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Adsorption and Formation of Small Na clusters on Pristine and Double-Vacancy Graphene for Anodes of Na-ion Batteries Zhicong Liang, Xiaofeng Fan, Weitao Zheng, and David J. Singh ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 05 May 2017 Downloaded from http://pubs.acs.org on May 5, 2017

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ACS Applied Materials & Interfaces

Adsorption and Formation of Small Na clusters on Pristine and Double-Vacancy Graphene for Anodes of Na-ion Batteries Zhicong Lianga, Xiaofeng Fana,*, Weitao Zhenga,b and David J. Singhc,d, *

a. Key Laboratory of Automobile Materials (Jilin University), Ministry of Education, and College of Materials Science and Engineering, Jilin University, Changchun, 130012, China b. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, China c. Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211-7010, USA d. College of Materials Science and Engineering, Jilin University, Changchun 130012, China

ABSTRACT Layered carbon is a likely anode material for Na-ion batteries (NIBs). Graphitic carbon has a low capacity of approximately 35 mAh/g due to the formation of NaC64. Using first-principles methods including van der Waals interactions, we analyze the adsorption of Na ions and clusters on graphene in the context of anodes. The interaction between Na ions and graphene is found to be weak. Small Na clusters are not stable on the surface of pristine graphene in the electrochemical environment of NIBs. However, we find that Na ions and clusters can be stored effectively on defected graphene that has double vacancies. In addition, the adsorption energy of small Na clusters near a double-vacancy is found to decrease with increasing cluster size. With high concentrations of vacancies the capacity of Na on defective graphene is found to be as much as 10-30 times higher than graphitic carbon.

KEYWORDS: Na clusters, Van der Waals interactions, Double-Vacancy Graphene, first-principles methods, Na-ion Batteries

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INTRODUCTION Li-ion batteries (LIBs) represent state-of-the-art technology that has been widely used over the last three decades1-7. However, there is increasing need for inexpensive and efficient large scale energy storage systems, for example in the power grid. This represents a challenge for current LIBs technology and motivates the investigation of alternatives. In addition, there are issues regarding safety, lifetime, low-temperature performance, and cost that further suggest the exploration of other systems4,

5, 8, 9

. Recently, room temperature sodium ion batteries

(NIBs) have received attention as an alternative energy storage technology due to the abundance and low cost of sodium and the use of aluminum current collectors10-15. Identification and optimization of electrode materials remains a focus of research. Considerable effort has been made to design efficient cathodes for NIBs. It might be possible to produce NIBs using metallic Na as an anode, e.g. with a solid electrolyte spacer. However, for practical NIBs an anode material that contains Na similar to the anodes in LIBs may be needed. The identification of suitable anode materials is more difficult than for LIBs because the ionic radius of the Na+ ion (~100 pm) is larger than that of the Li+ ion (76 pm). Graphite is a good anode for LIBs and has been adopted widely in present LIBs because of the reversible intercalation of Li between carbon layers with the formation of stable LiC6 as a stage-one graphite intercalation compound along with good kinetics for suitably processed graphite. However, graphitic carbon does not behave well for NIBs because of its extremely low capacity (~ 35 mAh/g). This is due to the formation of NaC6416, which is a consequence of the larger size of Na+ and the relatively high ionization potential8, 10, 14, 17-19. Nonetheless, layered carbon and particularly modifications of layered carbons remain a focus of investigation among potential NIB anodes. Different layered carbon

materials including hard carbon9, soft carbon20, expanded

graphite21, porous carbon, carbon nanoparticles, modified graphene 22-24, and so on, have been investigated for insertion and storage of Na ions. For example, hard carbon has been reported to have a capacity of about 300 mAh/g which is comparable to that of Li in graphite. Hard carbon is composed of disordered turbostratic nano domains, with empty space among domains. It is speculated that the rich variety of chemical environments, such as edge/defect sites on pore surfaces, interlayer space and empty pores, help to enhance the storage of Na 2


