Structural stability and bonding nature of Li–Sn–carbon nanocomposites as Li-ion battery anodes: first principles approach

Abstract

The atomic structural stability and electronic properties of Li_nSn₄–carbon nanotube (CNT) and Li_nSn₄–graphene nanocomposites were studied by first principles calculations. Results on isolated Li_nSn₄ clusters, with n = 0–10, revealed that the tetrahedron shaped Li₄Sn₄ Zintl cluster is the most stable owing to it having high symmetry as well as a largest highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gap. This Li_nSn₄ cluster weakly interacted with CNT as well as graphene for n ≤ 4, whereas a strong cation–π interaction is observed between them for n > 4 which significantly reduces the Li clustering. The interaction between the Sn cluster and CNT or graphene is mediated only through Li ions whose absence destabilizes the Sn–C composite. These results were further confirmed by electronic density of states and band structure calculations. In addition, our calculations on hexagonal assembly of Li_nSn₄–CNT imply that the volume change is minimal during lithiation and the average intercalation potential is estimated to be a maximum of ≈0.5 V, which shows its good anodic character.

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1. Introduction

Usage of carbonaceous materials in energy storage applications has increased tremendously since the discovery of several carbon nanostructures, such as carbon nanotubes (CNT),¹ C₆₀ bucky ball,² graphene,³ and carbon nanofibers.⁴ Among various energy storage devices, lithium ion batteries (LIB) are widely used in many portable electronic devices⁵ due to their high energy density and light weight, which make them of interest to scientific as well as industrial researchers. Several attempts have been made to design good materials for the components of lithium ion batteries, which are essentially the electrodes, the electrolyte, and the separator. In particular, materials for anodes have been focused in recent years because the specific capacity could possibly be raised to 4200 mA h g⁻¹ (theoretical capacity of Si).^6,7 Although the theoretical capacity of silicon has been found to be high, it has a severe problem of poor inter particle conductivity due to fractures in the particle's structure, which can be minimized by controlling particle size.⁸ Graphite is a common material used for anodes due to its low cost and long battery life.⁹ However, six carbon atoms together can capture only one Li ion to form stable LiC₆ stoichiometry, which results in a low theoretical specific capacity of 372 mA h g⁻¹,¹⁰ while graphene with a few layers carries a higher capacity of 700 mA h g⁻¹.¹¹ Compared to this, defect-free single walled CNTs (SWCNTs) have a specific capacity of only 400–460 mA h g⁻¹, but this reaches 1000 mA h g⁻¹ for side-wall defective CNTs¹² and this enhancement was reported to be due to the presence of high porosity and one-dimensionality. However, all these carbon nanostructures have several problems, such as the capacity fading during battery cycling and limitations in the capacity value. Hence, there are many attempts to replace the carbon with some other group IV elements such as Si, Sn, and Pb.^13–16 It is worth noting that these elements are capable of forming a Zintl phase compound with alkali metal atoms which act as the cation and Si_n, Sn_n or Pb_n clusters as the anion.^17,18 Compared to carbon, the Sn atom has the ability to bind with more Li ions, which results in the formation of a Li_4.4Sn compound with a high theoretical capacity of 994 mA h g⁻¹. However, the drawback in Sn compounds is the problem of a colossal volume change during the intercalation process, which leads to poor battery life.¹⁹

Concerning the battery life, it is important to find a material that exhibits good capacity with minimal volume change during cycling. Composites of nanostructured Sn with multiwalled CNT²⁰ and carbon nanofibres²¹ have been synthesized with a greater specific capacity of 889 mA h g⁻¹ with minimal volume change. Following these works, several reports^22–32 were published in which the Sn–C based composites were shown to be potential candidates for LIB anodes. Although theoretical understanding of mono-atomic thinned Sn nanowire with SWCNT has been reported,³¹ the structural stability of the Li–Sn alloy and its interactions with CNT have not been studied well. Our calculations shed light on the atomic structural stability and electronic properties of the Li–Sn–CNT composite within density functional theory formalism. We initially studied the growth of Li–Sn alloyed clusters and then stable clusters were identified and inserted into various sized CNTs in order to understand the interaction between them. We also carried out the deposition of those clusters onto graphene. Our results on Li_nSn₄ clusters with n = 0–10 reveal that the Li₄Sn₄ cluster has ultra-high stability with the largest highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gap as it reaches the Zintl's composition and hence, it interacts weakly with CNT as well as graphene, whereas the clusters with more Li ions (n > 4) bind strongly as a result of significant charge transfer from cluster to CNT, through cation–π interactions. These results were further confirmed by electronic density of states and band structure calculations. In addition, we performed the calculations on the assembly of Sn–Li cluster inserted CNTs revealing that the volume change is minimal during lithiation and the average intercalation voltage (AIV) was found to be a maximum of ≈0.5 V which shows its good anodic character.

