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High Mobility and High Storage Capacity of Lithium in spsp2 Hybridized Carbon Network: The Case of Graphyne Hongyu Zhang, Mingwen Zhao,* Xiujie He, Zhenhai Wang, Xuejuan Zhang, and Xiangdong Liu School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, Shandong, China ABSTRACT: We have carried out first-principles calculations to explore the energetics and dynamics of Li in graphyne, a novel carbon allotrope consisting of spsp2 hybridized carbon atoms, relevant for anode lithium intercalation in rechargeable Li-ion batteries. In contrast to graphite where Li diffusion is confined in the interlayer space (in-plane diffusion), the unique atomic arrangement and electronic structures enable both inplane and out-plane diffusion of Li ions in graphyne with moderate barriers, 0.530.57 eV. The highest Li intercalation density in graphyne can be LiC4, exceeding the up limit of LiC6 in the commonly used graphite. The high lithium mobility and high storage capacity make graphyne a promising candidate for the anode material in battery applications.
’ INTRODUCTION Rechargeable Li-ion batteries have been widely used in portable and telecommunication electronic devices and are becoming a key-enabling technology for electric vehicles and hybrid electric vehicles.1,2 The energy density and performance of Li-ion batteries largely depend on the physical and chemical properties of the anode materials. Graphite is the most commonly used anode material in current commercial batteries owing to its acceptable reversibility and charge capacity of ∼372 mA 3 h/g by forming intercalation compounds LiC6.3,4 In order to enhance the energy capacity, much effort has been made to explore new anode materials, including other carbonaceous materials,510 metal-oxides,1113 and silicon nanowires.1417 The Li mobility in the electrodes is crucial for the charging times as well as the power density of a Li-ion battery.18 Both experimental and theoretical investigations have confirmed that Li diffusion in defect-free graphite is restricted in the interlayer space (in-plane diffusion) because Li hopping between adjacent layers through a carbon hexagon is energetically extremely unfavorable (∼10 eV).19,20 The highly inherent anisotropic nature of Li diffusion limits the rate capability of the charge/discharge reactions.20,21 In order to achieve higher energy capacity and faster charge/discharge, Li-ion technology is urgently being optimized by using alternative materials. Graphyne, a new layered carbon allotrope, is composed of spand sp2-hybridized carbon atoms.22 The sp2-hybridized C atoms form hexagons which are joined together by acetylenic linkages (CtC), as shown in Figure 1a. The presence of acetylenic groups introduces a rich variety of optical and electronic properties that are quite different from those of graphite,23,24 e.g., the natural band gap opening due to the asymmetric π bindings. Considerable effort has been devoted to growing this novel material, and numerous monomeric and oligomeric substructures r 2011 American Chemical Society
have already been synthesized.2528 More excitingly, large-area graphdiyne, which belongs to the same family as graphyne, has recently been successfully grown on the surface of copper via a cross-coupling reaction using hexaethynylbenzene.29 The fabrication of graphyne can be greatly expected in the near future, since theoretical work shows that it is energetically more stable than graphdiyne. On the analogy of the Li-intercalated graphite, graphyne is also a candidate for anode materials in Li-ion battery applications.30 The porous structure, asymmetrically conjugated π electrons, and semiconducting features may open up exciting opportunities for more efficient Li-ion batteries. In this contribution, we performed first-principles calculations within density functional theory (DFT)3136 to investigate the energetics and dynamics of Li in graphyne materials. We found that, in contrast to graphite where Li diffusion is confined in the interlayer space, both inplane and out-plane Li transport can be achieved in bulk graphyne with moderate energy barriers, 0.530.57 eV. The Li storage capacity in graphyne can also be greatly improved to LiC4 compared to the up limit of LiC6 in graphite. The high mobility and high Li storage capacity make graphyne a promising candidate for the anode material in Li-ion battery applications.
