First-Principles Studies of Lithium Adsorption and Diffusion on

Subscriber access provided by Brought to you by ST ANDREWS UNIVERSITY LIBRARY

Article

First-Principles Studies of Lithium Adsorption and Diffusion on Graphene with Grain Boundaries Liu-Jiang Zhou, Zhu-Feng Hou, Li-Ming Wu, and Yong-Fan Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp5102175 • Publication Date (Web): 12 Nov 2014 Downloaded from http://pubs.acs.org on November 15, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

First-Principles Studies of Lithium Adsorption and Diffusion on Graphene with Grain Boundaries Liu-Jiang Zhou,†,‡ Z. F. Hou,∗,¶ Li-Ming Wu,∗,† and Yong-Fan Zhang§ State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, P. R. China, University of Chinese Academy of Sciences, Beijing 100039, P. R. China, Department of Electronic science, Xiamen University, Xiamen 361005, P. R. China, and Department of Chemistry, Fuzhou University, Fujian 350108, P. R. China E-mail: [email protected]; liming [email protected] Phone: +86–(0)591–83705401. Fax: +86–(0)591–83705401

∗

To whom correspondence should be addressed Fujian Institute of Research on the Structure of Matter ‡ University of Chinese Academy of Sciences ¶ Xiamen University § Fuzhou University †

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract To understand the effect of topological defects on the Li adsorption on graphene, we have performed first-principles calculations to study the adsorption and diffusion of a lithium adatom on graphene with (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) grain boundaries (GBs). Our results show that the adsorption of a Li adatom on defect-free graphene is endothermic with respect to the bulk Li and the adsorption of a Li adatom on the GBs of graphene is exothermic. In particular, the presence of a (2, 0)|(2, 0) GB leads to a decrease of about 0.92 eV in the adsorption of a Li adatom on graphene. This suggests that GBs would enhance the Li adsorption on graphene significantly. In three cases of GBs, the energy barrier for the diffusion of a Li adatom along the boundary is lower than that perpendicular to boundary, indicating that a Li adatom tends to diffuse along the boundary and to migrate from non-boundary sites toward the boundary zone. The difference charge density and the Bader charge analysis both show there is a significant charge transfer from the Li adatom to its nearest neighbouring carbon atoms.

Keywords Li-ion battery; graphene; grain boundary; adsorption and diffusion; first-principles

1

INTRODUCTION

Graphene, a two dimensional one-atom-thick honeycomb-like layered material, has attracted enormous attention due to its two dimensional (2D) crystal structure with atomic thickness, unique electronic structure, high intrinsic mechanical strength, high thermal conductivity, high surface area and superior electronic conductivity. 1 Graphene has been demonstrated as a potential alternative for graphite as anode of lithium-ion secondary batteries (LIBs). Compared with the three-dimensional graphite anode in most LIBs, which has the capacity limit


Page 2 of 26

Page 3 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of only 372 mAh/g, 2 graphene shows a good cyclic performance and a specific capacity from Li0.3 C6 to Li2 C6 . 3–6 Moreover, it is found that disordered graphene and oxidized graphene nanoribbons have much higher reversible capacities up to about 1000 mAh/g. 7,8 Therefore it is important to understand the role of structural defects in the Li storage of graphene. In order to better understand the origin for the higher capacities of Li storage of graphene, several theoretical studies based on density functional theory (DFT) have been done recently to investigate the Li adsorption on graphene. 3,9–13 It is found that the absorption energy of a Li adatom on perfect graphene is endothermic with respect to the bulk Li, indicating that the adsorption of a Li adatom on defect-free graphene is unfavorable. 13–17 However, point defects, doping, and edge effects in graphene can lead to an exothermic adsorption for a Li adatom. 13–19 These studies suggest that the ability of graphene as anode in LIB could be ascribed to the presence of structural defect in graphene and the modification of graphene by chemical doping. 20–24 It is experimentally observed that the growth of graphene in available macroscopic quantities through chemical vapor deposition (CVD) is usually accompanied by the emergence of polycrystalline, composed of many single crystalline graphene domains separated by grain boundaries (GBs). GB, an intrinsic topological defect of polycrystalline materials, 25 has been observed in graphene using various experimental techniques. 26–33 Like other structural defects such as monovacancy and Stone-Wales defect in graphene, GB also can induce defect states close to the Fermi level. 27,29 GB provides numerous novel possibilities for modifying the physics and chemistry properties of graphene, such as tuning the electronic, thermal, magnetic, mechanical, and transport properties. 34–40 However, the effect of the GB on the Li adsorption and diffusion on graphene has not been well understood yet. In our previous study, 19 we have studied the Li adsorption and diffusion on the divacancy (consisting of two pentagons and one octagon) and Stone-Wales defect (consisting of two pentagon-heptagon pairs) in graphene and found that these point defects can enhance the Li adsorption on graphene. Regarding that the GBs of graphene also consist of pentagons, heptagons and/or



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

octagons, we expect that GB would also have significant impacts on the Li adsorption and diffusion on graphene. In this work, we have extended our DFT calculations to study the adsorption and diffusion of a Li atom on the GBs of graphene. In addition, we have also studied the electronic structures of graphene modified by the GBs and the adsorbed Li atom.