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ions in these hard carbons. Graphene is considered to be a potential anode for storing Na ions because of the lack of geometric constraints associated with the narrow interlayer spacing of graphite. It has been reported that the reversible Li storage of graphene nanosheets can be very large25-30. Furthermore, it was recently reported that the expanded graphite can deliver a reversible capacity of 284 mAh/g. Theoretical studies of the adsorption and diffusion of isolated Na ion on graphene has been reported31-33. The behavior of Na ions on doped graphene was initially explored34-37. Based on a card-house model of hard carbon, it was suggested that Na ion can fill in the pore between domains. Here we focus on the effect of defects in the graphene sheets, specifically whether it is possible that small Na clusters can be stored by binding to the pores of defective graphene and whether defects that bind small clusters can be used to enhance the Na ion capacity. Here we explore Na storage in the form of Na ions and small Na clusters on pristine and defective graphene with the first-principles methods. We analyzed the isolated Na clusters and the possible formation of Na clusters with different sizes on pristine and double-vacancy defected graphene. The effect of double-vacancies and their concentration on the storage of Na was considered. The Na-C interaction was analyzed in terms of Na transfer between Na metal and graphene. Although Na ions do not bind sufficiently to be adsorbed effectively in high concentration on defect-free graphene, double-vacancies can enhance the storage of Na ions. Small Na clusters are found to be readily formed around the vacancies and may be the most important storage mechanism.

THEORETICAL METHOD The present calculations were performed within density functional theory using the accurate frozen-core full-potential projector-augmented-wave (PAW) method as implemented in the VASP code38-40. We used the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE)41 and with added van der Waals (vdW) corrections. The k-space integrals and the plane-wave basis sets were chosen to ensure that the total energy was converged at the 1 meV/atom level. A plane wave expansion kinetic energy cutoff of 450 eV was found to be sufficient. The calculated binding energy for bulk bcc Na is 1.08 eV with a lattice constant a = 4.29 3



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Å, which is consistent with experimental values (4.22-4.29 Å)42,

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and other theoretical

studies (4.05-4.24 Å)34, 44, 45. The lattice parameter of the primitive cell for graphene was chosen to be 2.464 Å on the basis of the calculation for graphite. This is consistent with the experimental value. Based on this primitive cell, different supercells including 3×3, 4×4, 5×5, 6×6 and 8×8 hexagonal structures as the ideal models were used to analyze the Na adsorption. The Brillouin zones were sampled by the Γ-centered grid with a k-point spacing of 0.04 Å-1. All the supercells were constructed with a vacuum space of 20 Å along the z direction to avoid spurious coupling effects between graphene layers. Additionally, the dipole corrections for potential and total energy were also included, as needed due to the supercell geometry. All the structures including the supercells of graphene with double-vacancy were fully relaxed upon the adsorption of Na atom/clusters. Because of the large polarizability of graphene, the effect of vdW interactions was found to be noticeable for the Na adsorption. The effect of dispersion interaction was considered by the empirical correction scheme of Grimme (DFT-D2)46, as implemented in the VASP code, in order to estimate accurately the adsorption strength of Na on graphene. To further assess the results from PBE without dispersion correction and DFT-D2, the other methods with an added non-local correlation functional which approximately accounts for dispersion forces, such as optPBE-vdW48 and vdW-DF249 were used to test the typical cases for the interaction between Na ions/clusters and graphene. The DFT-D2 has been successful in describing graphene-based materials47 and both optPBE-vdW and vdW-DF2 has been used to discuss the interaction between Li and graphene50. The initial structures were optimized by the uncorrected PBE method. For considering the effect of dispersion correction, the geometries from the results of PBE were reoptimized and analyzed by DFT-D2, optPBE-vdW and vdW-DF2, respectively. The geometrical structures from PBE didn’t change obviously after these methods with dispersion correction. As shown in Table 1 and Table S1-S2, the dispersion correction increases the binding energies of Na ions/clusters adsorbed on pristine and double-vacancy graphene. It was found that the correction of binding energy from DFT-D2 method was larger than that from methods with non-local correlation functional (optPBE-vdW and vdW-DF2). In the discussions later in the text, we adopted the results from DFT-D2 for vdW correction, unless otherwise indicated. It 4


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should be noticed that the Na atom was used in the calculation of the system with Na and graphene. Due to charge transfer, the stable configuration of Na adsorbed on graphene actually is the interaction between Na ion and graphene. Similarly, the neutral species for Na cluster is used in the calculation and the stable configuration is with the charged Na cluster adsorbed on graphene.

