprehensive environment of the local structure rather than the single parameter of lithium coordination number.
In the initial step, after geometry relaxation, tritium atoms were observed to move away from their initial positions and closed in with one of the nearest oxygen atoms in all 19 models. The OT distances are around 1 Å with very small deviations no more than 0.1 Å. The average value is 1.006 Å, slightly larger than the 0.985 Å predicted in Li2TiO3 by Murphy [23]. The OT direction pointed to the approximate center of the vacancy for all cases, i.e. the tritium atom stayed in the space left by the removal of the lithium atom. It can be inferred that the tritium is bonded to the oxygen atom. This result was similar to that observed in Li2O by R. Shah et al. [10], where the tritium atom is bonded with a nearby oxygen atom in the lithium vacancy. It is also observed in ternary lithium oxides Li2TiO3 by Murphy [23]. The SieO bond length of the oxygen atoms in question was noticeably stretched, and the oxygen atom moved slightly towards the vacancy center. The SiO4 tetrahedron rotated with the movement of this oxygen atom, and OeSieO angles in the tetrahedron were only slightly changed.
4. Lithium vacancy¡tritium defect complex (VLi¡T)
4.2. Formation energy and vacancytritium interaction energy
VLiT models were created by placing hydrogen atoms in the lithium vacancies. All tritium atoms were treated as hydrogen atoms as they present the same electronic properties within DFT calculations. The VLiT complexes were treated as neutral in this study. Considering he possible charge states of the lithium vacancy are 0 and 1, and the possible charge states of the tritium atom are þ1, 0 and 1, the neutral VLiT complexes could be formed by
Formation energies of the 19 VLiT complex models under Orich condition are in the range of 0.41e1.28 eV. For O-poor condition, the energy range is 1.94e2.82 eV. The VLiT formation energies are lower than the vacancy formation energies, which means VLiT complexes are easier to form. Comparing between O-rich and O-poor conditions, VLiT defects are easier to form under O-rich condition. The low formation energy also suggests that VLiT is a
Table 1 Formation energies (eV) of the lithium vacancies (VLi) and VLiT complexes under O-rich and O-poor conditions. Their respective structure configurations are also presented.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Ef (VLi(O-rich))
Ef (VLi(O-poor))
Ef (VLiT(O-rich))
Ef (VLiT(O-poor))
Structure
1.45 2.32 2.30 2.13 1.47 2.31 1.54 1.37 2.50 1.50 1.40 1.31 1.31 1.32 1.51 2.42 2.45 1.39 1.49
4.26 5.13 5.10 4.93 4.27 5.11 4.34 4.18 5.30 4.30 4.21 4.11 4.11 4.13 4.32 5.23 5.25 4.19 4.30
0.41 1.13 0.86 0.91 1.17 1.03 0.70 0.43 1.28 0.69 0.63 0.88 0.46 0.71 0.43 1.17 1.01 0.64 0.85
1.94 2.67 2.40 2.44 2.71 2.57 2.24 1.96 2.82 2.23 2.16 2.42 1.99 2.25 1.97 2.71 2.54 2.18 2.39
A A A B A A C A A A C C A C A A A A C
Y. Shi et al. / Journal of Nuclear Materials 467 (2015) 519e526
highly possible form of tritium residual in Li4SiO4. The vacancytritium interaction energy was also calculated. One model each from the three structure configurations were chosen for the calculation, namely No. 13, 04 and 12, because of their lowest formation energies within their configurations. The tritium interstitial sites were selected based on their structures. For example, 4 interstitial sites off the 4 surfaces of the tetrahedron of No. 13 were selected. Likewise, 6 and 8 interstitial sites were chosen for No. 04 and 12, respectively. The results showed that the interaction energies of No. 13, 04 and 12 were between 5.60 and 5.39 eV, 6.19~ 5.84 eV and 5.28~ 5.03 eV, respectively. The large negative values indicate it's energy favorable for tritium to stay in the lithium vacancy than outside as an interstitial atom. The vacancytritium interaction energy results predict the lithium vacancy in Li4SiO4 has strong tritium trapping capabilities. K. Moritani et al.'s work [24] suggests that, when under relatively low neutron fluence(<1018 cm2), tritium diffusion in Li4SiO4 is enhanced by decreasing neutron fluence. This was also observed in Li2O by V. Grishmanov et al. [25]. Low neutron fluence would mainly cause point defects, i.e. lithium vacancy, oxygen vacancy and silicon dangling bond. It is concluded that point defects impede tritium diffusion by trapping tritium atoms. Our calculation proved that lithium vacancy is one of such possible tritium trap sites. A number of annealing experiments [26e29] performed on irradiated lithium based breeder materials indicate that the annihilation of lithium vacancies does not lead to tritium release, and thus lithium vacancies have no significant tritium-trapping ability. Our study indicates that tritium trapped in lithium vacancy forms OeT bond which is not detected by electronic spin resonance (ESR), and is very stable when subjected to low temperature annealing. As a result, the above experimental results are not the direct proof of lithium vacancies' tritium trapping ability. M. Oyaidzu et al. [27] discussed that two tritium release peaks at 750e850 K could be caused by SieOT decomposing. 4.3. Tritium trap sites In the second step of our investigation, one vacancy model from each of the three configurations was selected for further study into multiple tritium sites. The model that had the lowest formation energy in each configuration was chosen, namely vacancy number 13, 04 and 12 for configuration A, B and C, respectively. The possible sites for tritium atom in these models were labeled and shown in Fig. 3, i.e. site B2 refers to the second tritium site in configuration B. There are 4, 5 and 6 possible sites in configuration A, B and C, respectively, corresponding to the number of nearest oxygen atoms. It is to be noted that some of the oxygen atoms in the selected vacancy models have mirror symmetry. However, the symmetry observed were not shared by those vacancies that were
523
not chosen. Thus, these oxygen atoms were treated separately. VLiT complex models were created by initially placing one tritium atom close to one of the nearest oxygen atoms, with the OT direction pointing to the center of the vacancy. The model was then subjected to geometry optimization to obtain the final structure. Tritium atoms in all 15 models closed in with their respective nearby oxygen atom to reach the force minimum. The defect structures were analyzed and summarized in Table 2. LieO distance represents the distance between the lithium atom before its removal and the oxygen atom, which shows the relative position of the oxygen atom. OT distance refers to the distance between the tritium atom and the nearby oxygen atom. No distinct difference was observed for the OT distances among three configurations and they were all very close to the value of 1 Å. OT directions all pointed towards the approximate center of the vacancy, showing a strong tendency for tritium atom to stay near the center of the vacancy, which is in agreement with the results obtained for Li2O in R. Shah et al.'s work [10]. Repulsion from the surrounding atoms is likely the cause of the tritium atom's positional preference. Formation energies were calculated and summarized in Table 2. There are four pairs of tritium sites that have mirror symmetry which can be observed in the table. The sites have nearly identical formation energies and structural parameters, namely A2-A3, B2eB3, C1eC2 and C3eC4. It is to be noted that one site from each configuration has already been obtained from the first step of the calculation, namely A4, B2 and C6. As the starting positions of relaxation are different, the obtained positions and formations energies from the two steps are slightly different. It appears that using the relax method in the first step (placing tritium atom at the lithium substitution site) would result in tritium closing in with the closest oxygen atom. Whilst the most stable site (that has the lowest formation energy) in configuration A and B was obtained by this relax method, C1/C2 was the most stable site instead of C6. As a result, treating tritium atom as a lithium substitution in relaxation does not guarantee to obtain the most stable site for tritium, and detailed investigation of all possible sites in the vacancy is necessary. The formation energy was closely related to the structure of VLiT complex. From Table 2 it can be concluded that, in each configuration, the formation energy was dependent on two factors with the major one being the LieO distance. With increasing LieO distance (which represents the distance of tritium atom from the center of the vacancy), formation energy also increases. Such tendency is illustrated in Fig. 4. The further the tritium atom is away from the vacancy center, the closer it is to the surrounding lithium atoms, the more repulsion it meets, resulting in higher formation energy. There is one exception in the Structure C series. The smallest LieO distance lead to the high formation energy, suggesting other structural characters may influence the formation energy as well. The second factor is the SieOT angle. From Table 2,
Fig. 3. Tritium sites of three lithium vacancy configurations. Tritium atoms are represented by grey balls. Oxygen atoms are represented by red balls. (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 2 Formation energy and structural parameters of tritium sites in the lithium vacancy of configuration A, B and C.