2

THEORETICAL CALCULATIONS

The DFT calculations were performed via the Vienna ab initio simulation program (VASP). 41 The ionic cores are described by all-electron projector augmented wave potentials. 42 The exchange-correlation function is treated by the Perdew-Burke-Ernzerhof(PBE) generalized gradient approximation (GGA). 43 The plane-wave basis set with a cutoff energy of 500 eV is used. A supercell model is employed to simulate the GB of graphene, which is defined by the matching vectors (n, m) in the left and right grain domains. In the present study, we consider three typical GBs of graphene, that is, an asymmetric GB, (5, 0)|(3, 3) GB with a misorientation θ = 30.0◦ , and two symmetric GBs, (2, 1)|(2, 1) GB with θ = 21.8◦ and (2, 0)|(2, 0) GB with θ = 0◦ . The last one is also denoted as an extended line defect (ELD). 27 According to a classification scheme proposed in ref. 44, the (5, 0)|(3, 3) GB belongs to class II, while the (2, 1)|(2, 1) and (2, 0)|(2, 0) GBs belong to class Ib. They are three typical GBs of graphene, which were observed in experiment 27,32,33 and widely investigated in theory. 44–48 The supercells of these three GBs are presented in Fig. 1. A vacuum thickness of 12 ˚ A along the normal direction of graphene sheet is chosen to avoid the spurious interaction between the graphene sheet and its periodic replicas. A 6 × 6 hexagonal supercell of graphene is employed to model graphene with a monovacany, divacancy and Stone-Wales defect as well as the adsorption of a Li atom on these point defects. 19 In the structural relaxation and the stationary self-consistent-field calculation, a k -point grid with 0.02 ˚ A−1 spacing is adopted and a 0.012 ˚ A−1 k -grid for the calculations of the density of states (DOS). In the geometry optimization, all atoms are allowed to relax until the forces on atoms are less than 0.02


Page 4 of 26

Page 5 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


eV/˚ A. It is well known that there are three typical adsorption positions for a Li adatom on perfect graphene: a hollow (H) site above the center a hexagon ring, a bridge (B) site above the midpoint of a C-C bond, and an on-top site directly above a carbon atom. As the hollow site is usually the most stable adsorption position for Li adatom on perfect and defective graphene, 13,19 in the present study we mainly consider the hollow sites above the center of polygon rings (pentagons, hexagons, heptagons, and octagons as shown in Fig. 1) in graphene with GBs for the adsorption of a Li atom. As the lithium mobility plays an important role in improving the performance of LIBs, it is important to study the diffusion of a Li adatom on graphene. Because a Li atom is much easier to diffuse on the surface of perfect graphene sheet with a smaller energy barrier rather than penetrate through graphene sheet, 13 the diffusion of a Li adatom on the surface of defective graphene sheet with GBs is mainly considered in the present study. To study the effect of GB on the diffusion of a Li adatom on graphene surface, we have calculated the energy barrier ∆E for the diffusion of a Li adatom via ab initio techniques. The climbing image nudged elastic band (CI-NEB) method 49,50 is used to seek the saddle points and minimum energy path. Four images between two end points are employed. Each image is relaxed until the forces on atoms are less than 0.02 eV/˚ A. The crystal orbital Hamilton populations (COHPs) 51 are calculated based on tightbinding linear muffin-tin orbital (TB-LMTO) method as implemented in the TB-LMTOASA 4.7 program. 52 The local density and atomic sphere approximations are used. The basis sets include 1s and 2s for Li, 2s and 2p for C, and s, p, and d for ”empty sphere”, respectively. The tetrahedral method is used to calculate the electron density of states. The accuracy in the energy convergence is set to 10−5 Ry.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3

Page 6 of 26

RESULTS AND DISCUSSION

3.1

Energetic Stability of a Li Atom Adsorbed on Graphene with Grain Boundaries

We first examine the stability of GBs in graphene by computing their formation energies as follows: ∆E0 (GB) =

1 (EGB − E0 ) d

(1)

where EGB and E0 are the total energies of graphene with a GB and the one of perfect graphene with the same number of carbon atoms, respectively. d is the length of the repeat vector d (as shown in Fig. 1) of graphene GB. For the (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) GBs considered here, their formation energies are 0.904, 0.657 and 0.485 eV/˚ A, respectively, indicating that the (2, 0)|(2, 0) and (2, 1)|(2, 1) GBs are more stable than the (5, 0)|(3, 3) GB. To assess the stability of a Li adatom on GBs, we calculate the adsorption energy of a Li adatom as defined below:

Ead,GB(Li) = ELi,GB − ELi − EGB

(2)

where EGB and ELi,GB are the total energies of graphene with a GB before and after absorbing a Li atom, respectively, and ELi for the total energy per atom of bulk Li with body-center cubic (bcc) structure. To describe the interaction between a Li adatom and a GB, we calculate their interaction energy according to the following equation:

Eint = (ELi,GB + E0 ) − (ELi,0 + EGB )