RESULTS AND DISCUSSION Isolated Na clusters and adsorption of Na ions on pristine graphene In the studies of surface adsorption, the adsorption energy is usually defined to describe the stability of the adsorbate on surfaces. For the system of graphene with Na ions/clusters, the adsorption energy is defined as, E ad = ( E g − nNa − E g − E Na * n) / n , (1)

where Eg-nNa,Eg, and ENa are the energies of the graphene with Na ion/clusters, pristine graphene (or defective graphene), and isolated Na atom, respectively. With this definition of adsorption energy, the binding energy of Na ion and graphene is the negative value of absorption energy with Eb=-Ead. This means the usual stable configuration with negative adsorption energy corresponds to positive binding energy. By simulating the adsorption of Na on graphene in a supercell model of 4x4, we found that the binding energy of Na ions with a content of x=1/32 was 0.88 eV/Na. For bulk Na, the binding energy is about 1.08 eV/Na, which is consistent with the value (1.07 eV/Na) calculated by Maylyiet al.34 and the experimental value (1.13 eV/Na) from Maezonoet al.51. This implies that Na ion with the content of x=1/32 will not readily reside on the surface of graphene, since the system would be unstable against separation into bulk Na and graphene. While it may be possible to prepare graphene with Na ions, according to our calculations this would be an unstable anode. In addition, we simulated the interaction between Na and the different surfaces of bulk Na. As shown in Table 2, it was found that the binding energy of the surface Na atoms was about 0.8~1.05 eV/Na. It means graphene will not be an effective anode material, even if we would consider the highly optimistic scenario in which kinetics makes the surface of bulk Na the reference state to evaluate the interaction between Na and graphene. 5



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It is found that the binding energy of Na adsorbed on graphene increases with the decrease of Na content. For example, the binding energy of Na with the content of x=1/128 is 1.16 eV/Na and is larger than the binding energy of bulk Na. Therefore, in the case of low concentration, it is possible that Na ions can reside on graphene in the experimental test of electrode. In the literature, Na can be stored in graphite with a content of x=1/64 due to the formation of intercalation compound NaC64 with eight-stages16,52. With an eight-stage model of ANaABABABA where AB presents the typical stacking way of graphite with the lowest energy and the insertion of Na results in the AA stacking for the layers which is near the Na ions. The binding energy of Na in NaC64 was calculated to be 1.46 eV/Na and larger than that in bulk Na. This may be simply understood that unlike the case of graphene, the Na in graphite has two neighboring surfaces to interact with. Considering the formation energy with bulk Na as the reference state, there will be phase transition for Na-graphene system with Na content. It implies the clusters of Na should be formed. We consider different size Na clusters with the cluster model of Solov’yovet al.53. The binding energy of a small Na cluster is found to be markedly less than that of bulk Na. As shown in Figure1A, the binding energy per Na increases as the cluster size increases. For the large-size cluster Na20 ( 20 Na atoms, Figure 1B ), the binding energy is approximately 0.79 eV/Na. This is smaller than the binding of Na on graphene (0.88 eV/Na with x=1/32) and the surface Na atoms (0.8~1.05 eV/Na). The implication is that small isolated Na clusters are unstable in the presence of graphene or graphite since the Na atoms of a randomly formed cluster will be transferred to the surface of graphene or graphite.