A1 A2 A3 A4 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 C6
Formation energy (eV)
LieO distance (Å)
OT distance (Å)
SieO distance (Å)
SieOT angle ( )
0.87 0.78 0.79 0.44 1.25 0.91 0.92 1.54 1.28 0.58 0.57 0.87 0.88 0.93 0.89
2.138 2.020 2.020 1.917 2.000 1.893 1.893 2.675 2.573 2.152 2.152 2.159 2.159 2.650 2.136
0.987 1.050 1.048 0.984 0.999 0.989 0.989 1.003 1.044 1.000 1.000 1.017 1.018 0.985 0.981
1.727 1.734 1.730 1.700 1.712 1.729 1.729 1.717 1.749 1.757 1.758 1.739 1.739 1.785 1.772
102.021 103.611 103.709 108.432 106.650 114.283 114.485 107.489 106.905 117.106 116.969 131.921 131.920 119.744 131.196
5. Vacancy¡helium complex
Fig. 4. Formation energies of VLiT complexes related to the LieO distances. The straight line, dashed line and dotted line represents formation energies of structure configuration A, B and C, respectively.
when LieO distances are nearly identical, the ones with larger SieOT angles have higher formation energies. Although we have very limited samples to make the second factor a general rule. It would be inaccurate to assume when SieOT angle is very small, the formation energy would still decrease with decreasing SieOT angle, as very small SieOT angle would mean great distortion in SieOT structure which would certainly lead to higher formation energy. 4.4. Electronic structure We further investigated the bonding properties of VLiT complexes by calculating the electronic structures. Site A1 was picked as an example for the calculation of valence charge density and Bader charge analysis [30]. The valence charge density is shown in Fig. 5a. The tritium atom is buried in the charge cloud of the oxygen atom, indicating the tritium atom is closely bonded with the oxygen atom. Bader charge analysis revealed that the tritium atom has 0.357 e valence charge; the oxygen atom bonded to a tritium atom has 7.494 e valence charge; the rest of the oxygen atoms have ~7.60 e valence charge and the lithium atoms have ~0.15 e valence charge. It indicates that the neutral tritium uses one electron to interact with an oxygen 2p orbital to form the OeT bond. The oxygen atom gets most of the valence charge from its strong electronic negativity.
Vacancyhelium complex models were created by initially putting helium atoms at lithium substitution sites and then performing geometry optimization on the models. One model for each of the 19 lithium vacancies was created. After geometry relaxation, helium atoms remained in the center of the vacancy in all 19 cases. Oxygen atoms situated around a helium atom that are closer to the vacancy center (LieO distance below 2.2 Å) are pushed outward noticeably, to an extent that the HeeO distance is no less than 2.1 Å, mostly around 2.2e2.3 Å. The outward displacement of other oxygen atoms is less obvious, some of these oxygen atoms even move closer to the center of vacancy. The oxygen atoms around the helium atom are rearranged in a way, such that the HeeO distances generally become similar and structural difference between vacancy structure configurations are reduced. Lithium atoms around the helium atom moved slightly as well, some of them inward while some of them outward. Because lithium atoms are further away from helium atoms, displacement of lithium atoms is likely caused by the rearrangement of oxygen atoms, rather than the direct influence from helium. Formation energies were calculated for the 19 vacancyhelium complexes, as shown in Table 3. Formation energies of vacancyhelium complexes were in the range of 1.97e3.43 eV under Orich condition, and 4.78e6.23 eV under O-poor condition. For helium, it is still harder to form the vacancyehelium complex under O-poor condition. The formation energy of VLieHe complex is higher than VLiT's, showing that lithium vacancy is not as energy favorable for helium as for tritium to reside. The lithium vacancy structure has no obvious impact on VLieHe complex formation energies, too. For helium, it can be inferred that the rearrangement of surrounding atoms by helium has diminished the VLi structural characters. The heliumevacancy interaction energy was calculated for VLieHe complex. As the helium has greatly changed the vacancy structure, choosing interstitial sites based on previous vacancies was no longer viable. Therefore, we have chosen only one interstitial site near the No. 14 VLieHe complex (with the lowest formation energy) for the calculation. The calculated interaction energy is 1.09 eV. It suggests that lithium vacancy can still attract helium interstitial atoms. However, the helium trapping capability is much weaker than tritium trapping capability. Taking the formation energy also into consideration, it is predicted that the VLiT concentration should be higher than the VLieHe concentration in Li4SiO4. Valence charge density and Bader charge distribution of vacancyhelium complexes were calculated. Vacancy number 13
Y. Shi et al. / Journal of Nuclear Materials 467 (2015) 519e526
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Fig. 5. Valence charge density contour of the (a) VLiT complex and the (b) VLieHe complex. Atom positions are marked by their respective element symbols.