(3)

E0 and ELi,0 are the total energies of perfect graphene before and after adsorbing a Li atom, respectively. Eint gives the energy change of a complex entity of a Li adatom and a GB with respect to the sum of the total energies of individual Li adatom and GB. The negative


Page 7 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(positive) sign of Eint defined in Eq. 3 indicates that the formation of a complex entity of a Li adatom and a GB is energetically favorable (unfavorable). It is obvious that Eq. 3 can be rewritten in the following way

Eint = (ELi,GB − EGB ) − (ELi,0 − E0 )

(4)

Therefore, the interaction energy of a Li adatom and a GB can be regarded as the difference between the adsorption energies of a Li atom adsorbed on perfect graphene and on defective graphene with a GB. The adsorption energies for a Li atom adsorbed at different hollow sites of the (5, 0)|(3, 3), (2, 1)|(2, 1), (2, 0)|(2, 0) GBs of graphene are presented in Fig. 2. It can be seen that a Li adatom energetically prefers the adsorption sites within the GB region rather than those in the bulk region of graphene for the above three cases. As shown in Fig. 1a, the (5, 0)|(3, 3) GB of graphene contains three heptagon-pentagon pairs. The most stable adsorption site for a Li adatom is the hollow site of a pentagonal ring (i.e., H9 site as shown in Fig. 1a). For the different hollow sites above the polygonal rings of the (5, 0)|(3, 3) GB, the stability of a Li adatom from high to low exhibits the following order: pentagonal ring ≈ heptagonal ring > hexagonal ring. The (2, 1)|(2, 1) GB of graphene contains one heptagon-pentagon pair. The adsorption of a Li atom at the hollow site of a heptagonal ring (i.e., H1 as shown in Fig. 1b) is more stable than that at the hollow sites of pentagonal and hexagonal rings. The (2, 0)|(2, 0) GB (i.e., an ELD as shown in Fig. 1c) of graphene consists of two pentagons and one octagon. The Li adatom is energetically favorable to be adsorbed at the hollow site of an octagonal ring. It also can be seen that the Li adatom on the (2, 0)|(2, 0) GB is more stable than that on the (5, 0)|(3, 3) and (2, 1)|(2, 1) GBs. This is because the (2, 0)|(2, 0) GB has robust defect states around the Fermi level, as discussed below. The interaction energies of a Li adatom and different structural defects (such as monovacancy, divacancy, Stone-Wales defect, and GB) are presented in Fig. 2b. It is noted that the values of Eint for a Li adatom and the structural defects as mentioned above all are



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

negative, indicating an attractive interaction between a Li adatom and a structural defect. We also find that among these structural defects the interaction between a Li adatom and a monovacancy is the strongest. As for the three types of GBs considered in the present study, their interactions with a Li adatom exhibit the following order from strong to weak: (2, 0)|(2, 0) GB > (5, 0)|(3, 3) GB > (2, 1)|(2, 1) GB. Therefore, the (2, 0)|(2, 0) GB (i.e., the ELD) would significantly enhance the Li atom adsorption on graphene. The calculated adsorption energy Ead , adsorption height h (defined as the vertical distance between the Li adatom and graphene substrate) for the most stable adsorption sites of a Li adatom on these three GBs of graphene are summarized in Table 1. The average Li–C bond lengths for a Li atom adsorbed on the (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) GBs (2.172, 2.227, and 2.231 ˚ A, respectively) are slightly shorter than that of a Li adatom on perfect graphene by 0.03 ∼ 0.09 ˚ A. In addition, the adsorption of a Li adatom on these three GBs of graphene do not induce structural distortion, in contrast to the case of a Li adatom on graphene with Stone-Wales defect, 19 which suggests that the Li atom adsorption on GB may avoid the volume effect for the application of graphene as an anode material in LIBs.

3.2

Electronic Structures of Graphene Modified by a Li Adatom

Figure 3 shows the band structures of graphene with (5, 0)|(3, 3), (2, 1)|(2, 1), (2, 0)|(2, 0) GBs before and after adsorbing a Li atom. Without the Li adsorption, the (5, 0)|(3, 3) GB opens a tiny band gap of about 0.05 eV (see Fig. 3a and the enlarged picture in Fig. 4a). The (2, 1)|(2, 1) GB exhibits zero band gap (see Fig. 3c), just like the perfect graphene. The (2, 0)|(2, 0) GB shows metallic behavior. Our results are consistent with the previous studies. 27,44 A remarkable feature is that in both cases of the (5, 0)|(3, 3) and (2, 0)|(2, 0) GBs there is a nearly flat band just above the Fermi level. The corresponding electron states are mainly localized at boundary region (see the wavefunction distribution in Fig. 4b and Fig. S1b in the Supporting Information). For the Li atom adsorbed at the most stable positions of these three GBs, the Fermi level shifts into the conduction bands due to the 8 ACS Paragon Plus Environment

Page 8 of 26

Page 9 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


electron donation of the Li adatom, resulting in a metallic characteristic. Charge transfer is most sensible to ionic bonding and less relevant to covalent. 12 To understand the bonding nature of a Li adatom on graphene, we calculate the difference charge density ∆ρ as defined below:

∆ρ = ρLi+G − (ρLi − ρG )

(5)

where ρLi+G represents the charge density for the whole system of graphene with a Li adatom, ρG the charge density of a graphene substrate (without Li adsorption), and ρLi the charge density of an isolated Li atom located at the same position as in the whole system. Figure 5 shows the difference charge densities for the most stable adsorption sites of a Li adatom on the (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) GBs of graphene. In all of these cases, there is a net gain of electron charge in the intermediate region between the adsorbed Li atom and the graphene sheet, while there is a net loss of electron charge just above the adsorbed Li atom, indicating a significant charge transfer from the Li adatom to its nearest neighbor C atoms. To quantitatively estimate the amount of charge transfer between the Li adatom and the graphene substrate, we have carried out the Bader charge analysis. 53,54 In this analysis, each atom of a compound is surrounded by a surface (called Bader regions) that runs through minima of the charge density, and the total charge of an atom is determined by integration within the Bader region. The Bader charge state of a Li adatom at the most stable adsorption sites for the (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) GBs are about +0.897|e|, +0.906|e|, and +0.907|e| (see Table 1), respectively, which are nearly the same value in the case of the perefect graphene (+0.904|e| for the Li adatom). The averaged Bader charge states of carbon atoms next to the Li adatom are -0.123, -0.090 and -0.101|e|, respectively, smaller than that in the case of a Li atom adsorbed on perfect graphene (-0.127|e|). This indicates that more electrons are distributed in the intermediate region between the Li adatom and the GB. Our results suggest that the bonding between Li and C atoms in the case of a Li



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

atom adsorbed on the GBs of graphene is predominantly ionic. The similar feature was also found in the case of a Li atom adsorbed on a divacancy of graphene. 19

3.3

Diffusion of a Li Adatom on Graphene

We first study the diffusion of a Li adatom on perfect graphene by using a 6 × 6 hexagonal supercell of graphene. The calculated energy barrier for the diffusion of a Li adatom from a hollow site to a nearest neighboring one on perfect graphene is about 0.277 eV (Fig. S2 in the Supporting Information). 19 For the diffusion of a Li adatom on the GBs of graphene, we consider two types of diffusion path, namely, the Li atom diffusions along and perpendicular to the GB. The calculated energy profiles for the Li atom diffusion between two neighboring sites (namely, H16 → H12 → H9 → H6 → H3 → H16, H9 → H7, H9 → H8, and H9 → H10 as indicated in Figs. 6a and 6c) on the (5, 0)|(3, 3) GB of graphene are shown in Figs. 6b and 6d. The energy barriers for the diffusion of a Li adatom along the boundary are predicted to be in a range from 0.245 eV to 0.289 eV, while the energy barriers for the diffusion paths perpendicular to the boundary are in the range from 0.302 eV to 0.331 eV, suggesting that a Li adatom would tend to diffuse along the boundary. The transition states are all located at the bridge sites. As mentioned above, the H9 site is the most stable adsorption position for a Li adatom on the (5, 0)|(3, 3) GB of graphene (see Fig. 2a). For the Li atom diffusion perpendicular the boundary (H9 → H7, H9 → H8, and H9 → H10 as indicated in Fig. 6c), the energy barriers for the forward diffusion of a Li adatom are larger than those of the backward diffusion (see Table 2). This suggests that a Li adatom is relatively harder to migrate from the boundary sites to the adjacent non-boundary sites. The similar trends are also found in the cases of the (2, 1)|(2, 1) and (2, 0)|(2, 0) GBs (see Table 2 and Figs. S3 and S4 in the Supporting Information). The above analysis indicates that a Li adatom is easier to migrate along the GB rather than perpendicular to the GB. This can be mainly attributed to the different stability of the corresponding transition states. Taking the diffusion paths of H9 → H6 (along the 10 ACS Paragon Plus Environment

Page 10 of 26

Page 11 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


GB) and H9 → H7 (perpendicular to the GB) for a Li adatom on the (5, 0)|(3, 3) GB into consideration as an example, we choose their corresponding transition states to examine the Li-C bonding by calculating the COHP (see Fig.7). The COHP plot as a function of electron energy better illuminates the hybridization between atom pairs that allows the bonding, nonbonding, and antibonding states to be visualized. Generally, a negative COHP indicates bonding interaction and a positive one indicates antibonding interaction. 51 The bonding strength between the same pair of atoms can be evaluated by the integrated COHP (ICOHP) values. For a certain pair of atoms, the more negative the ICOHP, the stronger the bonding interactions. 55 The bonding orbitals are partly filled above Fermi level, which is mainly due to the electron transfer from Li 2s states to the host. The antibonding states of Li–C interactions in the transition state structure in the diffusion path of H9 → H6 are closer to Fermi level than those in the diffusion path of H9 → H7. The integrated COHP (ICOHP) values of Li–C interactions in the transition state structure in the diffusion path of H9 → H6 are -0.712 and -0.839 eV/cell, respectively, while the ICOHP values of Li–C interactions in the transition state structure in the migration path of H9 → H7 are -0.748 and -0.667 eV/cell, respectively. This also suggests that the Li–C interaction in the transition state in the former migration path is relatively stronger than that in the latter one. Therefore the transition state structure in the diffusion path along the GB is more stable than that in the diffusion path perpendicular to the GB. This may be the reason why the diffusion of a Li adatom along the GB has a smaller energy barrier than that perpendicular to the GB.

