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Edited by George William Crabtree, Argonne National Laboratory, Argonne, IL, and approved December 16, 2016 (received for review October 31, 2016)
Significance
The 2016 Nobel Prize in Physics highlighted the importance of topological state in science and technology. Here we explore the possibility of using all-carbon-based topological semimetal (ACTS) for lithium-ion battery anode material based on the merits of intrinsic high electronic conductivity and ordered porosity. Using state-of-the-art theoretical calculations, we do show, by taking topological semimetal bco-C16 as an example, that ACTS structures can be promising anode materials with high specific capacity, fast ion kinetics, and slight volume change during operation. Our study would not only pave a pathway for design of high-performance anode materials going beyond the commercially used graphite but would also encourage further theoretical studies on topological phases of carbon materials.
Abstract
Topological state of matter and lithium batteries are currently two hot topics in science and technology. Here we combine these two by exploring the possibility of using all-carbon-based porous topological semimetal for lithium battery anode material. Based on density-functional theory and the cluster-expansion method, we find that the recently identified topological semimetal bco-C16 is a promising anode material with higher specific capacity (Li-C4) than that of the commonly used graphite anode (Li-C6), and Li ions in bco-C16 exhibit a remarkable one-dimensional (1D) migration feature, and the ion diffusion channels are robust against the compressive and tensile strains during charging/discharging. Moreover, the energy barrier decreases with increasing Li insertion and can reach 0.019 eV at high Li ion concentration; the average voltage is as low as 0.23 V, and the volume change during the operation is comparable to that of graphite. These intriguing theoretical findings would stimulate experimental work on topological carbon materials.
With the growing demand for portable energy sources, it is more and more urgent to improve the present lithium-ion batteries (LIBs) (1, 2). Apart from the cathode and electrolyte, the anode as one of the most important parts in LIBs has been extensively explored for better performance (3, 4). Although the graphite anode has good stability and low cost, its theoretical maximum specific capacity is only 372 mAh/g, which cannot meet the higher requirements of current and future technologies such as advanced electrical vehicles (5). Therefore, efforts have been devoted to finding new candidates with larger specific capacity. Among them, Si- and P-based materials are considered as promising candidates because their specific capacities can reach as high as 4,200 and 2,596 mAh/g (6, 7), respectively, which are much higher than that of the graphite anode. However, they both suffer from the poor reversibility caused by huge volume expansion (Si > 300%; P > 300%) and slow rate capability caused by low electronic conductivity (8, 9). Although the electrochemical performances can be improved via the thin-film technique, porous structures, nanotube/nanowire arrays, carbon coating, etc. (10, 11), the complex synthetic procedures and high fabrication costs prevent their practical applications. Thus, it remains a great challenge to develop an anode material with high capacity, good stability, and fast kinetics as well as low cost.
Considering the abundance in resources, flexibility in bonding, and variety in morphology (12, 13), carbon materials have some unique advantages in anode applications. In fact, graphene, carbon nanotubes (CNTs), carbon nanofibers (CNFs), carbon nanorings, and porous carbon (14⇓–16) have been extensively explored for this purpose (17, 18). For instance, pristine graphene shows a weak adsorption of Li and has low capacity whereas defective graphene can bind Li stably and has a higher capacity than graphite (19); the mesoporous graphene nanosheets have achieved an ultrahigh initial discharge capacity of 3,535 mAh/g (20). However, there are still some problems to be solved for the porous carbon anodes: Firstly, owing to the disorder of pores and structure defects, the electronic conductivity of amorphous porous carbon usually is relatively low, resulting in an unfavorable rate capability (18). Secondly, a high fraction of exposed edge planes in porous carbon will cause extremely irreversible side reactions with electrolyte solution which give rise to a low Coulombic efficiency (17). For example, the Coulombic efficiencies of the porous graphene nanosheets, CNFs, and CNTs are all smaller than 50% (15, 20). Considering that a full Li-ion cell has a limited Li inventory, this is a serious disadvantage in terms of achievable capacity. A simple way to minimize the associated irreversible capacity would be to decrease the direct exchange surface area. Thirdly, the ordered and small pores are highly desirable to improve the rate performance and packing density. Recently, Sander et al. demonstrated that electrodes with aligned pore channels fabricated via magnetic template can deliver faster charge transport kinetics with threefold higher area capacity than that of conventional Li-ion electrodes (21). However, the distribution and size of the pores cannot be easily controlled in experiments by using the conventional porous carbon (17, 18, 22). Motivated by these dissuasions, we wonder if we can find a 3D carbon material with intrinsic ordered nanopores as well as high electronic conductivity to avoid the problems discussed above.