Table 3 Formation energies (eV) of 19 vacancyhelium complexes under O-rich and O-poor conditions, shown by lithium atom numbers and their structure configurations. Ef (VLieHe 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2.26 2.91 3.13 2.71 2.48 2.88 2.45 2.03 3.43 2.42 2.09 2.00 2.03 1.97 2.28 2.98 3.26 2.07 2.46
(O-rich))
Ef (VLieHe 5.06 5.72 5.93 5.51 5.28 5.69 5.26 4.83 6.23 5.22 4.89 4.80 4.83 4.78 5.08 5.79 6.06 4.87 5.27
(O-poor))
Structure A A A B A A C A A A C C A C A A A A C
was selected, same as the VLiT calculations. Valence charge density is shown in Fig. 5b. From the figure it can be seen that helium atoms stayed in the center of the vacancy, without bonding to the surrounding atoms. There was a large zero-charge space between the charge cloud of helium atom and the charge cloud of the surrounding atoms. Bader charge analysis showed that helium atom has 2.05e valence charge, indicating no obvious electronic interaction has occurred with the surrounding atoms. 6. Conclusion In this work, a systematic study of all 19 types of lithium vacancy in Li4SiO4 and their tritium/helium trapped defect complexes were investigated. Lithium vacancies were categorized by their structural configurations into three groups. Possible tritium trap sites in lithium vacancy were studied in detail. Formation energies, interaction energies and electronic structures of VLiT/He complexes were calculated. We concluded that: 1) The tritium atom in the lithium vacancy is bonded to the oxygen atom surrounding the vacancy. The vacancytritium complex formation energies are in the range of 0.41e1.28 eV under O-rich condition. Formation energies under O-poor condition are higher. The calculated vacancytritium interaction energies are 6.19~ 5.03 eV showing strong tritium trapping
capabilities for the lithium vacancy. Vacancytritium defect complex might be a major type of tritium residual forms in Li4SiO4. 2) The Helium atom in the lithium vacancy stays in the center of the vacancy without bonding. Formation energies are 1.97e3.43 eV under O-rich condition, higher than the vacancytritium case. Moreover, the vacancyehelium interaction is much weaker than vacancyetritium interaction. Therefore helium atoms could escape the trapping of lithium vacancy relatively easier. It is predicted that the vacancyehelium complex shall have less concentration than the vacancyetritium complex. Acknowledgment This work was supported by the ITER Program (No. 2014GB125002), the Major Science and Technology Programs of China, the National Natural Science Foundation of the People's Republic of China under Grant No. 91326103, the Foundation of Key Laboratory of Neutron Physics, CAEP, and the Science and Technology Innovation Team of Sichuan Province under Grant No. 15CXTD0025. References [1] C.A. Chen, D.L. Luo, Y. Sun, et al., Fusion Eng. Des. 83 (2008) 1455e1460. [2] K.M. Feng, C.H. Pan, G.S. Zhang, et al., Fusion Eng. Des. 81 (2006) 1219e1224. [3] M. Gasparotto, R. Andreani, L.V. Boccaccini, et al., Fusion Eng. Des. 66e68 (2003) 129e137. [4] C.E. Johnson, J. Nucl. Mater. 258e263 (1998) 140e148. [5] C.E. Johnson, J. Nucl. Mater. 270 (1999) 212e220. [6] T. Hanada, S. Fukada, M. Nishikawa, K. Suematsu, N. Yamashita, T. Kanazawa, Fusion Eng. Des. 85 (2010) 998e1001. [7] C. Kang, X. Wang, C. Xiao, X. Gao, M. Gu, J. Liu, H. Wang, S. Peng, X. Chen, J. Nucl. Mater. 412 (2011) 62e65. [8] C. Xiao, X. Gao, M. Kobayashi, K. Kawasaki, H. Uchimura, K. Toda, C. Kang, X. Chen, H. Wang, S. Peng, X. Wang, Y. Oya, K. Okuno, J. Nucl. Mater. 438 (2013) 46e50. [9] A. Shluger, N. Itoh, K. Noda, J. Phys. Condens. Matter 3 (1991) 9895e9906. [10] R. Shah, A. De Vita, M.C. Payne, J. Phys. Condens. Matter 7 (1995) 69814992. [11] H. Tanigawa, S. Tanaka, J. Nucl. Mater. 307e311 (2002) 1446e1450. [12] K. Munakata, Y. Yokoyama, A. Baba, R.D. Penzhorn, M. Oyaidzu, K. Okuno, Fusion Eng. Des. 75e79 (2005) 673e678. [13] T. Tang, D.L. Luo, J. At. Mol. Sci. 1 (2010) 185e200. [14] T. Tang, P. Chen, W. Luo, D. Luo, Y. Wang, J. Nucl. Mater. 420 (2012) 31e38. [15] Y. Duan, K. Parlinski, Phys. Rev. B 84 (2011) 104113. [16] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [17] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. €chl, Phys. Rev. B 50 (1994) 17953. [18] P.E. Blo [19] G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758. [20] D. Tranqui, R.D. Shannon, H.Y. Chen, S. Iijima, W.H. Baur, Acta Crystallogr. B 35 (1979) 2479. [21] B.H.W.S. Dejong, D. Ellerbroek, A.L. Spek, Acta Crystallogr. B 50 (1994) 511. [22] S.T. Murphy, N.D.M. Hine, Chem. Mater. 26 (2014) 1629e1638.
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S.T. Murphy, J. Phys. Chem. C 118 (2014) 29525e29532. K. Moritani, H. Moriyama, J. Nucl. Mater. 248 (1997) 132e139. V. Grishmanov, S. Tanaka, J. Tiliks, Fusion Eng. Des. 39e40 (1998) 685e691. S. Akahori, E. Tega, Y. Morimoto, K. Okuno, M. Nishikawa, K. Munakata, H. Moriyama, K. Kawamoto, M. Okada, J. Radioanal. Nucl. Chem. 255 (2003) 257e260. [27] M. Oyaidzu, Y. Morimoto, H. Kodama, M. Sasaki, H. Kimura, K. Munakat, M. Okada, K. Kawamoto, H. Moriyama, M. Nishikawa, K. Okuno, J. Nucl. Mater.
329e333 (2004) 1313e1317. [28] Y. Nishikawa, M. Oyaidzu, A. Yoshikawa, K. Munakata, M. Okada, M. Nishikawa, K. Okuno, J. Nucl. Mater. 367e370 (2007) 1371e1376. [29] M. Oyaidzu, Y. Nishikawa, T. Suda, T. Shinozaki, A. Yoshikawa, Y. Oya, K. Munakata, H. Yamana, K. Okuno, J. Nucl. Mater. 375 (2008) 1e7. [30] R. Bader, Atoms in molecules: a quantum theory, Oxford University Press, New York, 1990.