4

CONCLUSIONS

In summary, based on density functional theory calculations, we have investigated the adsorption and diffusion of a Li adatom on graphene with (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) grain boundaries. Our results show that a Li atom is energetically favorable to be adsorbed at the hollow sites above the pentagonal, heptagonal, and octagonal rings for the (5, 0)|(3, 3),



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(2, 1)|(2, 1) and (2, 0)|(2, 0) grain boundaries, respectively. The (2, 0)|(2, 0) grain boundary exhibit more significantly attractive interaction with Li adatom, compared with other two types of grain boundary. Our results suggest that the presence of grain boundary in graphene would enhance the Li adsorption significantly. Moreover, our results show that the diffusion of a Li adatom along the gain boundary has a smaller energy barrier than that perpendicular to boundary, suggesting that the grain boundary could be the channel of Li atoms on graphene during the process of charge and discharge of graphene as an anode material of LIBs. These results would give an insightful understanding of the role of topological defects in the lithium storage of graphene as an anode material in LIBs. Not only the edge, point defect and dopant, but also the grain boundary can enhance the lithium adsorption of graphene, which would be very helpful for the design of the graphene-based anode materials of LIBs.

Supporting Information Available Additional results are presented: (1) Enlarged band structure for graphene with a (2, 0)|(2, 0) grain boundary and the squared wave functions for lowest conduction band at the Brillouin zone center; (2) Energy evolution for the Li atom diffusion on perfect graphene and defective graphene with (2, 1)|(2, 1) and (2, 0)|(2, 0) grain boundaries. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement This research was supported by the National Natural Science Foundation of China under projects (Nos. 20973175, 21233009) and Natural Science Foundation of Fujian Province (Nos. 2011J05036, 2011J05039).


Page 12 of 26

Page 13 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References (1) Schedin, F.; Geim, A. K.; Morozov, S. V.; Hill, E. W.; Blake, P.; Katsnelson, M. I.; Novoselov, K. S. Detection of individual gas molecules adsorbed on graphene. Nat. Mater 2007, 6, 652–655. (2) Tarascon, J.-M.; Armand, M. Issues and challenges facing rechargeable lithium batteries. Nature 2001, 414, 359–367. (3) Dahn, J. R.; Zheng, T.; Liu, Y.; Xue, J. S. Mechanisms for Lithium Insertion in Carbonaceous Materials. Science 1995, 270, 590–593. (4) Lian, P.; Zhu, X.; Liang, S.; Li, Z.; Yang, W.; Wang, H. Large reversible capacity of high quality graphene sheets as an anode material for lithium-ion batteries. Electrochim. Acta 2010, 55, 3909 – 3914. (5) Pollak, E.; Geng, B.; Jeon, K.-J.; Lucas, I. T.; Richardson, T. J.; Wang, F.; Kostecki, R. The Interaction of Li+ with Single-Layer and Few-Layer Graphene. Nano Lett. 2010, 10, 3386–3388. (6) Wang, G.; Shen, X.; Yao, J.; Park, J. Graphene nanosheets for enhanced lithium storage in lithium ion batteries. Carbon 2009, 47, 2049 – 2053. (7) Pan, D.; Wang, S.; Zhao, B.; Wu, M.; Zhang, H.; Wang, Y.; Jiao, Z. Li Storage Properties of Disordered Graphene Nanosheets. Chem. Mater. 2009, 21, 3136–3142. (8) Bhardwaj, T.; Antic, A.; Pavan, B.; Barone, V.; Fahlman, B. D. Enhanced Electrochemical Lithium Storage by Graphene Nanoribbons. J. Am. Chem. Soc. 2010, 132, 12556–12558. (9) Yao, F.; G¨ une¸s, F.; Ta, H. Q.; Lee, S. M.; Chae, S. J.; Sheem, K. Y.; Cojocaru, C. S.; Xie, S. S.; Lee, Y. H. Diffusion Mechanism of Lithium Ion through Basal Plane of Layered Graphene. J. Am. Chem. Soc. 2012, 134, 8646–8654. 13 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(10) Toyoura, K.; Koyama, Y.; Kuwabara, A.; Tanaka, I. Effects of Off-Stoichiometry of LiC6 on the Lithium Diffusion Mechanism and Diffusivity by First Principles Calculations. J. Phys. Chem. C 2010, 114, 2375–2379. (11) Zheng, J.; Ren, Z.; Guo, P.; Fang, L.; Fan, J. Diffusion of Li+ ion on graphene: A DFT study. Appl. Surf. Sci. 2011, 258, 1651–1655. (12) Chan, K. T.; Neaton, J. B.; Cohen, M. L. First-principles study of metal adatom adsorption on graphene. Phys. Rev. B 2008, 77, 235430. (13) Fan, X.; Zheng, W.; Kuo, J.-L. Adsorption and Diffusion of Li on Pristine and Defective Graphene. ACS Appl. Mater. Interfaces 2012, 4, 2432–2438. (14) Song, J.; Ouyang, B.; Medhekar, N. V. Energetics and Kinetics of Li Intercalation in Irradiated Graphene Scaffolds. ACS Appl. Mater. Interfaces 2013, 5, 12968–12974. (15) Lee, E.; Persson, K. A. Li Absorption and Intercalation in Single Layer Graphene and Few Layer Graphene by First Principles. Nano Lett. 2012, 12, 4624–4628. (16) Liu, M.; Kutana, A.; Liu, Y.; Yakobson, B. I. First-Principles Studies of Li Nucleation on Graphene. J. Phys. Chem. Lett. 2014, 5, 1225–1229. (17) Fan, X.; Zheng, W. T.; Kuo, J.-L.; Singh, D. J. Adsorption of Single Li and the Formation of Small Li Clusters on Graphene for the Anode of Lithium-Ion Batteries. ACS Appl. Mater. Interfaces 2013, 5, 7793–7797. (18) Uthaisar, C.; Barone, V. Edge Effects on the Characteristics of Li Diffusion in Graphene. Nano Lett. 2010, 10, 2838–2842. (19) Zhou, L.-J.; Hou, Z. F.; Wu, L.-M. First-Principles Study of Lithium Adsorption and Diffusion on Graphene with Point Defects. J. Phys. Chem. C 2012, 116, 21780–21787.