Here we show that the predicted 3D topological semimetal carbon structure bco-C16 can be such a system (23), in which all carbon atoms are sp2-bonded with ordered 1D channels, as seen from Fig. 1, providing good binding sites and efficient diffusion channels for Li ions. Moreover, electronic band structure calculations prove that bco-C16 is a topological node-line semimetal with a linear dispersion band structure near the Fermi level (23), indicating a high electronic conductivity. Then, a question arises naturally: Can the bco-C16 be a promising anode material for LIBs? To answer this question, we perform a detailed study on the Li intercalation and diffusion process in the bco-C16 based on the first-principles calculations. The results show that Li ions are able to intercalate into the bco-C16 with a binding energy of −0.63 eV at a dilute concentration, and it remains a negative value of −0.23 eV when the bco-C16 are fully intercalated with Li ions, indicating a stable Li adsorption instead of phase separation. The maximum Li concentration is Li-C4, showing an improved specific capacity compared with the graphite anode. Because of the significant structural anisotropy, Li diffusion in bco-C16 exhibits a strong directional anisotropy. At a dilute Li concentration, the migration barrier along the 1D channel (A path) is 0.53 eV, whereas for the diffusion perpendicular to the 1D channel (P path), it is a rather large value of 2.32 eV. At a high Li concentration, the migration barrier along 1D channel can decrease to a rather small value of 0.019 eV, while it remains a large value of 1.29 eV perpendicular to the 1D channel. Moreover, the 1D Li ion diffusion is robust against the compressive and tensile strains. The estimated average voltage is as low as 0.23 V, and the volume change during the Li charge/discharge is comparable to that of graphite. Based on these findings, bco-C16 is expected to be promising as an anode material with a high specific capacity, a high rate capability, as well as a low open-circuit voltage.
Fig. 1.
Structure of bco-C16 and the schematics of the possible Li-ion absorption sites in top and side views.
Results and Discussion
Single Li Atom Insertion and Diffusion in bco-C16.
As shown in Fig. 1, the crystal structure of bco-C16 can be regarded as 3D modification of graphite in AA stacking with benzene linear chains linked by ethene-type planar π-conjugation. Considering that the conventional exchange–correlation functionals of standard density functional theory (DFT) cannot give a reasonable interlayer distance of graphite (24) because of the poor description of the van der Waals (vdW) interactions, we first relaxed the crystal structure of bco-C16 with three different methods [Perdew–Burke–Ernzerhof (PBE) functional without vdW corrections; vdW-D2 with semiempirical corrections (25); and vdW-optPBE with vdW functional (26), respectively]. The results are shown in Table S1 and the graphite (27) is also included for comparison. We find that three different methods give almost the same lattice parameters of bco-C16, suggesting that vdW interactions in bco-C16 crystal are weak and negligible due to covalent bonding. Therefore, the subsequent computations of bco-C16 are based on the standard PBE exchange–correlation functional without vdW corrections.
View this table:
Table S1.
Lattice parameters a (Å), b (Å),and c (Å) of bco-C16 and graphite which are calculated with different methods
Then, we investigated the insertion of single Li atom into bco-C16. To avoid the interaction between two Li atoms, we adopted a 2 × 2 × 3 supercell of bco-C16. As seen from Fig. 1, three possible initial insertion sites are considered: the bridge site M (above the midpoint of the C–C bond in a benzene linear chain), the hollow site H (above the center of the C hexagon), and the interstitial site I (above the midpoint of the interstitial C–C bond between two adjacent benzene linear chains). We find that Li atoms on both M and I sites moved to the neighboring H sites after full relaxation, suggesting that H sites are the most stable adsorption sites for Li atoms. And, the adsorbed Li atoms on H sites tend to get closer to the up C hexagon hollows for the upward bending of linking C–C bonds; the calculated distance between the Li atom and the up (d0)/down (d1) C hexagon hollows is 1.60/1.87 Å. The Bader charge population analysis shows that there is about 0.73 |e| charge transfer from Li to bco-C16, namely, Li atoms donate almost all their s electrons and become Li ions, thus leading to a strong Coulomb repulsion interaction between the adsorbed Li ions that prevents them from clustering.