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Density functional study of lithium vacancy in Li4SiO4: Trapping of tritium and helium Yanli Shi a, b, Tiecheng Lu a, b, *, Tao Gao c, **, Xiaogang Xiang a, b, Qinghua Zhang a, b, Xiaohe Yu a, b, Yichao Gong a, b, Mao Yang a, b a b c
Department of Physics and Key Laboratory for Radiation Physics & Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610064, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 March 2015 Received in revised form 9 September 2015 Accepted 10 September 2015 Available online 12 September 2015
Li4SiO4 is a solid breeder material that has important applications in future fusion reactors. The interaction of tritium/helium with lithium vacancy is investigated implementing pseudopotential plane wave method within density functional theory. Models of all types of lithium vacancies and vacancytritium/ helium defect complexes are created. Possible tritium trap sites in lithium vacancies are examined and the formation energies, vacancytritium/helium interaction energies and electronic structures of the defects are calculated. The results indicate that the tritium atom trapped in the lithium vacancy bonds with one of the surrounding oxygen atoms. The formation energies of the vacancytritium complexes are in the range of 0.41e1.28 eV under oxygen-rich condition. The interaction energy calculation shows the lithium vacancy has strong tritium trapping capabilities. Moreover, the vacancyhelium complex formation energies are in the range of 1.97e3.43 eV under O-rich condition. The vacancyhelium interaction is relatively weaker, suggesting the helium atom may escape the lithium vacancy more easily. © 2015 Published by Elsevier B.V.
Keywords: Density functional theory Li4SiO4 Lithium vacancy Tritium Helium
1. Introduction Solid state breeder is one of the most significant designs used in Test Blanket Module (TBM) for future fusion reactors. Potential materials for solid state breeder include many lithium based compounds, such as Li2O, Li2TiO3, L2SiO3 and Li4SiO4. Li4SiO4, known for its excellent lithium density, tritium release capability and material compatibility, has been chosen in both Chinese [1,2] and European [3] TBM designs. Thus, it is vital to understand the tritium release behavior of Li4SiO4. Over the years, extensive out-of-pile and in-pile experiments under various conditions have been conducted to study the tritium release process in Li4SiO4 [4,5]. T. Hanada et al. [6] studied the effect of surface water on the tritium release behavior based on parameters obtained from reactor operation. They also found an optimal
* Corresponding author. Department of Physics and Key Laboratory for Radiation Physics & Technology of Ministry of Education, Sichuan University, Chengdu 610064, PR China. Tel.: þ86 13678124898. ** Corresponding author. Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610064, PR China. Tel.: þ86 13688350443. E-mail address: [email protected] (T. Lu). http://dx.doi.org/10.1016/j.jnucmat.2015.09.017 0022-3115/© 2015 Published by Elsevier B.V.
grain size for tritium release. C. Kang et al. [7] performed out-of-pile tritium release experiments with different water contents. They found the portion of gaseous form of tritium decreases with water content whereas the HTO portion increases. C. Xiao et al. [8] performed out-of-pile annealing experiments on Li4SiO4 pebbles, and the diffusion process within crystal grains was found to play a major role in the tritium release process, whereas diffusion in grain boundaries showed little effect. The diffusion coefficients of tritium in the crystal grains were also determined. Theoretical studies of solid state breeder materials have mainly focused on the tritium behavior in crystal grains and on material surfaces. Tritium diffusion in crystal grains has been shown to be an important step of the tritium release process. It is affected by various irradiation induced defects (lithium vacancy, oxygen vacancy and broken bond). Lithium vacancy is considered as a primary irradiation induced defect in lithium based breeder materials, as lithium atoms are constantly knocked out of their positions or consumed to generate tritium under irradiation. Lithium vacancy in Li2O has been studied in detail in previous theoretical works. A. Shluger et al. [9] investigated tritium diffusion in Li2O with a quantum-chemical approach and concluded that the majority of the tritium release from Li2O is determined by the triton ion's
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diffusion via a vacancy mechanism. R. Shah et al. [10] performed ab initio studies on tritium point defects in Li2O and calculated the activation energy for tritium diffusion. Tritium behavior with charged defects in Li2O has also been worked on [11]. Possibly due to its complex crystal structure, studies on Li4SiO4 have been less extensive. K. Munakata et al. [12] studied the crystal structures and electron states of Li4SiO4 using linear combination of atomic orbital and Hartree-Fock (LCAO-HF) ab initio electron calculation. T. Tang et al. [13,14] also reported crystal structures and electronic structures of Li4SiO4 implementing ab initio calculation within density functional theory (DFT). Y. Duan et al. [15] studied the structural, electronic, and thermodynamic properties of Li4SiO4 as a CO2 capture material within DFT. To the best of our knowledge, there has not been any reported work on the tritium behavior in Li4SiO4 so far. Due to the important role of lithium vacancy in tritium release, we believe it is necessary to study the tritium behavior with lithium vacancy in Li4SiO4. On the other hand, as helium bubble formation is a common issue in irradiated materials, and the lithium vacancy is a possible helium nucleation site, the helium behavior with lithium vacancy is also worth looking into. In this study, lithium vacancy and its interaction with tritium/ helium in Li4SiO4 were studied within DFT implementing pseudopotential plane wave method. Models of lithium vacancies and vacancytritium/helium complexes were created based on a Li4SiO4 super cell model. A systematic investigation of all types of lithium vacancies and vacancytritium/helium complexes were conducted. All possible tritium trap sites in the vacancy were analyzed. Formation energies, vacancytritium/helium interaction energies and electronic structures of the defect structures were also calculated. Our study could help towards the understanding of tritium/helium behavior in Li4SiO4 grains. 2. Theoretic methods and model In this study, plane wave DFT calculations were performed within the Vienna Ab initio Simulation Package (VASP) [16]. The generalized gradient approximation (GGA) of Perduw-BurkeErnzerhof (PBE) [17] was implemented. Projector augmentedwave (PAW) [18] potentials generated by G. Kresse [19] were used. The valence states electrons of Li, Si and O atoms include 2s1, 3s23p2 and 2s22p4, respectively. Convergence tests were conducted to determine the energy cutoff of the plane wave basis and the K-point grid. We finally set 400 eV as the energy cutoff. And gamma point centered K-point mesh of 1 1 1 was chosen for geometry optimization and 2 2 2 for energy and electronic structure calculation, respectively. The Gaussian band smearing method with a width of 0.05 eV was utilized. The electronic self-consistent loops were converged to 104 eV/cell and the geometry relaxation was considered to be completed when the total force on the atom is less than 0.02 eV Å1. Both the atom positions and the size/shape of the cell were allowed to change during the geometry relaxation. The crystal structure of Li4SiO4 proposed by Tranqui et al. [20] was used in this study. It is a monoclinic structure with space group P21/m (No. 11). A total of 126 atoms are in this crystal structure, of which 56 are lithium, 14 are silicon and 56 are oxygen. All lithium atoms in this model are full occupied as opposed to an earlier model proposed by Dejong et al. [21], in which 4 types of lithium atoms are partially occupied. In our study, a 1 2 1 super cell of Li4SiO4 was adopted and then its geometry was optimized using DFT calculation, as is shown in Fig. 1a. Crystal parameters of the optimized super cell are as follows: a ¼ 11.443 Å, b ¼ 12.108 Å, c ¼ 16.607 Å, b ¼ 99.408 . They are all in good agreement with previous studies [13e15,20]. The deviations from electron diffraction data [20] are no more than 0.77%.