Page 14 of 26

Page 15 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(20) Reddy, A. L. M.; Srivastava, A.; Gowda, S. R.; Gullapalli, H.; Dubey, M.; Ajayan, P. M. Synthesis Of Nitrogen-Doped Graphene Films For Lithium Battery Application. ACS Nano 2010, 4, 6337–6342. (21) Wu, Z.-S.; Ren, W.; Xu, L.; Li, F.; Cheng, H.-M. Doped Graphene Sheets As Anode Materials with Superhigh Rate and Large Capacity for Lithium Ion Batteries. ACS Nano 2011, 5, 5463–5471. (22) Yu, Y.-X. Can all nitrogen-doped defects improve the performance of graphene anode materials for lithium-ion batteries? Phys. Chem. Chem. Phys. 2013, 15, 16819–16827. (23) Mukherjee, R.; Thomas, A. V.; Datta, D.; Singh, E.; Li, J.; Eksik, O.; Shenoy, V. B.; Koratkar, N. Defect-induced plating of lithium metal within porous graphene networks. Nat. Commu. 2014, 5 . (24) Hardikar, R. P.; Das, D.; Han, S. S.; Lee, K.-R.; Singh, A. K. Boron doped defective graphene as a potential anode material for Li-ion batteries. Phys. Chem. Chem. Phys. 2014, 16, 16502–16508. (25) Sutton, A. P.; Balluffi, R. W. Interfaces in Crystalline Materials; Clarendon Press: Oxford, 1995. (26) Loginova, E.; Nie, S.; Th¨ urmer, K.; Bartelt, N. C.; McCarty, K. F. Defects of graphene on Ir(111): Rotational domains and ridges. Phys. Rev. B 2009, 80, 085430. (27) Lahiri, J.; Lin, Y.; Bozkurt, P.; Oleynik, I. I.; Batzill, M. An extended defect in graphene as a metallic wire. Nat. Nano. 2010, 5, 326–329. (28) Tapasztó, L.; Nemes-Incze, P.; Dobrik, G.; Jae Yoo, K.; Hwang, C.; Biró, L. Mapping the electronic properties of individual graphene grain boundaries. Appl. Phys. Lett. 2012, 100, 053114.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ˇ (29) J. Cervenka, J.; Flipse, C. F. J. Structural and electronic properties of grain boundaries in graphite: Planes of periodically distributed point defects. Phys. Rev. B 2009, 79, 195429. (30) Nemes-Incze, P.; Yoo, K. J.; Tapasztó, L.; Dobrik, G.; Lábár, J.; Horváth, Z. E.; Hwang, C.; Bir, L. P. Revealing the grain structure of graphene grown by chemical vapor deposition. Appl. Phys. Lett. 2011, 99, 023104. (31) Huang, P. Y.; Ruiz-Vargas, C. S.; van der Zande, A. M.; Whitney, W. S.; Levendorf, M. P.; Kevek, J. W.; Garg, S.; Alden, J. S.; Hustedt, C. J.; Zhu, Y. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 2011, 469, 389–392. (32) Kim, K.; Lee, Z.; Regan, W.; Kisielowski, C.; Crommie, M. F.; Zettl, A. Grain Boundary Mapping in Polycrystalline Graphene. ACS Nano 2011, 5, 2142–2146. (33) Yang, B.; Xu, H.; Lu, J.; Loh, K. P. Periodic Grain Boundaries Formed by Thermal Reconstruction of Polycrystalline Graphene Film. J. Am. Chem. Soc. 2014, 136, 12041– 12046. (34) Mesaros, A.; Papanikolaou, S.; Flipse, C. F. J.; Sadri, D.; Zaanen, J. Electronic states of graphene grain boundaries. Phys. Rev. B 2010, 82, 205119. (35) Bagri, A.; Kim, S.-P.; Ruoff, R. S.; Shenoy, V. B. Thermal transport across Twin Grain Boundaries in Polycrystalline Graphene from Nonequilibrium Molecular Dynamics Simulations. Nano Lett. 2011, 11, 3917–3921. (36) Yu, S. S.; Zhang, X. M.; Qiao, L.; Ao, Z. M.; Geng, Q. F.; Li, S.; Zheng, W. T. Electronic and magnetic properties of nitrogen-doped graphene nanoribbons with grain boundary. RSC Adv. 2014, 4, 1503–1511.