’ METHODS AND COMPUTATIONAL DETAILS All the DFT calculations were performed using the DMol3 package.31,32 Spin-unrestricted calculations in the generalizedgradient approximation (GGA) with Becke exchange (B88) and LeeYangParr (LYP) correlation functional33,34 were used throughout the calculations. The atomic orbital basis set was of Received: February 1, 2011 Revised: March 15, 2011 Published: April 13, 2011 8845
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Figure 1. (a) Layer structure of graphyne in a 2 2 supercell. The dashed lines indicate a unit cell. (b) Top view of bulk graphyne with an AB stacking sequence. The A and B layers are indicated by different colors. Panels c and d are the isosurfaces of the electron density of highest occupied valence band (HOVB) and lowest unoccupied conduction band (LUCB), respectively. The isovalue is 0.05 e/Å3. (e) Electrostatic potential projected on a plane containing both H and h sites and perpendicular to the graphyne plane. The rainbow is in units of au/Å3.
double-numerical quality with inclusion of polarization functions (DNP). The validity of this scheme in the study of Ligraphitic compounds has been demonstrated in the previous works.6,7 The KohnSham equations were solved self-consistently with a convergence of 105 hartree on the total energy. A Fermi smearing of 0.005 hartree was used to improve computational performance. All the equilibrium configurations presented herein were obtained by full relaxation without any symmetric constraints until the maximal forces were less than 0.002 hartree/Å. The linear or quadratic synchronous transit (LST/QST) method35 combined with conjugate gradient refinements was adopted for the transition state (TS) search. To determine if the transition state connects to the relevant reactant and product, we performed minimum-energy pathway (MEP) calculations using the nudged elastic band (NEB) method.36 Two-dimensional periodic boundary conditions were applied to the single-layer graphyne, while a vacuum region of 20 Å was applied in the direction perpendicular to the graphyne plane to exclude the mirror interactions between adjacent images. Bulk graphyne was modeled by a supercell containing two graphyne layers with an AB stacking sequence, as shown in Figure 1b. Analogous to graphite, the interlayer interaction in bulk graphyne is mainly dominated by weak van der Waals (vdW) interaction, which cannot be described efficiently by the present DFT calculations.37,38 However, for the bulk graphyne containing intercalants, the Coulomb interaction mediated by the intercalants is much stronger than the vdW interaction and thus can be reproduced well by the DFT calculations. Therefore, the multilayer effects on the energetic and kinetic behaviors of Li ions in bulk graphyne revealed by the above-mentioned theoretical strategy are reasonable.
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’ RESULTS AND DISCUSSION We first relaxed a 2 2 supercell of a single-layer graphyne, as shown in Figure 1a. The optimized lattice constant is 6.86 Å, in good agreement with other DFT calculations.23 The bond length between the sp2-hybridized C atoms is 1.42 Å, identical to that in graphene. The short distance between sp-hybridized carbon atoms (1.22 Å) in the chain indicates that the CtC triple bond is formed between them. The CC bond connecting sp- and sp2hybridized C atoms has the length of 1.40 Å. Due to the existence of two-coordinated (sp-hybridized) carbon atoms, graphyne is energetically unfavorable than graphene by about 0.56 eV/atom. However, graphdiyne containing more sp-hybridized C atoms has already been synthesized successfully.29 Our calculations indicate that graphyne is even more stable than graphdiyne by about 0.09 eV/atom, implying its high synthetic feasibility. Previous studies have confirmed that Li adsorption on graphitic surfaces takes place preferentially over the center of a hexagon (hollow site).6,7,18,19 Different from graphene, the graphyne network has two types of carbon hexagons: the large hexagon consisting of 12 C atoms and the small one containing 6 C atoms, as shown in Figure 1a. The diameters of these two hexagons (measured from the diameter of the inscribed circle) are 3.96 and 2.46 Å, respectively. The size of the large hexagon is much larger than that in graphene, which may facilitate the Li adsorption and diffusion in graphyne. Two hollow sites for Li adsorption which lie right above the centers of large and small hexagons are denoted as H and h hereafter. The adsorption height is defined as the distance between the adsorbate and the graphyne plane. The structural distortion caused by Li adsorption on both hollow sites was found to be very slight. The binding energies of Li on graphyne