The neutral defect formation energy in this study was calculated by
Ef ¼ EðdÞ EðpÞ
X
ni mi
(1)
i
where E(d) is the total energy of the defect model, and E(p) is the total energy of the perfect 1 2 1 super cell. ni is the number of the species added to the perfect unit cell, of which positive number means atoms added to the unit, while negative number means atoms removed from the unit. mi is the chemical potential of the specie. We considered two conditions for the selection of reference materials for chemical potential calculation. For the O-rich condition, we chose H2O for tritium, Li2O for lithium and O2 for oxygen. For the O-poor condition, we chose H2 for tritium and Li metal for lithium. In this case, the formation energy of the lithium vacancy can be written as:
1 Ef ðVLi Þ ¼ EðLi4 SiO4 ; VLi Þ EðLi4 SiO4 Þ þ EðLi2 OÞ 2 1 EðO2 ÞðO richÞ 4
(2)
Ef ðVLi Þ ¼ EðLi4 SiO4 ; VLi Þ EðLi4 SiO4 Þ þ EðLimetal ÞðO poorÞ (3) The formation of tritium trapped in lithium vacancy can be written as:
1 Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; TÞ EðLi4 SiO4 Þ þ EðLi2 OÞ 2 1 EðH2 OÞðO richÞ 2
(4)
Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; TÞ EðLi4 SiO4 Þ þ EðLimetal Þ 1 EðH2 ÞðO poorÞ 2
(5)
For helium trapped in lithium vacancy, the formation energy was calculated by:
1 Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; HeÞ EðLi4 SiO4 Þ þ EðLi2 OÞ EðHeÞ 2 1 EðO2 ÞðO richÞ 4 (6) Ef ðTLi Þ ¼ EðLi4 SiO4 ; VLi ; HeÞ EðLi4 SiO4 Þ þ EðLimetal Þ EðHeÞðO poorÞ
(7)
The vacancytritium/helium interaction energy was also calculated. The interaction energy Ei is written by:
Ei ðVLi ; T=HeÞ ¼ EðLi4 SiO4 ; VLi ; T=HeÞ þ EðLi4 SiO4 Þ EðLi4 SiO4 ; T=HeÞ EðLi4 SiO4 ; VLi Þ
(8)
EðLi4 SiO4 ; VLi ; T=HeÞ is the energy of the Li4SiO4 model containing both the lithium vacancy and tritium/helium. EðLi4 SiO4 Þ is the energy of the perfect Li4SiO4 super cell. EðLi4 SiO4 ; T=HeÞ is the energy of the model with a tritium/helium interstitial atom. EðLi4 SiO4 ; VLi Þ is the energy of the model with a lithium vacancy.
Y. Shi et al. / Journal of Nuclear Materials 467 (2015) 519e526
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Fig. 1. (a) Super cell model of Li4SiO4. (b) Li4SiO4 model viewed from [0 1 0], with numbered lithium atom positions. Lithium atoms are represented by purple balls. Silicon atoms are represented by yellow balls. Oxygen atoms are represented by red balls. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Lithium vacancy 3.1. Defect structure A systematic analysis was performed to study the various lithium vacancies in Li4SiO4. A 126-atom Li4SiO4 single cell is composed of two centrosymmetric sets of 63 atoms. Each set has 19 unique lithium atoms (28 in total) floating around 7 groups of isolated SiO4 units. Thus, there are 19 unique lithium atoms. The lithium atoms are numbered accordingly as shown in Fig. 1b. The oxygen atoms are positioned as the first nearest neighbor around lithium atoms and the coordination number varies between the different lithium atoms. Thus, according to their coordination number with oxygen atoms and the relative positions of these oxygen atoms, the 19 unique lithium atoms can be categorized into three groups (Configuration A, B and C), as shown in Fig. 2. The lithium atom of Configuration A has 4 nearest oxygen atoms which constitute a tetrahedral configuration (Fig. 2a). There are thirteen unique lithium atoms in Configuration A, which are No. 1, 2, 3, 5, 6, 8, 9, 10, 13, 15, 16, 17 and 18. Each lithium atom has a slightly different tetrahedral structure. LieO distances are in the range of 1.881e2.054 Å, which is in agreement with that reported by Tranqui et al. [20].
The lithium atom of Configuration B is 5-fold coordinated with the nearest oxygen atoms (Fig. 2b). Lithium atom No. 4 is in Configuration B. Spatial structure of Configuration B is a triangular bipyramid with the lithium atom in the center. Tranqui et al. [20] excluded the oxygen atom at the bottom of the structure shown in Fig. 2b from the configuration and classified it as a tetrahedron. However, this study showed that the LieO distances of the bottom oxygen atom and top oxygen atom shown in Fig. 2b are 2.573 Å and 2.675 Å, respectively. As a result, it is more reasonable to include the bottom oxygen atom in the space configuration. The remaining 3 LieO distances are smaller and in the range of 1.893e2.000 Å. Spatial structure of Configuration C is an octahedron with 6 oxygen atoms at vertex positions and lithium atom in the center (Fig. 2c). The five lithium atoms of Configuration C are No. 7, 11, 12, 14 and 19. Five of the six LieO distances are in a narrow distribution less than 0.13 Å. However, the sixth LieO distance is significantly larger. In the work of Tranqui et al. [20], No. 7 and 19 lithium atoms are excluded from this group possibly for the larger sixth LieO distances. However, the differences between the smallest and the largest LieO distances are 0.98 Å, 0.23 Å, 0.52 Å, 0.12 Å and 0.46 Å for lithium atom No. 7, 11, 12, 14 and 19, respectively. Therefore, it is more reasonable to include No. 7 and 19 in Configuration C. The real Li vacancies are expected to be charged. The work of
Fig. 2. Spatial configurations of three groups of lithium atoms. Lithium atoms are represented by purple balls. Oxygen atoms are represented by red balls. (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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Murphy et al. [22] indicates that 1 charged Li vacancies have lower formation energies than neutral ones in Li2TiO3, thus have better chances to exist in Li2TiO3. Our calculation showed that neutral Li vacancies have lower formation energies when the Fermi level is located near the edge of the valence band in the band gap, however, charged defects are beyond the scope of this investigation and would be discussed in future works. In this study, only neutral defects were investigated. By removing lithium atoms from the structure, a total of 19 lithium vacancy models categorized in 3 configurations were created. These models were subsequently relaxed by DFT calculation, and afterwards used in formation energy calculations and tritium/helium defect study.
either VLi 0 þT0 or VLi 1 þTþ. It was observed that the oxygen dangling bonds created by the removal of lithium atom would be the most probable sites for tritium atom. Configuration A, B and C each has 4, 5 and 6 such oxygen dangling bond, respectively. As there are 19 types of lithium vacancy, it would not be possible to study all these sites within our resources. Thus, we first created 19 VLiT models by positioning tritium atoms at the original positions of Li before their removal and then subjecting these models through geometry relaxation. A general picture of how the 19 types of lithium vacancies affect tritium behavior can be achieved through this approach. Secondly, one lithium vacancy from each configuration was selected to study all the possible sites of tritium.