Page 16 of 26

Page 17 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(37) Dai, Q. Q.; Zhu, Y. F.; Jiang, Q. Electronic and Magnetic Engineering in Zigzag Graphene Nanoribbons Having a Topological Line Defect at Different Positions with or without Strain. J. Phys. Chem. C 2013, 117, 4791–4799. (38) Han, J.; Ryu, S.; Sohn, D.; Im, S. Mechanical strength characteristics of asymmetric tilt grain boundaries in graphene. Carbon 2014, 68, 250–257. (39) Zhang, T.; Li, X.; Kadkhodaei, S.; Gao, H. Flaw Insensitive Fracture in Nanocrystalline Graphene. Nano Lett. 2012, 12, 4605–4610. (40) Li, A.-P.; Clark, K. W.; Zhang, X.-G.; Baddorf, A. P. Electron Transport at the Nanometer-Scale Spatially Revealed by Four-Probe Scanning Tunneling Microscopy. Adv. Funct. Mater. 2013, 23, 2509–2524. (41) Kresse, G.; Furthm¨ uller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186. (42) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 1999, 59, 1758–1775. (43) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (44) Yazyev, O.; Louie, S. Electronic transport in polycrystalline graphene. Nat. Mater. 2010, 9, 806–809. (45) Liu, Y.; Yakobson, B. I. Cones, Pringles, and Grain Boundary Landscapes in Graphene Topology. Nano Lett. 2010, 10, 2178–2183. (46) Yazyev, O. V.; Louie, S. G. Topological defects in graphene: Dislocations and grain boundaries. Phys. Rev. B 2010, 81, 195420. (47) Zhang, J.; Zhao, J.; Lu, J. Intrinsic Strength and Failure Behaviors of Graphene Grain Boundaries. ACS Nano 2012, 6, 2704–2711. 17 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(48) Kou, L.; Tang, C.; Guo, W.; Chen, C. Tunable Magnetism in Strained Graphene with Topological Line Defect. ACS Nano 2011, 5, 1012–1017. (49) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000, 113, 9901–9904. (50) Henkelman, G.; Jónsson, H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 2000, 113, 9978–9985. (51) Dronskowski, R.; Blöchl, P. E. Crystal orbital Hamilton populations (COHP): energyresolved visualization of chemical bonding in solids based on density-functional calculations. J. Phys. Chem. 1993, 97, 8617–8624. (52) Tank, G.; Jepsen, O.; Burkhardt, A.; Andersen, O. K. The TB-LMTO-ASA Program, Version 4.7.; 1998; Max-Planck-Inst. F¨ ur Festkörperforschung Stuttg. Ger. (53) Henkelman, G.; Arnaldsson, A.; Jónsson, H. A fast and robust algorithm for Bader decomposition of charge density. Comput. Mater. Sci. 2006, 36, 354–360. (54) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: New York, 1990. (55) Dronskowski, R.; Hoffmann, R. Computational Chemistry of Solid State Materials: A Guide for Materials Scientists, Chemists, Physicists and others; Wiley-VCH: Verlag GmbH, 2005.


Page 18 of 26

Page 19 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1: Adsorption energies Ead of a Li atom adsorbed on different sites of graphene with grain boundary. System Site (5, 0)|(3, 3) H9 (2, 1)|(2, 1) H1 (2, 0)|(2, 0) H1 Perfect Hollow

Ead (eV) dC−C (˚ A) dLi−C (˚ A) -0.396 1.413 2.172 -0.067 1.411 2.227 -0.705 1.433 2.231 0.215 1.426 2.263

Height (˚ A) 1.818 1.570 1.378 1.434

Bader charge (|e|) +0.897 +0.906 +0.907 +0.904

Table 2: Energy barriers (∆E, in eV) for the diffusion of a Li adatom on graphene with (5, 0)|(3, 3), (2, 1)|(2, 1) and (2, 0)|(2, 0) grain boundaries. The value in the parenthesis correspond to the energy barrier of a backward diffusion. System (5, 0)|(3, 3)

path ∆E path ∆E (2, 1)|(2, 1) path ∆E (2, 0)|(2, 0) path ∆E Perfect ∆E

Along boundary H16 → H12 H12 → H9 H9 → H6 0.254 (0.312) 0.277 (0.291) 0.289 (0.261) H6 → H3 H3 → H16 0.270 (0.274) 0.284 (0.276) H2 → H1 H1 → H4 H4 → H2 0.274 (0.271) 0.387 (0.281) 0.262 (0.299) H2 → H1 0.365 (0.311) 0.277