Adsorption of Na clusters on pristine and defected graphene We calculated the adsorption of Na clusters with different sizes on graphene. For each size, we construct the initial configurations by considering the possible adsorption sites for Na atom in the clusters and different orientations to place the clusters on graphene with symmetry to obtain the most stable configuration, as shown in Figure S1 and S2 about Na3 and Na10. The adsorption energy per Na atom of the most stable configuration as the function of cluster

size is plotted in Figure 2A. We find that if the dispersion force is not considered, the absolute value of adsorption energy of Na clusters is obviously smaller than that of Na ion on the (111) 6


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surface of Na. In addition, with the increase of cluster size, the absolute value of adsorption energy does not show an decreasing trend. However, with the inclusion of vdW interactions, the adsorption strength on graphene is substantially enhanced and the absolute value of adsorption energy becomes larger than that of Na ion on a Na surface. But the absolute values of adsorption energies in the most cases are still less than the binding energy of bulk Na. There just are two special configurations, which areNa4 and Na10 and expected to be stable on graphene in the electrode test. The adsorption energies of Na4 and Na10 (Figure 2C, 2D, S5A and S5B), are -1.16 eV/Na and -1.12eV/Na, respectively. The hexagonal site on graphene is the most stable site for Na adsorption. This is similar to the adsorption of Li on graphene. However, because of the interaction between Na ions, it is not possible that all the Na in the cluster occupy the hexagonal sites. As shown in Figure 2C, the cluster Na4 has a tetrahedral structure and the three Na ions near graphene deviate noticeably from the hexagonal sites. By the introduction of other Na ions via increase of the cluster size, the added ions will try to occupy the nearby hexagonal site. However, this kind of adsorption geometry on graphene may reduce the interaction between the new added Na and other Na ions in cluster due to strain and unfavorable shape of the cluster. With the competition of two kinds of forces (interaction with graphene and with other Na ions in cluster), another cluster Na10 with lower energy shown in Figure 2C can adsorbed stably on graphene. We discuss the interaction of clusters with graphene using the cohesive energy defined on the basis of the isolated Na cluster, E c = ( E g − nNa − E g − E Na − clu . ) / n , (2)

where ENa-clu.is the energy of isolated Na cluster with n atoms of Na. The result is plotted in Figure 2B. It is found that the absolute value of cohesive energy per Na atom has a decreasing trend with increasing cluster size, except for the small cluster Na2. This trend is opposite to that of the binding energy of Na clusters with the consequence that the absolute value of adsorption energy does not have a simple increasing trend. With the double-vacancy, Na ions can be adsorbed effectively on defect graphene with binding energy of 2.217 eV which is larger than that of bulk Na. Due to the trapping of 7



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double-vacancy, it is possible there are more Na ions adsorbed near the defect. By considering the possible adsorption sites for Na atom in the clusters near double-vacancy with symmetry, we obtain the stable configuration with the lowest energy from the initial configurations for each size, as shown in Figure S3 and S4 about Na3 and Na10. The adsorption energy of low-energy configuration for each size is plotted Figure 3A. With the contribution of dispersion force, the absolute values of adsorption energies of all the Na clusters are larger than the binding energy of bulk Na. With the smaller dispersion correction from vdW-D2 method, the Na clusters adsorbed on double-vacancy graphene are stable with the reference state of metallic Na (bulk Na) when cluster size n is lesser than 12. Obviously, in the interaction between Na cluster and double-vacancy graphene the contribution of van der Waals isn't ignored. This is because there is the large polarization for Na atom, similar to Li atom. Actually, in the system, such as that with Na (Li, K, etc.) and layered materials the van der Waals interaction is possible to be very important. It is also found that the absolute values of adsorption energy decreases with the increase of cluster size. The cluster Na3 with the adsorption energy of -1.62 eV/Na is the most stable one. As the cluster size increases to n=16, the adsorption becomes to be near the binding energy of bulk Na. This means the double-vacancy may not trap effectively large-size cluster. With the formula (2), the cohesion on a per Na basis between cluster and defective graphene decreases quickly by following the increase of cluster size, as shown in Figure 3B. This implies the formation of Na crystal core merged from larger Na cluster is controlled easily in the charge/discharge processes. Therefore, double-vacancy graphene has the potential to limit the formation of Na dendritic crystals in the processes of Na intercalation. Next, we explore how the concentration of Na and of double-vacancies affects the adsorption energy. As shown in Figure 4A, the change of the adsorption energy is analyzed with increasing double-vacancy concentration. For small cluster sizes (n 1/32 is less than the binding energy of Na on (001) surface of Na. This implies Na clusters will tend to form. These clusters while providing an apparently high Na capacity may lead to dendrite formation. Calculations including van der Waals interactions show that some cluster configurations, such as Na4 and Na10 may be adsorbed possibly on pristine graphene in the context of NIBs when the content of Na is lower. In any case, we find that the binding of Na to single layer graphene is inadequate relative to the binding of Na in Na metal or even on Na surfaces. Therefore, while porous carbons or other carbon structures where Na ions may interact with multiple surfaces may bind Na, pristine graphene itself will not have sufficient 11



