SnS₂ nanotubes: a promising candidate for the anode material for lithium ion batteries

Abstract

First-principles calculations were employed to investigate the adsorption and diffusion of lithium atoms (Li) on various SnS₂ nanostructures, i.e., bulk, bilayer, monolayer, nanoribbons and nanotubes. Our results show that on the SnS₂ bulk and bilayer, Li adsorption is more stable than the counterparts of the monolayer, nanoribbons and nanotubes, but the diffusion is unfavorable. Although the SnS₂ monolayer can greatly increase the mobility of Li, its adsorption strength is relatively weak with respect to other nanostructures. When cutting the monolayer into one-dimensional zigzag nanoribbons, the binding energies of Li do not increase, leading to them being excluded as an electrode material for Li-ion batteries. Interestingly, when rolling the monolayer into one-dimensional nanotubes, the adsorption strength is enhanced and the diffusion of Li atoms becomes kinetically favorable. Therefore, SnS₂ nanotubes would be expected to be a very promising anode material in Li-ion batteries.

---

1. Introduction

As one of the most important energy storage devices, lithium ion batteries (LIBs) have attracted lots of attention from scientists. They are widely used in various products from portable electronics like mobile phones, laptops and digital cameras to electric vehicles and electric grids, which play an indispensable role in today's society. However, with the high-speed development of society, the demands of LIBs with higher storage capacity, stability and safety increase simultaneously. To this end, lots of effort has been applied to developing new electrode materials, especially anode materials to meet these specifications.^1–6

During the past decades, Sn-based materials, especially SnS₂, which can provide ideal space for Li atom intercalation as it has a layered structure, play an important role in LIBs.^7–14 For example, Zhong et al. have synthesized the ultrathin SnS₂ nanosheets which showed an average capacity as high as 1050 mA h g⁻¹ at 1 C.⁷ Laterally confined (<150 nm) 2D layered SnS₂ nanoplates have been prepared by Seo et al., these nanoplates presented a large irreversible discharge capacity of 1311 mA h g⁻¹ at the first cycle-life and an average capacity of 583 mA h g⁻¹ after 30th cycles.⁸ Besides these pure materials, their composites have also been fabricated, which show a superior performance to the bare ones. Chang et al. synthesized the SnS₂/SnO₂ composites, which exhibited high reversible capacities and good cycling performances when used as anode materials of Li-ion batteries.¹⁵ Zhuo et al. have prepared SnS₂/graphene nanocomposites, which can exhibit remarkably improved Li-storage ability with a good cycling life and high capability superior to that of the pristine SnS₂.⁹

Not to be outdone, first principle calculations were emerging as a very powerful tool to design and screen the new generation anode material. Recently, Tibbetts et al. have studied the diffusion of a Li atom on the single-walled TiS₂ nanotubes. Their computational results unveiled that the mobility of Li on the nanotube surface is very fast and the diffusion barrier is 0.2 eV lower than that of the TiS₂ bulk.¹⁶ Li et al. investigated the adsorption and diffusion of Li on the three-dimensional (3D) MoS₂ bulk, two-dimensional (2D) MoS₂ nanosheets (NSs) and one-dimensional (1D) MoS₂ zigzag nanoribbons (ZNRs). Their results showed that as the dimensionality of MoS₂ reduces from 3D to 2D, the Li diffusion barrier can significantly decrease, but unfortunately, accompanying by the reduction in binding energy. Interestingly, with the dimensionality further decreasing, MoS₂ ZNR exhibits a remarkably enhanced binding energy without sacrificing the mobility of Li.¹⁷ Because a good anode material always requires a strong Li binding strength but an appropriate low diffusion barrier (or a high Li mobility) in the process of Li “intercalation” and “deintercalation”, thus, MoS₂ ZNR is believed as a promising electrode material.