calculated by the difference between the energy of Li-containing graphyne and the sum of energies of pristine graphyne and an isolated Li atom are 2.56 eV (H site) and 1.76 eV (h site), respectively. The corresponding adsorption heights for H and h sites are 0.90 and 1.75 Å, respectively. Therefore, the Li atom prefers to adsorb on the H site rather than the h site. We also investigated the Li adsorption on graphene as references. Our calculations yielded a binding energy of 1.33 eV with an adsorption height of 1.74 Å, in good agreement with the previous work.39,40 Similar to the case of Ligraphene compound,37,41 substantial charge transfer occurs from the Li atom to the graphyne for both hollow sites, as revealed by Mulliken population analysis, indicating the ionic interaction between Li and C atoms of graphyne. However, the Li adsorption on graphyne is energetically more preferable, owing to the unique structural properties and hybridization of C atoms. For an ionically bonded adatom, the binding energy and adsorption height result from a balance of the electrostatic attraction between oppositely charged adatom and host layer and the short-range electron repulsion.39 It is clear from the present calculations that Li prefers to adsorb at the H site of graphyne rather than the h site. The adsorption height for the H site is also smaller than that for the h site by about 0.85 Å. This is related to the asymmetric π-binding between differently hybridized C atoms in graphyne. Our first-principles calculations of graphyne show that the highest occupied valence band (HOVB) is contributed mainly by the π-binding between sp2-hybridized C atoms and between sp-hybridized C atoms, whereas the lowest unoccupied conduction band (LUCB) arises mainly from the π-binding between the sp2- and sp-hybridized C atoms, as shown in Figure 1, parts c and d. When a Li atom adsorbs on graphyne, 8846
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Figure 2. Diffusion path (bottom panel) and energy profile (middle panel) as a function of adsorption sites of Li on a graphyne layer. The schematic drawings of the diffusion path and the corresponding transition states (TS) (top panel) are presented.
charge transfer from Li to graphyne shifts the Fermi level of graphyne to its conduction bands, leading to the metallization of semiconducting graphyne. Therefore, the electrons occupying the conduction bands of graphyne reside in the region between the sp2- and sp-hybridized C atoms, i.e., the negative charges of Li-graphyne distribute along the long sides of large hexagons. This makes the H site energetically more preferable for Li (positively charged) adsorption than the h site. This can be further confirmed by the electrostatic potential of singly negatively charged graphyne on the plane containing both H and h sites and perpendicular to the graphyne plane, as shown in Figure 1e. It can be clearly seen that both H and h sites are situated in potential valleys, with the lowest and second lowest electrostatic potential, respectively. Therefore, positively charged Li energetically favors these locations. The distinction of adsorption height between these two locations can also be manifested from the electrostatic potential profiles. Considering the importance of Li mobility in improving the performance of Li-ion batteries, we then investigated the Li diffusion barriers as it moves between neighboring adsorption sites on graphyne. The calculated diffusion paths (h f H and H f H) and the corresponding energy profile are shown in Figure 2. The results indicate that the transition states (TS) reside on top of the midpoint of the CC bond between two neighboring hollow sites (bridge site). Starting from the TS and moving down toward the minima along both the reactant and the product directions, the reaction pathway was followed. As expected, no minima were found on the pathway other than the reactant and product. Therefore, the TS predicted using the LST/QST method does connect the reactant and product. The energy barrier for the Li diffusion along the h f H direction is only 0.12 eV. However, the reverse diffusion (H f h) has a relatively high energy barrier of about 0.92 eV, due to the energetic favorability of the H site over the h site. The energy barrier for Li hoping between two adjacent H sites was identified to be 0.72 eV, slightly higher than that for Li diffusion on graphene, 0.320.48 eV.39,40,42 This is related to the small adsorption height of H site adsorption. In view of the energetic
Figure 3. Energy profiles for Li passing through (a) the small hexagon and (b) the large hexagon on a graphyne layer as a function of adsorption height. The energies of equilibrium adsorption configurations are set to zero, respectively.