To further check the ionic binding with the substrate, we calculate the Li binding energy (Eb), which is defined as
The rate performance plays an important part in the electrode material which is mainly determined by the Li-ion mobility. It is desirable to estimate the diffusion of Li ion in the bco-C16. Different from the graphite where Li ion is located on the 2D isotropic graphene sheet, the bco-C16 shows obvious structural anisotropy along the x- and y directions. Therefore, we need to investigate the diffusion barriers for Li ions along two different possible migration paths: one is path H0–H1, which is along the benzene linear chains (A path); the other is the path H0−H2, which is perpendicular to the benzene linear chain (P path), as shown in Fig. 2 A and B.
Fig. 2.
Schematics of the Li diffusion pathways along the A path (H0–H1) and P path (H0–H2) in the top (A) and side (B) views, respectively, where H0, H1, and H2 denote the initial and end points. The corresponding energy profiles are presented in C and D.
Based on climbing-image nudge elastic band (CI-NEB) calculations, the energy profiles along the A path and P path are presented in Fig. 2 C and D. For the case of Li diffusion along the benzene linear chain (A path), there is only one energy peak of 0.53 eV. The calculated diffusion barrier is slightly larger than that of graphite (0.218–0.4 eV) (24, 28, 29) but comparable to that of commercially used anode materials based on TiO2 with a barrier of 0.35–0.65 eV (30⇓⇓–33) (Table 1), indicating that Li ions can diffuse easily along the A path. In contrast, for the diffusion perpendicular to the benzene linear chain (P path), a rather large barrier of 2.32 eV is found, which means an unfavorable Li diffusion along this path. To further compare the diffusion property between these two paths, the temperature-dependent diffusion constant (D) can be evaluated by the Arrhenius equation (29):
View this table:
Table 1.
Comparison of specific capacity, diffusion barrier and open-circuit voltage of candidate anode materials for LIB
Li Storage Capacity and Vacancy Diffusion.
Next, we explore the fully Li-intercalated bco-C16 which directly determines the maximum Li capacity. The binding energy Eb is calculated as −0.23 eV with all H sites occupied by the Li ions; the absolute value is larger than that of graphite (LiC6: −0.11 eV) and close to that of VS2 monolayer (Li2VS2: −0.26 eV) (37), suggesting that Li atom can be adsorbed stably in bco-C16 and the phase separation problem can be safely avoided at such a high Li concentration. The theoretical specific capacity of bco-C16 is 558 mAh/g, corresponding to the Li-C4, which is 1.5 times larger than that of graphite (Li-C6).
In the previous sections, we only considered the single Li-ion diffusion in bco-C16; to gain a more complete picture, it is necessary to estimate the diffusion in high Li concentration. We remove one Li ion from the fully Li-intercalated bco-C16 and relax the structure again. Accompanying the removal of the Li ion, its nearest-neighboring Li ion will move to the M site because of electrostatic repulsion, leading to a vacancy. Then we perform the calculations of migration energy barriers for an isolated vacancy in a 2 × 2 × 3 supercell along both the A path and the P path; the results are presented in Fig. 3. The calculated energy barriers for the A path and the P path are 0.019 and 1.29 eV, respectively. Compared with that of single Li ion, the energy barriers for the isolated vacancy are both reduced dramatically; the reason can be ascribed to the enlarged size along the z direction and strong Coulomb repulsions between Li ions. Especially for the A path, the value of the vacancy hopping energy barrier is about 15 times smaller than that of graphite (0.283 eV) (24), and close to the single Li-ion migration energy barrier of 2D Ti3C2 (0.068 eV), Mo2C (0.043 eV), and black phosphorus (0.08 eV) (34, 38, 39) (Table 1). Therefore, it is reasonable to expect that the mobility of Li ions becomes higher with the increasing Li concentration and achieves a high rate of performance at a high Li concentration. At the same time, we compare the vacancy diffusion property between the A path and P path by estimating the temperature-dependent diffusion constant according to Eq. 2. The mobility of Li along the A path is about 2.57 × 1021 times larger than that along the P path at room temperature, suggesting that the significantly 1D diffusion can still be observed with a high Li concentration at room temperature.