Since Sn-based materials exhibit a great prospect as anode material in LIBs and the dimensionality plays a paramount role toward the performance of LIBs, an interesting question arises naturally: could the performance of SnS₂ in LIBs be enhanced by decreasing their dimensionality? To the best of our knowledge, this issue has not been addressed up to now.

In this contribution, by means of first-principle calculations, we systematically studied the adsorption and diffusion of Li on various SnS₂ nanostructures, including its 3D bulk, 2D NSs, 1D NRs and nanotubes (NTs). Our results show that the performance of SnS₂ in LIBs can indeed be enhanced by decreasing their dimensionality. Specially, bulk and bilayer SnS₂ have higher binding energies than the counterparts of other SnS₂-derived nanostructures, but also have the relative higher diffusion barriers of ∼0.60 eV. For SnS₂ monolayer, the diffusion barrier sharply decreases to 0.17 eV, demonstrating a great enhancement of Li mobility, however, the binding energy also has a large reduction (from 2.20 to 1.21 eV). By cutting the SnS₂ monolayer into 1D nanoribbons, the binding energy of Li does not notably increase as expecting. Thus, it is also not a suitable candidate. Interestingly, when rolling up the SnS₂ monolayer into 1D nanotubes, the binding energy increases and simultaneously the calculated diffusion barrier is only ∼0.16 eV, which is very close to the one on the monolayer. Therefore, SnS₂ NTs would be a very promising anode material for the applications in Li-ion batteries.

2. Computational details

The generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) form^18,19 and a 350 eV cutoff for plane-wave basis set were adopted as implemented in the Vienna ab initio simulation package (VASP).^20,21 The projector-augmented plane wave (PAW)²² method was employed to model the ion–electron interaction and 5s²5p² electrons states of Sn atom, 3s²3p⁴ electrons states of S atom and 2s¹ electron state of Li atom were considered as valences. The convergence threshold was set to be 1 × 10⁻⁵ eV and 2 × 10⁻² eV Å⁻¹ for energy and force, respectively. The vacuum space at least 12 Å is adopted to avoid the interaction between two periodical units.

Brillouin zones were sampled with 3 × 3 × 4, 5 × 5 × 1, and 1 × 1 × 6 k-point grids for 3D SnS₂ bulk, 2D bilayer/monolayer and 1D nanoribbons/nanotubes, respectively. The energy cutoff and k points settings are proved to be sufficient for achieving converged results. The supercells we used here are large enough to avoid the interference between two neighboring Li atoms (i.e., we used a 4 × 4 × 2 supercell for 3D bulk structure, and quadrupled/doubled the size along the growth direction for 2D/1D systems, respectively). Particularly, to give an accurate description of weak interactions, we adopted the PBE+D2 method with the Grimme vdW correction²³ for bulk and bilayer SnS₂. The transition states (TS) were roughly located by using the climbing nudged elastic band method (CNEB),^24,25 which starts by inserting a series of image structures between the initial and final states of the reaction. The TSs were further optimized to the saddle point with the quasi-Newton algorithm until the residual forces were less than the standard we set (2 × 10⁻² eV Å⁻¹). Vibration analyses were then carried out to confirm each TS having only one negative frequency. For SnS₂ NTs, the basic building unit of S–Sn–S triple layer leads to NTs easily containing several hundreds of atom, resulting in too large computational burden for typical ab initio calculations. Here, we use a curved surface technique, which have been proved to be an efficient method to handle such a large NT system.^16,26

Over the computation, the binding energy is defined as

E_b = (E_SnS2 + E_Li) − E_SnS2−Li

where E_SnS2−Li and E_SnS2 are total energy of SnS₂ with and without the adsorption of Li, respectively. E_Li is the energy of Li atom in its metal crystal (with body-centered cubic structure and a lattice constant of 3.491 Å). According to this definition, a more positive E_b indicates a more stable adsorption of Li atom on SnS₂ structures.