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binding for NIB anodes. In contrast, Na ions can be effectively stored on graphene with double vacancies. Na clusters can also be formed due to the trapping of double-vacancies. We found that the absolute value of adsorption energy decreases with increasing size of Na clusters. With the analysis of the content of defects and Na ions with different cluster size, it implies that the double-vacancy can enhance the storage of Na on graphene, while the dendritic crystals are suppressed. It is predicted that on double-vacancy graphene with the defect concentration of 5.56%, the capacity of Na can reach to 1117 mAh/g. In addition, the adsorption of Na cluster does not markedly change the band structure of double-vacancy graphene except for the shift of Fermi level because of the charge transfer. Therefore defective graphene with vacancies is expected to be a promising anode material for Na-ion batteries.

ASSOCIATED CONTENT Supporting Information Adsorption energies of Na clusters on pristine graphene and double-vacancy graphene calculated from different methods; different configurations for cluster Na3 and Na10 on pristine graphene and double-vacancy graphene; different configurations of Na clusters on double-vacancy graphene with high concentration. AUTHOR INFORMATION Corresponding Author * Email: [email protected] (X. F.); [email protected] ( D. J. S) ORCID Xiaofeng Fan: 0000-0001-6288-4866 Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The research was supported by the National Key Research and Development Program of China (Grant No. 2016YFA0200400) and the National Natural Science Foundation of China (Grant No. 11504123 and No.51627805) . REFERENCES 1. Ellis, B. L.; Lee, K. T.; Nazar, L. F., Positive Electrode Materials for Li-Ion and Li-Batteries. Chem. Mat. 2010, 22, 691-714. 2.

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33. Peles-Lemli, B.; Kánnár, D.; Nie, J. C., Some Unexpected Behavior of the Adsorption of Alkali Metal Ions onto the Graphene Surface Under the Effect of External Electric Field. J. Phys. Chem. C 2013, 117, 21509-21515. 34. Malyi, O. I.; Sopiha, K.; Kulish, V. V.; Tan, T. L.; Manzhos, S.; Persson, C., A Computational Study of Na Behavior on Graphene. Appl. Surf. Sci. 2015, 333, 235-243. 35. Datta, D.; Li, J.; Shenoy, V. B., Defective Graphene as a High-Capacity Anode Material for Naand Ca-Ion Batteries. ACS Appl. Mater. Inter. 2014, 6, 1788-1795. 36. Ling, C.; Mizuno, F., Boron-Doped Graphene as a Promising Anode for Na-Ion Batteries. Phys. Chem. Chem. Phys. 2014, 16, 10419-10424. 37. Yao, L. H.; Cao, W. Q.; Cao, M. S., Doping Effect on the Adsorption of Na Atom onto Graphenes. Curr. Appl. Phys. 2016, 16, 574-580. 38. Blöchl, P. E., Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953-17979. 39. Kresse, G.; Hafner, J., Ab Initiomolecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558-561. 40. Kresse, G.; Furthmüller, J., Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mat. Sci. 1996, 6, 15-50. 41. Perdew, J. P.; Burke, K.; Ernzerho, f. M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. 42. Böhm, B.; Klemm, W., Zur Kenntnis Des Verhaltens Der Alkalimetalle Zueinander. Z. Anorg. Allg. Chem. 1939, 1, 69-85. 43. Berliner, R.; Fajen, O.; Smith, H. G.; Hitterman, R. L., Neutron Powder-Diffraction Studies of Lithium, Sodium, and Potassium Metal. Phys. Rev. B 1989, 40, 12086-12097. 44. Haas, P.; Tran, F.; Blaha, P., Calculation of the Lattice Constant of Solids with Semilocal Functionals. Phys. Rev. B 2009, 79, 085104. 45. Malyi, O. I.; Kulish, V. V.; Tan, T. L.; Manzhos, S., A Computational Study of the Insertion of Li, Na, and Mg Atoms into Si(111) Nanosheets. Nano Energy 2013, 2, 1149-1157. 46. Grimme., S., Semiempirical gga-type density functional constructed with a long-range dispersion correction. J. Comp. Chem. 2006, 27, 1787. 47. Fan, X. F.; Zheng, W. T.; Chihaia, V.; Shen, Z. X.; Kuo, J.-L., Interaction between Graphene and the Surface of SiO2. J. Phys.: Condens. Matter 2012, 24, 305004. 48. Klimeš, J.; Bowler, D. R.; Michaelides, A., Chemical Accuracy for the Van Der Waals Density Functional. J. of Physi.: Condens. Matter 2010, 22, 022201. 15