Fig. 3.
Schematics of the vacancy diffusion pathways along the A path (H0–H1) and P path (H0–H2) are presented in the top (A) and side (B) views, respectively, where H0, H1, and H2 denote the initial and end points of vacancies. The corresponding energy profiles are presented in C and D.
Effect of Li Concentration and Theoretical Voltage Profile.
Open-circuit voltage is another key factor which is widely used for characterizing the performance of the Li battery. In theory, we can obtain the open-circuit voltage curve by calculating the average voltage over parts of the Li composition domain. The charge/discharge processes of bco-C16 comply with the following half-cell reaction vs. Li/Li+:
Thus, neglecting the volume, pressure, and entropy effects, the average voltage of Lix-bco-C16 in the concentration range of x1 < x < x2 can be estimated as (40)
Before calculating V, we first search the most stable Li occupying configurations at different intermediate Li concentrations. The formation energy for a given Li-vacancy arrangement with composition x in Lix-bco-C16 is defined as
Fig. 4.
(A) Formation energies predicted by CE method for the 150 different Li configurations with 5 stable intermediate phases. (B) Corresponding voltage profile (marked in red) and binding energy profile (marked in blue) calculated along the minimum energy path.
Fig. S1.
Configurations of five stable intermediate phases.
Assessments of the Cycling Stability and Strain Effect on Li Ions Diffusion.
Cycling stability is another factor that needs to be considered, which is mainly determined by the volume changes during the Li charging /discharging. We compare the fully lithiated bco-C16 with the pristine one and find that no bond breaking occurs and the total volume expansion is 13.4%, which is comparable to that of graphite (10%). Moreover, being similar to that of graphite, the volume changes are mainly in the z direction (10.3%). This anisotropic volume expansion can be understood from the changes of chemical bonds. Along the x and y directions, the elastic deformation involves the stretch of in-plane C–C bond length, which needs a larger energy, whereas for the z axis it involves the rotation of an out-of-plane C–C bond, which corresponds to a smaller energy. Thus, when Li ions are inserted into bco-C16, it tends to expand first along the z axis; moreover, the rotation of the C–C bond can tolerate a large volume change without bond breaking. To further assess the cyclic stability, the stress−strain relations of bco-C16 are calculated within 15% uniaxial compressive strain and tensile strain. Three kinds of uniaxial load conditions along the x, y, and z axes are considered, respectively; the corresponding results are presented in Fig. 5 A–C. For all three directions, the stresses increase continuously with the growing strain and exhibit an approximate linear dependence within a large range of compressive and tensile strain; no abrupt decrease or nonlinear platform occurs, indicating that the bco-C16 is able to sustain a large strain. According to the continuum mechanics, the Young’s modulus E can be derived from the slope of stress−strain curves with strain up to 4%. The calculated Young’s moduli along the x and y directions are 795 and 824 GPa, respectively, close to that of graphene (1,000 GPa) (44), whereas they are much smaller in the z direction (only 150 GPa). These anisotropic Young’s moduli are consistent with the volume expansion. Considering the modest volume expansion of Li insertion and the large fracture strains, it can be concluded that the bco-C16 anode is able to accommodate the volume changes during lithiation/delithiation and shows a good cycling stability.
Fig. 5.
Compressive and tensile stress σ as a function of uniaxial strain ε along the (A) x, (B) y, and (C) z direction, respectively.
Next we investigate the strain effect on Li-ion diffusion for further understanding of the underlying mechanism and possible improvements. The diffusion barriers for Li along two different migration paths are calculated under the 5% uniaxial compressive and tensile strains, respectively. The corresponding results are summarized in Table 2, the detailed energy profiles are shown in Fig. S2 A–F. It can be found that uniaxial compressive strains along the x (z) axis and tensile strains along the z (x) axis are able to reduce (increase) the energy barrier of both A path and P path, respectively, whereas the strains along the y axis have little influence on energy barriers. By comparing the strained bco-C16 structures, we find that both uniaxial compressive strains along the x (z) axis and tensile strains along the z (x) axis can increase (reduce) the channel size along the z direction and reduce (increase) the interaction between Li ions and bco-C16 host. However, the strains along the y axis have little influence on the channel size along the z direction. Therefore, the channel size along the z direction plays a decisive role in the migration energy barrier, which is similar to that of graphite where interlayer distance has a significant effect on the in-plane Li diffusion (24). Meanwhile, the calculated ratio of diffusion constant along the A path (DA) and P path (DP) at 300 K according to Eq. 2 remains a large value under different strains, suggesting that the Li diffusion along the P path is prohibited and the 1D Li-ion diffusion is robust against the strains.