3. Results and discussion

3.1 Adsorption and diffusion of single Li on 3D SnS₂ bulk

Bulk SnS₂ is a IV–VI group semiconductor with an indirect energy gap and has a hexagonal crystal structure of the type CdI₂.^27–29 The optimized lattice parameters are a = b = 3.67 Å, c = 5.94 Å, which is in excellent agreement with the experimental values (a = 3.64 Å, c = 5.90 Å).²⁸

Two representative sites for Li adsorption are available in SnS₂ bulk, as shown in the insert of Fig. 1: the octahedral site (O_h), where Li atom binds to three S atoms from each of the triple layer and the tetrahedral site (T_h), which is constructed by three S atoms from the upper layer and one S atoms from the lower triple layer. The calculated binding energies (E_b) of Li at the O_h and T_h sites are 2.20 and 1.72 eV, respectively (Fig. 1). The preference adsorption at the O_h site is also proved in the SnSe₂ (ref. 26) and MoS₂ (ref. 17) bulk. The Li–S bond lengths are uniform 2.58 Å when Li adsorbs at the O_h site. In the case of Li adsorption at the T_h site, the Li–S bond lengths are 2.25 and 2.38 Å on the upper and lower layer, respectively.

Fig. 1 Diffusion barrier profiles of Li in SnS₂ bulk and bilayer from an octahedral site to another, passing through a tetrahedral site. The inserts are the corresponding structures of Li adsorbed at the octahedral and tetrahedral site as well as the transition state.

Besides a strong binding strength with the electrode, the diffusion barrier of Li is of vital important which is directly related to the mobility of the Li, and further concerns the performance of the batteries. Here, Li diffusion can be schemed from an O_h site to another, passing through a T_h site. As seen from Fig. 1, Li needs to overcome an energy barrier (E_a) of 0.60 eV when migrates between two O_h sites. In comparison with MoS₂ and TiS₂ bulk,^16,17 the barrier is relatively higher, thus, it should be further reduced to enhance the mobility.

It is noteworthy that recent experiments reported that MoS₂ undergoes a structural transition from the 2H phase to the 1T phase under lithiation.^30,31 In this work, this issue is not under consideration. This is because (i) in the SnS₂ case, the phase transition has not been reported yet, and (ii) the phase transition occurs only when Li ion concentration reaches a high threshold value (i.e., greater than 28% on MoS₂ (ref. 32)), which is not the case for the present one as we only concentrate on the early lithiation process.

3.2 Adsorption and diffusion of single Li on 2D SnS₂ NSs

Next, the behaviors of Li adsorption and diffusion on the 2D SnS₂ NSs, including SnS₂ bilayer and monolayer, are examined.

Similar to the SnS₂ bulk, two representative Li adsorption sites are available in SnS₂ bilayer: O_h site and T_h site. Compared with the geometry of the bulk SnS₂, the interlayer distance is almost unchanged (5.96 and 5.94 Å for bilayer and bulk, respectively). Thus, it can be expected that the results on the bilayer would be close to the ones on the bulk. The calculated result verify this conjecture: the E_b at O_h and T_h site are 2.10 and 1.63 eV, respectively, and the E_a is 0.57 eV (Fig. 1).

When the SnS₂ bulk is exfoliated into monolayer, there are also two representative adsorption sites for lithiation: the top site (T), where Li is directly above one Sn atom; the hollow site (H) in which Li is, from the top view, above the center of Sn₃S₃ hexagon (Fig. 2). For both cases, Li is coordinated by three S atoms and the Li–S bond lengths are always 2.45 Å. Calculation results show that the binding energies are greatly decreased compared with the ones on the bulk, and the H site (1.21 eV) has a higher one than the T site (1.17 eV). The latter scenario is different from the previous investigations on the MoS₂ and VS₂ monolayer where the lithiation at the T site is more favorable.^17,33 Moreover, we also examined the adsorption site of atop S; however, after full relaxation, Li drifts to the neighboring H site, in according with the cases on other metal dichalcogenides, such as MoS₂ or VS₂ monolayer.^17,33

Fig. 2 Diffusion barrier profiles of Li in SnS₂ monolayer from an H-site to another, passing through a T-site. The inserts are the corresponding structures of Li adsorbed at the H-site and T-site as well as the transition state.