2. Computational methods

First principles density functional calculations were performed to understand the structural and electronic properties of Li–Sn cluster inserted SWCNT as implemented in the Vienna Ab initio Simulation Package (VASP).³³ In our calculations, all the atoms were described by projector augmented wave pseudopotential method³⁴ and electron–electron interaction was correlated by generalized gradient approximations.³⁵ For Li_nSn₄ clusters, a cubic box with a = 15 Å is used to give enough vacuum space between the cluster and its periodic images, to avoid the interaction between them. In the case of isolated CNTs, sufficiently large a and b lattice constants were chosen so that CNT and its periodic images are at least 9 Å apart. Along the z-direction, four super cells were constructed with periodicity maintained. For sampling the Brillouin zone, Monkhorst–Pack 1 × 1 × 1, 1 × 1 × 4, and 2 × 2 × 4 k-meshes were used for optimizing the Li–Sn clusters, cluster inserted CNT, and its assembly, respectively. We also repeated the calculations for clusters with a denser k-mesh (3 × 3 × 3) to ensure its accuracy and negligible energy difference, with a maximum of 0.025 eV per atom observed when compared to Γ-point calculations. Further, a 1 × 1 × 50 k-mesh was employed to obtain the density of states (DOS) and band structure of all the systems. All the ions were relaxed self-consistently without considering any symmetry and the iterative relaxation process was repeated until the absolute force on each ion converged to the order of 0.01 eV Å⁻¹. The convergence for energy was also set to be 10⁻⁵ eV throughout our calculations. We repeated all calculations with the above-mentioned criteria to find the magnetic solution of the system, which is favoured for clusters with odd number of electrons. Note that the magnetism in this cluster is completely quenched when it is inserted into SWCNT as significant charge transfer between these two systems is observed from our calculations.

3. Results and discussion

We initially considered the Sn₄ cluster to understand the lithiation process on it by first principles calculations. Among various isomers, the Sn₄ rhombus is found to be more stable by 5 meV per atom than the next most stable tetrahedron isomer, which is in accordance with earlier work.³⁶ Further, for addition of Li ions on the Sn₄ cluster, both rhombus and tetrahedron isomers (shown in Fig. 1) are considered as this small energy difference between these isomers will be compensated by the Sn–Li alloying energy. First, a single Li ion is introduced into various possible sites such as the terminal, edge, and face. Our calculations show that Li ion prefers to occupy the facial site (shown in Fig. 1) rather than the edge and terminal sites. The terminal addition is energetically least feasible by 0.22 eV as compared to facial addition; however, the energy of facial and edge Li ion added isomers differ by only 0.01 eV. Hence, a further three more Li ions are independently introduced one by one, on the faces and edges of the isomers. Interestingly, it is observed that the optimized geometry of both Li₄Sn₄ isomers converges into a tetrahedron structure. This cluster is commonly known as a Zintl cluster and it has an Sn₄⁴⁻ anion³⁷ which is surrounded by four Li ions acting as cations. By addition of further Li ions on the edge (the next feasible site) of this cluster, the geometry is transformed to a butterfly like structure^38,39 for Li₆Sn₄ and becomes planar for Li₈Sn₄ (Fig. 1). The above discussions indicate that the addition of Li ions strengthens the Sn–Sn bonds by donating electrons to the Sn–Sn bonding orbitals until n = 4; beyond this, the geometry of the cluster is finally converted to a planar structure with larger Sn–Sn bonds, which is attributed by the filling of Sn–Sn anti-bonding orbitals (Fig. S1, ESI†). In addition, clustering of Li ions is also observed for the n > 4 case (Table 1). The calculated Sn–Sn, Sn–Li, and Li–Li bond distances are reported in Table 1 and these values are quite consistent with the earlier work.^38,39 Thus, our study reveals that the structural change in the pure Sn cluster is unavoidable during the Sn–Li alloying process. Such structural changes affect the battery cycle life.