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Table 1 Binding energies of Na on pristine graphene (two models with x=1/32 and 1/128) and double-vacancy graphene (two models with x=1/30 and 1/126) calculated from different methods including GGA-PBE, DFT-D2, vdW-DF2 and optPBE-vdW. Note that x is the ratio of Na to C. Pristine graphene x=1/32 x=1/128

Double-vacancy graphene x=1/32 x=1/128

PBE

0.497

0.776

1.646

1.807

DFT-D2

0.884

1.160

2.055

2.217

vdW-DF2

0.632

0.877

1.673

1.836

optPBE-vdW

0.703

0.961

1.760

1.906

Table 2 Binding energies of Na adsorbed on different surfaces of bulk Na.

Surface Na(001)

Eb 0.969

Na(011)

0.798

Na(111)

1.048

Na(210)

1.037

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Figure1

Figure1.(A) Binding energy of a Na atom in Na cluster as a function of cluster size (the number of Na atoms) and in bulk Na and on the (001) surface of Na, and the adsorption energy of Na ion on graphene with the content of Na, x=1/32 and 1/128, and (B)schematic representations of the structures of typical clusters Na3, Na4, Na8, Na9, Na13,and Na20.

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Figure 2

Figure 2. (A) The adsorption energy on graphene and (B) cohesive energy between Na cluster and graphene as a function of cluster, and the schematic representations of the structures of cluster (C) Na4and (D) Na10 adsorbed on graphene.

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Figure 3

Figure 3. (A) The adsorption energy on double-vacancy graphene and (B) cohesive energy between Na cluster and double-vacancy graphene as a function of cluster, and the schematic representations of the structures of cluster (C) Na4and (D) Na10 adsorbed on double-vacancy graphene.

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Figure 4

Figure 4. The adsorption energy of small Na clusters as a function of the concentration of (A) double-vacancy in defective graphene and (B) Na ions. Note that the concentration of double-vacancy is defined by the formula, xdef=Ndef/HC and the concentration of Na ions is defined by the formula, xNa= NNa/NC, where Ndef, NC,HCandNNa are the number of double vacancy defects, carbon atoms on defective graphene, carbon atoms on corresponding pristine graphene and Na ions adsorbed on defective graphene.

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Figure5

Figure 5. Top views of the charge redistributions obtained by calculating charge density difference in real space for pristine graphene with (A)Na ion and (B) Na4 cluster, and (C) double-vacancy graphene with Na ion and (D) Na4 cluster. Note that yellow and red correspond to charge accumulation and charge depletion, respectively.

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Figure6

Figure 6. Band structures of (A) graphene, (B)Na-adsorbed graphene, (C) Na4-adsorbed graphene, (D) two-vacancy graphene, (E) two-vacancy graphene with adsorption of Na ion, (F) two-vacancy graphene with Na4cluster.

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Figure7

Figure 7.The density of states (DOS) and partial density of states (PDOS) of(A) graphene, Na-adsorbed andNa4-adsorbed graphene, and (B) double-vacancy graphene, Na-adsorbed andNa4-adsorbed double-vacancy graphene.

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Adsorption and Formation of Small Na Clusters on ... - ACS Publications

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