In Fig. 2, Li diffusion on the SnS₂ monolayer is illustrated, where Li migrates from an H site to another, passing through a T site. Surprisingly, the calculated barrier is just 0.17 eV, indicating that Li can readily diffuse on the monolayer. Note that this value is much lower than that of SnS₂ bulk or bilayer. The difference of energy barrier will have a huge effect on the transportation of Li, since the diffusion coefficient in general varies exponentially with the energy barrier according to Arrhenius formula (D ∝ e^(E_a/kT)). Form the bulk to the monolayer, Li diffusion barrier reduces by 0.43 eV. These differences would result in an increase in Li mobility by a factor of 10⁷ at room temperature.

Although SnS₂ monolayer can greatly improve the diffusion of Li atom compared with SnS₂ bulk, unfortunately, the relative low binding energy would hinder it becoming an ideal and high performance anode material. Therefore, decreasing the diffusion barriers without sacrifice the binding energy is urgently needed. Recently, 1D MoS₂ ZNRs (ref. 17) and TiS₂ NTs (ref. 16) have been reported to show superior performance to their bulk phases for the applications as electrodes in Li-ion battery. Thus, in the next Sections, we turn our attention to 1D SnS₂ NRs and NTs which are obtained by cutting or rolling up SnS₂ monolayer, respectively. Our aim is to explore the effect of dimensionality on the performance of LIBs and further to screen what form of SnS₂ nanostructure could be more qualified as an anode material.

3.3 Adsorption of Li on 1D SnS₂ NRs

According to a previous investigation, SnS₂ zigzag nanoribbons are more stable than armchair ones with a comparable width,³⁴ therefore, only SnS₂ ZNRs were considered. Here, 8-ZNR was chosen as the prototype.

For SnS₂ 8-ZNR as shown in Fig. 3, there are totally 16 adsorption sites, including 7 H-sites (labeled as H₁ to H₇), 7 T-sites (T₁ to T₇) and 2 edge sites (E₁ and E₂). In addition, T8 site is also under consideration, however, the initial adsorbed Li will spontaneously move to the H₇ site upon relaxation, indicating that T8 is not a local minimum. All the calculated binding energies are labeled in Fig. 3. It can be seen that the highest E_b of 1.21 eV occurs at H₁ site, and E_b ranges from 1.07 to 1.19 eV at the remaining sites. Moreover, lithiation at H_i sites are always more stable than their corresponding T_i sites, which is in according with the case of SnS₂ monolayer, but in contradiction with MoS₂ ZNR.¹⁷ One may notice that, the adsorption strength of Li on the SnS₂ ZNR does not improve compared with the monolayer. Thus, further investigation toward the diffusion of Li is unnecessary.

Fig. 3 All adsorption sites of Li on SnS₂ 8-ZNR and their corresponding binding energies (in eV).

3.4 Adsorption and diffusion of Li on 1D SnS₂ NTs

Different from SnSe₂ NTs whose electronic properties are dependent on their chirality (ZNTs are metal while ANTs are semiconductor),^26,35 SnS₂ NTs always present a semiconducting property.³⁶ Therefore, both kinds of NTs should be considered and the corresponding results are presented in Fig. 4 and Table 1.

Fig. 4 The adsorption sites and transition states on inner and outer shells of SnS₂ ZNT (a and b) and ANT (c and d), the (16, 0) and (12, 12) NT were selected as prototypes. The red dash lines represent the diffusion path of Li atoms.