stability and kinetics, the in-plane Li diffusion on graphyne is mainly dominated by the H f H hoping with an energy barrier of 0.72 eV. We next explored the Li diffusion from one side of a graphyne layer to another side along the direction perpendicular to the graphyne plane (out-plane diffusion). In the calculations of the potential energy profiles (PEP) for Li out-plane diffusion, the C atoms nearest and second nearest to the Li were fully relaxed while other C atoms were kept fixed. Figure 3 gives the PEP of two typical paths. The energy barrier for Li diffusion through a small hexagon is as high as 8.25 eV, close to the value for Li passing through a hexagon of graphene.19 Such a high energy barrier implies that the out-plane diffusion of Li through a small hexagon is energetically prohibited under normal conditions. Interestingly, our calculations revealed that Li can easily pass through the large hexagon by overcoming a very small energy barrier of only 0.18 eV. Therefore, the large void formed by the sp2- and sp-hybridized C atoms in graphyne facilitates not only the Li adsorption but also the Li out-plane diffusion. To take the interlayer interactions into account, we modeled bulk graphyne with a 2 2 1 supercell by applying threedimensional periodic conditions. The supercell contains two graphyne layers with an AB stacking sequence and interlayer spacing of 3.45 Å (see Figure 1b), which has been predicted as the most stable stacking arrangement of bulk graphyne.24 Accordingly, Li atoms can be sandwiched between two graphyne planes at two types of sites, HH (between centers of large hexagons of two adjacent layers) and hH (between centers of a small hexagon and a large hexagon of two adjacent layers). When a Li atom is intercalated into an HH site, the equilibrium distance between the Li and the two adjacent layers is identical, which is about 1.72 Å. The relevant binding energy is about 3.14 eV. For the Li residing at an hH site, it is closer to the large hexagon with a distance of 1.23 Å, and the separation between the Li and small 8847
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Figure 5. (a) Top view and (b) side view of optimized Li-intercalated graphyne compound LiC4. Figure 4. (a) In-plane diffusion pathway of Li in bulk graphyne and (b) the corresponding energy profile as a function of intercalation sites. (c) Out-plane diffusion pathway of Li in bulk graphyne and (d) the corresponding energy profile as a function of intercalation sites.
hexagon is 2.22 Å. The binding energy is 2.86 eV. Obviously, the intercalated Li prefers to occupy an HH site rather than an hH site. However, for both cases, the Ligraphyne interaction is enhanced in bulk graphyne compared to that in a single graphyne layer. This is a direct result of Coulomb attraction of adjacent layers to the Li atom. In addition, upon lithium intercalation, the interlayer separation between two graphyne layers alters very slightly, within the 0.6% range. This implies that graphyne as an anode material will not suffer significant structural degradation upon cycling. This is contrary to the case of Li-intercalated graphite, which undergoes structural disordering upon prolonged cycling resulted from the large Li-driven interlayer swing (∼10.5% for LiC6).4345 Consequently, as far as reversibility is concerned, graphyne as an anode may be superior to the conventional graphite anode. We also examined the influence of interlayer interactions on the in-plane and out-plane diffusivity of Li in bulk graphyne. For the AB stacking arrangement, two typical in-plane diffusion pathways were considered, as shown in Figure 4a. The energy barrier for Li diffusing between two adjacent hH sites was calculated to be 0.53 eV (see Figure 4, parts a and b). On the other hand, the energy barrier from the hH site to the HH site is 0.57 eV, whereas that from HH to hH is 0.85 eV. By comparing the diffusion pathways and the corresponding barriers, we can conclude that, similar to the case of a single graphyne layer, the continuous in-plane Li diffusion in bulk graphyne can be achieved through the hoping between adjacent hH sites, forming a zigzag trajectory. However, the energy barrier of 0.53 eV is lower than that (0.72 eV) in a single graphyne layer. This suggests that the interlayer interactions facilitate not only the Li intercalation but also the Li in-plane diffusion. The interlayer interactions in bulk graphyne also affect the out-plane diffusion. The Li atom located at an HH site can pass through the large hexagon of the adjacent layer by overcoming an energy barrier of 0.56 eV, as shown in Figure 4, parts c and d. This barrier is higher than that in a single graphyne layer (0.18 eV). A continuous out-plane diffusion along the direction perpendicular to the graphyne plane can be achieved by a series of steps of HH f HH hoping. For the Li atom residing at an hH site, the