Perpendicular H9 → H7 0.331 (0.145) H9 → H10 0.321 (0.181) H1 → H5 0.337 (0.222) H1 → H4 0.535 (0.121)

to boundary H9 → H8 0.302 (0.207)

H1 → H3 0.379 (0.206) H3 → H4 0.473 (0.096)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: Optimized atomic structures of graphene with (a) (5, 0)|(3, 3) (θ = 30.0◦ ), (b) (2, 1)|(2, 1) (θ = 21.8◦ ) and (c) (2, 0)|(2, 0) (θ = 0◦ ) grain boundaries. The hollow sites for the adsorption of a Li atom are indicated by the pink dotted circles with numbers. The non-hexagons in the region of grain boundary are highlighted in blue (heptagon or octagon) and light green (pentagon) colors. The blue dashed line indicates the periodic boundary. The length of repeat √ vector d for the (5, 0)|(3, 3) grain boundary of graphene in panel (a) is defined as d = a0 n2 + nm + m2 , where a0 is the length of unit vectors of perfect graphene (hexagonal) lattice.


Page 20 of 26

Page 21 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2: (a) The adsorption energy of a Li adatom on different sites (shown in Fig. 1) in the (5, 0)|(3, 3), (2, 1)|(2, 1), and (2, 0)|(2, 0) grain boundaries (GBs). (b) Interaction energy of a Li adatom with different structural defects such as a monovacancy, a divacancy, a Stone-Walse defect, a (5, 0)|(3, 3) GB, a (2, 1)|(2, 1) GB, and a (2, 0)|(2, 0) GB. Note that the results for the monovacancy, divacancy, and Stone-Wales defect are adopted from our previous work. 19 Insets are the local atomic structures for the most stable adsorption sites of a Li adatom on these five structural defects.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3: Band structures for graphene with grain boundaries (GBs) before and after adsorbing a Li atom: (a) (5, 0)|(3, 3) GB, (b) a Li atom adsorbed at the hollow site (H9 as shown in Fig. 1a) of an octagonal ring of the (5, 0)|(3, 3) GB, (c) (2, 1)|(2, 1) GB, (d) a Li atom adsorbed at the hollow site (H1 as shown in Fig. 1b) of an octagonal ring of the (2, 1)|(2, 1) GB, (e) (2, 0)|(2, 0) GB, and (f) a Li atom adsorbed at the hollow site (H1 as shown in Fig. 1c) of an octagonal ring of the (2, 0)|(2, 0) GB. The length of repeat vector d √ of graphene GB: d = a0 n2 + nm + m2 , where a0 is the length of unit vectors of graphene (hexagonal) lattice. The energy of zero is set to the Fermi energy.


Page 22 of 26

Page 23 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4: (a) Enlarged band structure of graphene with a (5, 0)|(3, 3) grain boundary. (b) The isosurface (3.0 × 10−3 e/˚ A3 ) of squared wavefunction |ψ|2 for lowest conduction band at the Brillouin zone (marked by the red point in left panel).

Figure 5: Isosurface (1.5×103 e/˚ A3 , yellow for ∆ρ > 0 and blue for ∆ρ < 0) of the difference charge density ∆ρ for the most stable configurations of a Li adatom on graphene with (a) (5, 0)|(3, 3), (b) (2, 1)|(2, 1), and (c) (2, 0)|(2, 0) grain boundaries.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: (a) The schematic diffusion path (H16 → H12 → H9 → H6 → H3 → H16) and (b) the energy evolution for the diffusion of a Li adatom along the boundary of the (5, 0)|(3, 3) grain boundary (GB). (c) The schematic diffusion paths (H9 → H7, H9 → H8 and H9 → H10) and (d) the energy evolution for the diffusion of a Li adatom perpendicular to the boundary of the (5, 0)|(3, 3) GB. The insets show the local atomic structures of transition states. The forward energy barrier ∆E for the diffusion of a Li adatom is indicated.


Page 24 of 26

Page 25 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7: Crystal orbital Hamilton population (COHP) of selected Li–C interactions in the transition state structures in the migration paths of (a) and (b) H9 → H6 (schematically shown in Fig. 6a), (c) and (d) H9 → H7 (schematically shown in Fig. 6b) for a Li adatom on the (5, 0)|(3, 3) grain boundary. It is noted that in the transition state structures the Li atom is adsorbed at the bridge site of a C–C bond. The lengths of the Li–C bonds considered in panels (a), (b), (c), and (d) are 2.105, 2.127, 2.114, and 2.125 ˚ A, respectively. The energy of zero is taken as the Fermi level.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphical TOC Entry


Page 26 of 26

First-Principles Studies of Lithium Adsorption and Diffusion on

Recommend Documents