3.2. Formation energy
4.1. Defect structure
The formation energies of 19 lithium vacancies were calculated and summarized in Table 1. For O-rich condition, formation energies are in the range of 1.31e2.50 eV. For O-poor condition, formation energies are in the range of 4.11e5.30 eV. It is clear that formation energies of lithium vacancies in Li4SiO4 are much higher under O-poor condition. It indicates that lithium vacancies are easy to form in O-rich condition but difficult to form in O-poor condition. There appears to be no correlation between the structure configuration and its formation energy, as no obvious energy difference was found among the three configurations. Lithium vacancies of Configuration A have a wide distribution of formation energies covering the minimum and maximum of 19 formation energies, while formation energies of Configuration C are in the range of 1.31e1.54 eV. The difference in formation energies seems to be dependent on the comprehensive environment of the local structure rather than the single parameter of lithium coordination number.
In the initial step, after geometry relaxation, tritium atoms were observed to move away from their initial positions and closed in with one of the nearest oxygen atoms in all 19 models. The OT distances are around 1 Å with very small deviations no more than 0.1 Å. The average value is 1.006 Å, slightly larger than the 0.985 Å predicted in Li2TiO3 by Murphy [23]. The OT direction pointed to the approximate center of the vacancy for all cases, i.e. the tritium atom stayed in the space left by the removal of the lithium atom. It can be inferred that the tritium is bonded to the oxygen atom. This result was similar to that observed in Li2O by R. Shah et al. [10], where the tritium atom is bonded with a nearby oxygen atom in the lithium vacancy. It is also observed in ternary lithium oxides Li2TiO3 by Murphy [23]. The SieO bond length of the oxygen atoms in question was noticeably stretched, and the oxygen atom moved slightly towards the vacancy center. The SiO4 tetrahedron rotated with the movement of this oxygen atom, and OeSieO angles in the tetrahedron were only slightly changed.
4. Lithium vacancy¡tritium defect complex (VLi¡T)
4.2. Formation energy and vacancytritium interaction energy
VLiT models were created by placing hydrogen atoms in the lithium vacancies. All tritium atoms were treated as hydrogen atoms as they present the same electronic properties within DFT calculations. The VLiT complexes were treated as neutral in this study. Considering he possible charge states of the lithium vacancy are 0 and 1, and the possible charge states of the tritium atom are þ1, 0 and 1, the neutral VLiT complexes could be formed by
Formation energies of the 19 VLiT complex models under Orich condition are in the range of 0.41e1.28 eV. For O-poor condition, the energy range is 1.94e2.82 eV. The VLiT formation energies are lower than the vacancy formation energies, which means VLiT complexes are easier to form. Comparing between O-rich and O-poor conditions, VLiT defects are easier to form under O-rich condition. The low formation energy also suggests that VLiT is a
Table 1 Formation energies (eV) of the lithium vacancies (VLi) and VLiT complexes under O-rich and O-poor conditions. Their respective structure configurations are also presented.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Ef (VLi(O-rich))
Ef (VLi(O-poor))
Ef (VLiT(O-rich))
Ef (VLiT(O-poor))
Structure
1.45 2.32 2.30 2.13 1.47 2.31 1.54 1.37 2.50 1.50 1.40 1.31 1.31 1.32 1.51 2.42 2.45 1.39 1.49
4.26 5.13 5.10 4.93 4.27 5.11 4.34 4.18 5.30 4.30 4.21 4.11 4.11 4.13 4.32 5.23 5.25 4.19 4.30
0.41 1.13 0.86 0.91 1.17 1.03 0.70 0.43 1.28 0.69 0.63 0.88 0.46 0.71 0.43 1.17 1.01 0.64 0.85
1.94 2.67 2.40 2.44 2.71 2.57 2.24 1.96 2.82 2.23 2.16 2.42 1.99 2.25 1.97 2.71 2.54 2.18 2.39
A A A B A A C A A A C C A C A A A A C
Y. Shi et al. / Journal of Nuclear Materials 467 (2015) 519e526
highly possible form of tritium residual in Li4SiO4. The vacancytritium interaction energy was also calculated. One model each from the three structure configurations were chosen for the calculation, namely No. 13, 04 and 12, because of their lowest formation energies within their configurations. The tritium interstitial sites were selected based on their structures. For example, 4 interstitial sites off the 4 surfaces of the tetrahedron of No. 13 were selected. Likewise, 6 and 8 interstitial sites were chosen for No. 04 and 12, respectively. The results showed that the interaction energies of No. 13, 04 and 12 were between 5.60 and 5.39 eV, 6.19~ 5.84 eV and 5.28~ 5.03 eV, respectively. The large negative values indicate it's energy favorable for tritium to stay in the lithium vacancy than outside as an interstitial atom. The vacancytritium interaction energy results predict the lithium vacancy in Li4SiO4 has strong tritium trapping capabilities. K. Moritani et al.'s work [24] suggests that, when under relatively low neutron fluence(<1018 cm2), tritium diffusion in Li4SiO4 is enhanced by decreasing neutron fluence. This was also observed in Li2O by V. Grishmanov et al. [25]. Low neutron fluence would mainly cause point defects, i.e. lithium vacancy, oxygen vacancy and silicon dangling bond. It is concluded that point defects impede tritium diffusion by trapping tritium atoms. Our calculation proved that lithium vacancy is one of such possible tritium trap sites. A number of annealing experiments [26e29] performed on irradiated lithium based breeder materials indicate that the annihilation of lithium vacancies does not lead to tritium release, and thus lithium vacancies have no significant tritium-trapping ability. Our study indicates that tritium trapped in lithium vacancy forms OeT bond which is not detected by electronic spin resonance (ESR), and is very stable when subjected to low temperature annealing. As a result, the above experimental results are not the direct proof of lithium vacancies' tritium trapping ability. M. Oyaidzu et al. [27] discussed that two tritium release peaks at 750e850 K could be caused by SieOT decomposing. 4.3. Tritium trap sites In the second step of our investigation, one vacancy model from each of the three configurations was selected for further study into multiple tritium sites. The model that had the lowest formation energy in each configuration was chosen, namely vacancy number 13, 04 and 12 for configuration A, B and C, respectively. The possible sites for tritium atom in these models were labeled and shown in Fig. 3, i.e. site B2 refers to the second tritium site in configuration B. There are 4, 5 and 6 possible sites in configuration A, B and C, respectively, corresponding to the number of nearest oxygen atoms. It is to be noted that some of the oxygen atoms in the selected vacancy models have mirror symmetry. However, the symmetry observed were not shared by those vacancies that were