Table 1 The binding energies and diffusion barriers of Li atoms on SnS₂ NTs (in eV)

		Ho	To	Hi	Ti
(16, 0)	Eb	1.55	1.34	1.70	1.66
	Ea	0.224		0.181
(18, 0)	Eb	1.50	1.35	1.69	1.65
	Ea	0.190		0.179
(22, 0)	Eb	1.47	1.36	1.66	1.62
	Ea	0.166		0.176
(10, 10)	Eb	1.84	1.60	1.85	1.87
	Ea	0.287		0.153
(12, 12)	Eb	1.71	1.53	1.85	1.89
	Ea	0.234		0.173
(14, 14)	Eb	1.71	1.58	1.85	1.89
	Ea	0.202		0.167

---

For SnS₂ ZNTs, (16, 0), (18, 0) and (22, 0) were selected as prototypes; and for SnS₂ ANTs, (10, 10), (12, 12) and (14, 14) NTs were chosen. Note that SnS₂ nanotubes have been successfully synthesized³⁷ and the stability has also been confirmed by ab initio calculations.³⁶ For each NT, four typical adsorption sites are selected: the top sites (T_i and T_o, here the subscript “i” and “o” denote “inside” and “outside” the tube, respectively) where Li is directly above one Sn atom; the hollow sites (H_i and H_o) where the Li locates on the center of Sn₃Se₃ hexagon (Fig. 4). The calculated binding energies can be found in Table 1. One can conclude that (i) at the same adsorption site, the binding energies on the inner shells are higher than those on the outer shells; (ii) the H site is always more stable (or comparable in stability) than the T site at a certain tube; and (iii) with the increase of the diameter, the binding energy takes a decrease tendency, which would be expected to approach its monolayer limit.

The binding energies in the Table 1 also indicate that the curved surface is more favorable for Li adsorption. It is evidenced that, from the monolayer to ZNR to ZNT to ANT, the highest binding energy varies from 1.21 to 1.21 to 1.70 to 1.89 eV. As can be seen, although the magnitudes of E_b on the NTs are still lower than those of the bulk, they are significantly improved compared with the one on the SnS₂ monolayer. It is worth noting that the calculated highest binding energy on the ANTs is only ∼0.3 eV lower than the one on the bulk, thus, the diffusion behavior is something to look forward to.

No matter on the inside or on the outside NTs, Li diffusion always occurs between two neighboring H site, passing through a T site (Fig. 4). We first address Li diffusion on the ZNTs. The calculated energy barriers are shown in Table 1. For (16, 0) ZNT, the barriers are calculated to be 0.181 and 0.224 eV on the inner and outer shell, respectively. With the increase of tube diameter, the E_a decreases to 0.179/0.190 and 0.176/0.166 eV on the inner/outer shell of (18, 0) and (22, 0) ZNT, respectively. Such a curvature effect induced by the different diameters has been revealed in SnSe₂ ZNTs.²⁶

The calculated energy barriers on the outer shell of (10, 10), (12, 12) and (14, 14) ANTs are respectively 0.287, 0.234 and 0.202 eV, once again indicating that the E_a decreases with the increase of tube diameters. One can deduce that if the diameter continuously increases, the barrier is expected to reach the monolayer limit, 0.17 eV. It is exciting that, because the magnitudes of E_a on the inner shell seem insensitive to the surface curvature (tube diameter) of SnS₂ ANT, the lowest diffusion barrier is just 0.153 eV, which is essentially the same as the one on the monolayer. The insensitivity characteristic is derived from the fact that compared with the outer, the inner suffers less structural distortion (small compressive strain) with the tube diameter, which will be discussed in the following. Recalling that the inner shell has stronger binding strength than the outer one, one can imagine that the inner channel of the NTs should be more suitable for Li adsorption and diffusion, thereby plays a more important role in the application of an anode material. In fact, by means of molecular dynamic simulations, Song et al. believed that Li outside the tube would result in a very strong adsorption enhancement as Li receives additional interactions from the neighboring NTs of a NT bundle, thus, Li storage capacity in this case is possibly irreversible.³⁸

It is interesting that the diameter plays an opposite role toward the diffusion barrier and the binding strength, especially on the outside tube. As described above, with the increase of the diameter, the binding energy tends to decrease and gets close to the monolayer limit. On the other hand, it seems that the diffusion barrier begins to decline and approach the monolayer limit with the increase of diameter. That is to say, NTs with a smaller diameter favors Li adsorption, but disfavors Li diffusion. Therefore, a suitable diameter should be optimized if SnS₂ NTs are really applied in the practical applications in LIBs.