direct out-plane diffusion is blocked by a small hexagon. However, it can first move to an adjacent HH site through in-plane diffusion by overcoming an energy barrier of 0.57 eV and then diffuse along HH f HH continuously, as shown in Figure 4, parts c and d. Overall, the energy barrier of the Li out-plane diffusion (0.560.57 eV) in bulk graphyne is only slightly higher than that of the Li in-plane diffusion in graphite (0.320.48 eV). This suggests that the Li diffusion in bulk graphyne is not restricted within the interlayer space, and the diffusion along the direction perpendicular to basal plane is also possible under experimental conditions. The three-dimensional diffusion behavior of Li in bulk graphyne may find applications in the development of anode materials of a Li-ion battery with a very high rate capability. We evaluated the Li storage capacity in bulk graphyne. Due to the appearance of sp-hybridized C atoms, the separation between adjacent adsorption sites (HH or hH) in graphyne is larger than 3.96 Å, which is larger than the average LiLi bond length of the Li system confined within carbon nanotubes (2.91 Å).6,7 The Li atoms residing at these sites separate naturally, avoiding too high electrostatic repulsion between them. Therefore, both HH and hH sites of bulk graphyne can be fully occupied by the intercalated Li atoms, as shown in Figure 5, corresponding to the lithium capacity of LiC4, which is much higher than the maximum value of graphite, LiC6. This has been confirmed by our first-principles calculations. We modeled the LiC4 crystal using a 2 2 1 supercell with HH and hH sites being fully filled. Structural relaxation showed that this configuration is quite stable. The average binding energy between Li and graphyne is about 2.00 eV/Li. As expected, the Li intercalation has little effect on the interlayer spacing between adjacent graphyne layers. To further clarify the issue, we defined the intercalation energy (Ein) using the expression Ein ¼ Et ½graphyne þ nLi Et ½graphyne þ ðn 1ÞLi Et ½Li where Et[graphyne þ xLi] is the total energy of the Ligraphyne compound with x Li atoms and Et[Li] is the total energy of an isolated Li atom. The variation of intercalation energy as a function of Li/C ratio is shown in Figure 6. The principles in the construction of Li-graphyne compounds with different Li/C ratios are that the Li atoms tend to occupy HH sites preferentially and are separated as far as possible. From Figure 6 we can see the following features: (1) The intercalation energy increases with 8848
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’ ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Nos. 10974119, 11075097), the Natural Science Fund for Distinguished Young Scholars of Shandong Province (No. JQ201001), and the Independent Innovation Foundation of Shandong University (IIFSDU, No. 2009JQ003). ’ REFERENCES Figure 6. Variation of intercalation energy (Ein) as a function of Li/C ratio.
the increase of Li/C ratio in a steplike fashion. This is a direct consequence of the competition between LiLi repulsive interactions and LiC attractive Coulomb interactions. The steplike structures correspond to different stable intercalation morphologies (Li occupation patterns). (2) Although intercalation energy depends on the Li occupation patterns, it is negative as the Li/C ratio is lower than 0.25. This indicates that the whole Li intercalation process up to 0.25 Li/C ratio is energetically favorable. Overall, the unique structure of graphyne enhances not only the lithium diffusion rate but also the amount of insertable Li ions, both leading to superior electrode performance. The intercalating and releasing processes of Li in graphyne are also quite important for its application in a Li-ion battery. We therefore employed a nanoribbon model to evaluate the adsorption and diffusion of Li near the edges. The Coulomb attraction between Li ion and graphyne arising from the electron transfer facilitate entry of Li ions, similar to the cases of the Licarbonnanotube system.6,7 The adsorption of Li at the inner region of the nanoribbon is energetically more stable than that at the edge for both hollow sites. Therefore, Li encounters lower diffusion barriers when it moves from the edge toward the inner region of the nanoribbons compared to the diffusion in the opposite direction, which allows rapid entry of Li ions for quick battery charging. Similar to the case of silicon nanostructures,17 the reverse process (Li releasing) is energetically disadvantageous. However, this can be overcome by the voltage between the anode and cathode of the Li-ion battery during the discharge process.
’ CONCLUSIONS In summary, our first-principles calculations indicate that the unique atomic arrangement of graphyne composed of sp- and sp2-hybridized C atoms facilitates not only the Li diffusion but also the storage capacity. In contrast to the commonly used graphite material where Li diffusion is restricted in the interlayer space (in-plane diffusion), three-dimensional Li diffusion (both in-plane and out-plane) can be achieved by overcoming energy barriers of about 0.530.57 eV. The highest Li storage capacity in bulk graphyne can be LiC4, which is higher than that in graphite, LiC6. The Li intercalation has little effect on the interlayer spacing between adjacent graphyne layers and thus is advantageous for charging processes. The high mobility and high Li storage capacity make graphyne a promising candidate for the anode material in battery applications. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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