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not chosen. Thus, these oxygen atoms were treated separately. VLiT complex models were created by initially placing one tritium atom close to one of the nearest oxygen atoms, with the OT direction pointing to the center of the vacancy. The model was then subjected to geometry optimization to obtain the final structure. Tritium atoms in all 15 models closed in with their respective nearby oxygen atom to reach the force minimum. The defect structures were analyzed and summarized in Table 2. LieO distance represents the distance between the lithium atom before its removal and the oxygen atom, which shows the relative position of the oxygen atom. OT distance refers to the distance between the tritium atom and the nearby oxygen atom. No distinct difference was observed for the OT distances among three configurations and they were all very close to the value of 1 Å. OT directions all pointed towards the approximate center of the vacancy, showing a strong tendency for tritium atom to stay near the center of the vacancy, which is in agreement with the results obtained for Li2O in R. Shah et al.'s work [10]. Repulsion from the surrounding atoms is likely the cause of the tritium atom's positional preference. Formation energies were calculated and summarized in Table 2. There are four pairs of tritium sites that have mirror symmetry which can be observed in the table. The sites have nearly identical formation energies and structural parameters, namely A2-A3, B2eB3, C1eC2 and C3eC4. It is to be noted that one site from each configuration has already been obtained from the first step of the calculation, namely A4, B2 and C6. As the starting positions of relaxation are different, the obtained positions and formations energies from the two steps are slightly different. It appears that using the relax method in the first step (placing tritium atom at the lithium substitution site) would result in tritium closing in with the closest oxygen atom. Whilst the most stable site (that has the lowest formation energy) in configuration A and B was obtained by this relax method, C1/C2 was the most stable site instead of C6. As a result, treating tritium atom as a lithium substitution in relaxation does not guarantee to obtain the most stable site for tritium, and detailed investigation of all possible sites in the vacancy is necessary. The formation energy was closely related to the structure of VLiT complex. From Table 2 it can be concluded that, in each configuration, the formation energy was dependent on two factors with the major one being the LieO distance. With increasing LieO distance (which represents the distance of tritium atom from the center of the vacancy), formation energy also increases. Such tendency is illustrated in Fig. 4. The further the tritium atom is away from the vacancy center, the closer it is to the surrounding lithium atoms, the more repulsion it meets, resulting in higher formation energy. There is one exception in the Structure C series. The smallest LieO distance lead to the high formation energy, suggesting other structural characters may influence the formation energy as well. The second factor is the SieOT angle. From Table 2,
Fig. 3. Tritium sites of three lithium vacancy configurations. Tritium atoms are represented by grey balls. Oxygen atoms are represented by red balls. (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 2 Formation energy and structural parameters of tritium sites in the lithium vacancy of configuration A, B and C.
A1 A2 A3 A4 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 C6
Formation energy (eV)
LieO distance (Å)
OT distance (Å)
SieO distance (Å)
SieOT angle ( )
0.87 0.78 0.79 0.44 1.25 0.91 0.92 1.54 1.28 0.58 0.57 0.87 0.88 0.93 0.89
2.138 2.020 2.020 1.917 2.000 1.893 1.893 2.675 2.573 2.152 2.152 2.159 2.159 2.650 2.136
0.987 1.050 1.048 0.984 0.999 0.989 0.989 1.003 1.044 1.000 1.000 1.017 1.018 0.985 0.981
1.727 1.734 1.730 1.700 1.712 1.729 1.729 1.717 1.749 1.757 1.758 1.739 1.739 1.785 1.772
102.021 103.611 103.709 108.432 106.650 114.283 114.485 107.489 106.905 117.106 116.969 131.921 131.920 119.744 131.196
5. Vacancy¡helium complex
Fig. 4. Formation energies of VLiT complexes related to the LieO distances. The straight line, dashed line and dotted line represents formation energies of structure configuration A, B and C, respectively.
when LieO distances are nearly identical, the ones with larger SieOT angles have higher formation energies. Although we have very limited samples to make the second factor a general rule. It would be inaccurate to assume when SieOT angle is very small, the formation energy would still decrease with decreasing SieOT angle, as very small SieOT angle would mean great distortion in SieOT structure which would certainly lead to higher formation energy. 4.4. Electronic structure We further investigated the bonding properties of VLiT complexes by calculating the electronic structures. Site A1 was picked as an example for the calculation of valence charge density and Bader charge analysis [30]. The valence charge density is shown in Fig. 5a. The tritium atom is buried in the charge cloud of the oxygen atom, indicating the tritium atom is closely bonded with the oxygen atom. Bader charge analysis revealed that the tritium atom has 0.357 e valence charge; the oxygen atom bonded to a tritium atom has 7.494 e valence charge; the rest of the oxygen atoms have ~7.60 e valence charge and the lithium atoms have ~0.15 e valence charge. It indicates that the neutral tritium uses one electron to interact with an oxygen 2p orbital to form the OeT bond. The oxygen atom gets most of the valence charge from its strong electronic negativity.