To explain the curvature effect of the nanotube, the diffusion barrier for the strained SnS₂ monolayer is further investigated as the outer/inner of the tube can be regarded as the tensile/compressive strain. As seen in Fig. 5, from the compressive to tensile strain, the barrier displays a parabolic curve. The unstrained monolayer has the lowest Li diffusion barrier and the barrier increases with the enhancement of both tensile and compressive strains. The increase of the strain can be viewed as the decrease of the tube diameter, thus, the fact that the barrier decreases with the increase of the tube diameter can be rationalized by the strain which is induced by the tube curvature.

Fig. 5 The diffusion barriers of Li on SnS₂ monolayer under different levels of strain.

Finally, to straightforwardly compare the performance of various SnS₂ structures in LIBs, the diffusion barrier as a function of the binding energy is plotted as shown in Fig. 6. Obviously, the more close to “the origin point”, the better performance this material has. It can be vividly seen that SnS₂ NTs have a better performance than the others. Thus, NTs can be regarded as a very promising anode material.

Fig. 6 The comparison of the adsorption energies and diffusion barriers between SnS₂ bulk, bilayer, monolayer and nanotubes.

4. Conclusion

In summary, first-principle computations were performed to investigate the adsorption and diffusion of Li on SnS₂ 3D bulk, 2D bilayer and monolayer, 1D nanoribbons and nanotubes. The results show that the diffusion barrier of Li is decreased with the reduction of dimensionality. The relative lower binding energy of Li on SnS₂ monolayer makes it not suitable to act as an ideal candidate for electrode materials. When cutting the monolayer into NRs, the binding energy does not significantly improve. However, by rolling up the monolayer into NTs, the adsorption strength becomes stronger without sacrificing the diffusion barrier, leading them to be a very promising candidate of an anode material in Li ion batteries. In closing, we hope our theoretical investigation will stimulate further experimental and theoretical studies on the nanotubes, especially as a novel anode material in the LIBs.

Acknowledgements

This work was supported by National Younger Natural Science Foundation of China no. 21203001, Natural Science Foundation of China no. 21373012 to S. F. Wang, Natural Science Foundation of Anhui Province no. 1408085MKL22. The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