View this table:
Table 2.
Calculated diffusion barriers along A path and P path, and the corresponding ratio of diffusion constant at 300 K under different compressive and tensile strains, respectively
Fig. S2.
Migration energy profiles under 5% compressive strain along x (A), y (B), and z (C) directions, respectively. The corresponding migration energy profiles under 5% tensile strains are shown in D, E, and F, respectively.
Summary
In this study we have explored the possibility of using all-carbon-based topological semimetal for LIB anode material which has the merits of intrinsic high electronic conductivity and ordered porosity for Li-ion transport; moreover, carbon is abundant in resources, flexible in bonding, and ever-changing in morphology. Taking bco-C16 as an example, we systematically examined the energetics and kinetics of Li-ion insertion and diffusion, and can draw the following conclusions: (i) Li ions can be inserted into bco-C16 stably without clustering; (ii) The maximum capacity of bco-C16 is 558 mAh/g, corresponding to the Li-C4, which is much higher than that of graphite (Li-C6); (iii) The average voltage is 0.23 V, which is rather low as an anode and can supply larger operating voltage and capacity once connected with the cathode; (iv) The Li ions in bco-C16 exhibit a remarkable 1D Li-ion diffusion; moreover, the migration energy barrier can reach a quite low value at high Li-ion concentration due to the enlarged size of the channel, strong Coulomb repulsions from the neighboring Li ions; (v) The 1D Li-ion diffusion is robust against the compressive and tensile strains; and (vi) The volume changes during the Li insertion/de-insertion are comparable to that of graphite, suggesting a good reversibility. With all of these extraordinary characteristics, bco-C16 should have a great potential to be applied as anode material for LIBs. It is encouraging to note the possible presence of boc-C16 phase in detonation and chimney soot as suggested by an excellent match between the simulated and measured X-ray diffraction patterns (23). We hope that the present study can stimulate further experimental effort on this subject to develop all-carbon-based porous structures with conducting topological properties for novel LIB anode materials.
Methods
Our first-principles calculations are based on density-functional theory (DFT) implemented in Vienna Ab initio Simulation Package (VASP) (45) with the exchange–correlation functional in the PBE form (46). The projector-augmented wave (47) method is used to describe the electrons, and the cutoff energy of the plane-wave basis set is set to be 550 eV. Based on the convergence test, a (7 × 11 × 16)/(3 × 4 × 6) Monkhorst–Pack k-point mesh is adopted to represent the reciprocal space of the unit cell/(2 × 2 × 3 supercell), respectively, during the whole computational process. The conjugated gradient method is applied to optimize the structure, and convergence criteria of total energy and force components are set to be 1 × 10−4 eV and 0.01 eV/Å, respectively. The diffusion barriers for Li ions are calculated on the basis of the CI-NEB method as implemented in the VASP transition state tools (48, 49). The convergence criterion of force is also set to be 0.01 eV/Å.
As there are a large number of possible Li-vacancy configurations at an intermediate Li concentration, it is impossible to calculate all of their energies. Here, we use the CE method to describe the configurational energy and to search for the most energy-favorable Li configurations, which has been widely used in the previous studies of electrode materials such as Lix-graphite (24), LixCoO2 (50, 51), etc. Based on the CE method, the Lix-bco-C16 can be treated as alloy systems. For each possible Li site i, we can represent it with an occupation variable
where the indices i, j, and k range over all occupation sites, φα is the product of occupation variables σi, σj … σk that form a cluster configuration
Acknowledgments
This work is partially supported by the National Key Research and Development Program of China (Grant 2016YFB0100200), and the National Natural Science Foundation of China (Grants NSFC-11274023 and 21573008).
Footnotes
- ↵1To whom correspondence should be addressed. Email: sunqiang{at}pku.edu.cn.
Author contributions: Q.S. designed research; J.L. performed research; J.L., S.W., and Q.S. analyzed data; and J.L., S.W., and Q.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1618051114/-/DCSupplemental.
References
Topological semimetal carbon for battery anode
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