Vacancyhelium complex models were created by initially putting helium atoms at lithium substitution sites and then performing geometry optimization on the models. One model for each of the 19 lithium vacancies was created. After geometry relaxation, helium atoms remained in the center of the vacancy in all 19 cases. Oxygen atoms situated around a helium atom that are closer to the vacancy center (LieO distance below 2.2 Å) are pushed outward noticeably, to an extent that the HeeO distance is no less than 2.1 Å, mostly around 2.2e2.3 Å. The outward displacement of other oxygen atoms is less obvious, some of these oxygen atoms even move closer to the center of vacancy. The oxygen atoms around the helium atom are rearranged in a way, such that the HeeO distances generally become similar and structural difference between vacancy structure configurations are reduced. Lithium atoms around the helium atom moved slightly as well, some of them inward while some of them outward. Because lithium atoms are further away from helium atoms, displacement of lithium atoms is likely caused by the rearrangement of oxygen atoms, rather than the direct influence from helium. Formation energies were calculated for the 19 vacancyhelium complexes, as shown in Table 3. Formation energies of vacancyhelium complexes were in the range of 1.97e3.43 eV under Orich condition, and 4.78e6.23 eV under O-poor condition. For helium, it is still harder to form the vacancyehelium complex under O-poor condition. The formation energy of VLieHe complex is higher than VLiT's, showing that lithium vacancy is not as energy favorable for helium as for tritium to reside. The lithium vacancy structure has no obvious impact on VLieHe complex formation energies, too. For helium, it can be inferred that the rearrangement of surrounding atoms by helium has diminished the VLi structural characters. The heliumevacancy interaction energy was calculated for VLieHe complex. As the helium has greatly changed the vacancy structure, choosing interstitial sites based on previous vacancies was no longer viable. Therefore, we have chosen only one interstitial site near the No. 14 VLieHe complex (with the lowest formation energy) for the calculation. The calculated interaction energy is 1.09 eV. It suggests that lithium vacancy can still attract helium interstitial atoms. However, the helium trapping capability is much weaker than tritium trapping capability. Taking the formation energy also into consideration, it is predicted that the VLiT concentration should be higher than the VLieHe concentration in Li4SiO4. Valence charge density and Bader charge distribution of vacancyhelium complexes were calculated. Vacancy number 13
Y. Shi et al. / Journal of Nuclear Materials 467 (2015) 519e526
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Fig. 5. Valence charge density contour of the (a) VLiT complex and the (b) VLieHe complex. Atom positions are marked by their respective element symbols.
Table 3 Formation energies (eV) of 19 vacancyhelium complexes under O-rich and O-poor conditions, shown by lithium atom numbers and their structure configurations. Ef (VLieHe 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2.26 2.91 3.13 2.71 2.48 2.88 2.45 2.03 3.43 2.42 2.09 2.00 2.03 1.97 2.28 2.98 3.26 2.07 2.46
(O-rich))
Ef (VLieHe 5.06 5.72 5.93 5.51 5.28 5.69 5.26 4.83 6.23 5.22 4.89 4.80 4.83 4.78 5.08 5.79 6.06 4.87 5.27
(O-poor))
Structure A A A B A A C A A A C C A C A A A A C
was selected, same as the VLiT calculations. Valence charge density is shown in Fig. 5b. From the figure it can be seen that helium atoms stayed in the center of the vacancy, without bonding to the surrounding atoms. There was a large zero-charge space between the charge cloud of helium atom and the charge cloud of the surrounding atoms. Bader charge analysis showed that helium atom has 2.05e valence charge, indicating no obvious electronic interaction has occurred with the surrounding atoms. 6. Conclusion In this work, a systematic study of all 19 types of lithium vacancy in Li4SiO4 and their tritium/helium trapped defect complexes were investigated. Lithium vacancies were categorized by their structural configurations into three groups. Possible tritium trap sites in lithium vacancy were studied in detail. Formation energies, interaction energies and electronic structures of VLiT/He complexes were calculated. We concluded that: 1) The tritium atom in the lithium vacancy is bonded to the oxygen atom surrounding the vacancy. The vacancytritium complex formation energies are in the range of 0.41e1.28 eV under O-rich condition. Formation energies under O-poor condition are higher. The calculated vacancytritium interaction energies are 6.19~ 5.03 eV showing strong tritium trapping
capabilities for the lithium vacancy. Vacancytritium defect complex might be a major type of tritium residual forms in Li4SiO4. 2) The Helium atom in the lithium vacancy stays in the center of the vacancy without bonding. Formation energies are 1.97e3.43 eV under O-rich condition, higher than the vacancytritium case. Moreover, the vacancyehelium interaction is much weaker than vacancyetritium interaction. Therefore helium atoms could escape the trapping of lithium vacancy relatively easier. It is predicted that the vacancyehelium complex shall have less concentration than the vacancyetritium complex. Acknowledgment This work was supported by the ITER Program (No. 2014GB125002), the Major Science and Technology Programs of China, the National Natural Science Foundation of the People's Republic of China under Grant No. 91326103, the Foundation of Key Laboratory of Neutron Physics, CAEP, and the Science and Technology Innovation Team of Sichuan Province under Grant No. 15CXTD0025. References [1] C.A. Chen, D.L. Luo, Y. Sun, et al., Fusion Eng. Des. 83 (2008) 1455e1460. [2] K.M. Feng, C.H. Pan, G.S. Zhang, et al., Fusion Eng. Des. 81 (2006) 1219e1224. [3] M. Gasparotto, R. Andreani, L.V. Boccaccini, et al., Fusion Eng. Des. 66e68 (2003) 129e137. [4] C.E. Johnson, J. Nucl. Mater. 258e263 (1998) 140e148. [5] C.E. Johnson, J. Nucl. Mater. 270 (1999) 212e220. [6] T. Hanada, S. Fukada, M. Nishikawa, K. Suematsu, N. Yamashita, T. Kanazawa, Fusion Eng. Des. 85 (2010) 998e1001. [7] C. Kang, X. Wang, C. Xiao, X. Gao, M. Gu, J. Liu, H. Wang, S. Peng, X. Chen, J. Nucl. Mater. 412 (2011) 62e65. [8] C. Xiao, X. Gao, M. Kobayashi, K. Kawasaki, H. Uchimura, K. Toda, C. Kang, X. Chen, H. Wang, S. Peng, X. Wang, Y. Oya, K. Okuno, J. Nucl. Mater. 438 (2013) 46e50. [9] A. Shluger, N. Itoh, K. Noda, J. Phys. Condens. Matter 3 (1991) 9895e9906. [10] R. Shah, A. De Vita, M.C. Payne, J. Phys. Condens. Matter 7 (1995) 69814992. [11] H. Tanigawa, S. Tanaka, J. Nucl. Mater. 307e311 (2002) 1446e1450. [12] K. Munakata, Y. Yokoyama, A. Baba, R.D. Penzhorn, M. Oyaidzu, K. Okuno, Fusion Eng. Des. 75e79 (2005) 673e678. [13] T. Tang, D.L. Luo, J. At. Mol. Sci. 1 (2010) 185e200. [14] T. Tang, P. Chen, W. Luo, D. Luo, Y. Wang, J. Nucl. Mater. 420 (2012) 31e38. [15] Y. Duan, K. Parlinski, Phys. Rev. B 84 (2011) 104113. [16] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [17] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. €chl, Phys. Rev. B 50 (1994) 17953. [18] P.E. Blo [19] G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758. [20] D. Tranqui, R.D. Shannon, H.Y. Chen, S. Iijima, W.H. Baur, Acta Crystallogr. B 35 (1979) 2479. [21] B.H.W.S. Dejong, D. Ellerbroek, A.L. Spek, Acta Crystallogr. B 50 (1994) 511. [22] S.T. Murphy, N.D.M. Hine, Chem. Mater. 26 (2014) 1629e1638.
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