References

1. M. Reddy, G. Subba Rao and B. Chowdari, Chem. Rev., 2013, 113, 5364.
2. M. S. Whittingham, Chem. Rev., 2004, 104, 4271.
3. J.-M. Tarascon and M. Armand, Nature, 2001, 414, 359.
4. M. Winter and R. J. Brodd, Chem. Rev., 2004, 104, 4245.
5. C. R. Sides and C. R. Martin, Adv. Mater., 2005, 17, 125.
6. V. Etacheri, R. Marom, R. Elazari, G. Salitra and D. Aurbach, Energy Environ. Sci., 2011, 4, 3243.
7. H. Zhong, G. Yang, H. Song, Q. Liao, H. Cui, P. Shen and C.-X. Wang, J. Phys. Chem. C, 2012, 116, 9319.
8. J. w. Seo, J. t. Jang, S. w. Park, C. Kim, B. Park and J. Cheon, Adv. Mater., 2008, 20, 4269.
9. L. Zhuo, Y. Wu, L. Wang, Y. Yu, X. Zhang and F. Zhao, RSC Adv., 2012, 2, 5084.
10. T.-J. Kim, C. Kim, D. Son, M. Choi and B. Park, J. Power Sources, 2007, 167, 529.
11. H. Mukaibo, A. Yoshizawa, T. Momma and T. Osaka, J. Power Sources, 2003, 119, 60.
12. J. Choi, J. Jin, I. G. Jung, J. M. Kim, H. J. Kim and S. U. Son, Chem. Commun., 2011, 47, 5241.
13. B. Luo, B. Wang, X. Li, Y. Jia, M. Liang and L. Zhi, Adv. Mater., 2012, 24, 3538.
14. T. Brousse, S. Lee, L. Pasquereau, D. Defives and D. Schleich, Solid State Ionics, 1998, 113, 51.
15. K. Chang, W. X. Chen, H. Li and H. Li, Electrochim. Acta, 2011, 56, 2856.
16. K. Tibbetts, C. R. Miranda, Y. S. Meng and G. Ceder, Chem. Mater., 2007, 19, 5302.
17. Y. Li, D. Wu, Z. Zhou, C. R. Cabrera and Z. Chen, J. Phys. Chem. Lett., 2012, 3, 2221.
18. J. P. Perdew, J. Chevary, S. Vosko, K. A. Jackson, M. R. Pederson, D. Singh and C. Fiolhais, Phys. Rev. B: Condens. Matter Mater. Phys., 1992, 46, 6671.
19. J. P. Perdew and Y. Wang, Phys. Rev. B: Condens. Matter Mater. Phys., 1992, 45, 13244.
20. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169.
21. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758.
22. P. E. Blöchl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953.
23. S. Grimme, J. Comput. Chem., 2006, 27, 1787.
24. G. Henkelman, B. P. Uberuaga and H. Jónsson, J. Chem. Phys., 2000, 113, 9901.
25. G. Henkelman and H. Jonsson, J. Chem. Phys., 2000, 113, 9978.
26. C. Ling, Y. Huang, H. Liu, S. Wang, Z. Fang and L. Ning, J. Phys. Chem. C, 2014, 118, 28291.
27. C. Julien, M. Eddrief, I. Samaras and M. Balkanski, Mater. Sci. Eng., B, 1992, 15, 70.
28. F. Al-Alamy, A. Balchin and M. White, J. Mater. Sci., 1977, 12, 2037.
29. Y. Huang, C. Ling, Z. Fang and S. Wang, Phys. E, 2014, 59, 102.
30. L. Wang, Z. Xu, W. Wang and X. Bai, J. Am. Chem. Soc., 2014, 136, 6693.
31. Y. Cheng, A. Nie, Q. Zhang, L.-Y. Gan, R. Shahbazian-Yassar and U. Schwingenschlogl, ACS Nano, 2014, 8, 11447.
32. H. Wang, Z. Lu, S. Xu, D. Kong, J. J. Cha, G. Zheng, P.-C. Hsu, K. Yan, D. Bradshaw and F. B. Prinz, Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 19701.
33. Y. Jing, Z. Zhou, C. R. Cabrera and Z. Chen, J. Phys. Chem. C, 2013, 117, 25409.
34. L. Li, H. Li, J. Zhou, J. Lu, R. Qin, Z. Gao and W. N. Mei, J. Comput. Theor. Nanosci., 2010, 7, 2100.
35. Y. Huang, C. Ling, H. Liu, S. Wang and B. Geng, J. Phys. Chem. C, 2014, 118, 9251.
36. H. Chang, E. In, K.-j. Kong, J.-O. Lee, Y. Choi and B.-H. Ryu, J. Phys. Chem. B, 2005, 109, 30.
37. A. Yella, E. Mugnaioli, M. Panthöfer, H. A. Therese, U. Kolb and W. Tremel, Angew. Chem., Int. Ed., 2009, 48, 6426.
38. B. Song, J. Yang, J. Zhao and H. Fang, Energy Environ. Sci., 2011, 4, 1379.

---