Fig. 1 The ball and stick models of optimized geometries of stable Li_nSn₄ clusters are shown along with the Sn₄ tetrahedron and rhombus isomers. The n value of each cluster is given in parentheses. Yellow and green balls represent Sn and Li atoms, respectively.

Table 1 The average Sn–Sn, Sn–Li, Li–Li, and C–Li bond distances are given for Li–Sn clusters inserted into CNT or deposited on graphene along with E_ad and the Bader charge per Sn atom (Q_B). Values for isolated clusters are provided in parentheses

System cluster/CNT	Sn–Sn Å	Sn–Li Å	Li–Li Å	C–Li Å	Ead eV	QB e^−
Sn4/(8,8)	3.04(2.90)	—	—	—	−2.37	4.00(4.00)
Li1Sn4/(8,8)	2.87(2.93)	3.08(2.95)	—	2.44	0.43	4.08(4.22)
Li2Sn4/(8,8)	2.87(2.89)	2.93(2.92)	—	2.42	0.41	4.40(4.50)
Li3Sn4/(8,8)	2.87(2.95)	3.00(2.86)	—	2.45	0.80	4.44(4.75)
Li4Sn4/(8,8)	3.04(3.06)	2.96(2.81)	—	2.58	0.50	4.75(5.00)
Li6Sn4/(8,8)	3.02(3.09)	2.95(2.78)	3.25(3.08)	2.5	3.02	4.92(5.50)
Li8Sn4/(9,9)	3.05(3.02)	2.90(2.79)	3.12(3.08)	2.50	2.44	5.41(6.00)
Sn4/Gr	3.05(2.90)	—	—	—	−1.21	4.00(4.00)
Li2Sn4/Gr	2.85(2.89)	3.03(2.92)	—	2.53	0.91	4.44(4.50)
Li4Sn4/Gr	3.01(3.06)	2.91(2.81)	—	2.65	0.11	4.73(5.00)
Li6Sn4/Gr	3.04(3.09)	2.87(2.78)	3.23(3.08)	2.39	1.55	4.98(5.50)
Li8Sn4/Gr	3.05(3.02)	2.89(2.79)	2.96(3.08)	2.45	1.02	5.46(6.00)

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The binding energies per atom (BE) of the Li_nSn₄ clusters were calculated to understand their structural stability from:

where E(Li_nSn₄) is the total energy of the Li_nSn₄ cluster and E(Sn) and E(Li) are atomic energies of Sn and Li atoms, respectively. The calculated BE values are reported in Fig. 2. The results imply that the BE of Li_nSn₄ clusters decreases with n. Note that all clusters with even n values were found to be more stable than the clusters with odd n due to the presence of unpaired electron in the HOMO of the latter clusters. Among all the clusters, the Li₄Sn₄ cluster shows the highest stability and largest HOMO–LUMO energy gap, which is consistent with earlier work.³⁸ Such high stability in this cluster is due to the presence of T_d symmetry and the completely filled bonding orbitals (see Fig. S1, ESI†).

Fig. 2 BE and HOMO–LUMO gap of Li_nSn₄ clusters with n = 0–10.

To understand the interaction between the clusters and CNT, pristine Sn₄, and Li_nSn₄ (n = 0–8) clusters were chosen to insert into various sized (m,m) armchair CNTs, where m is the chiral index varying from 7 to 10. The adsorption energy (E_ad) is calculated from:

E_ad = E(Li_nSn₄) + E(CNT) − E(Li_nSn₄ + CNT) (2)

where, E(Li_nSn₄), E(CNT), and E(Li_nSn₄ + CNT) are total energies of the Li_nSn₄ cluster, pristine (m,m) armchair CNT, and Li_nSn₄ inserted CNT, respectively. The E_ad values are reported in Table 1 and for pristine Sn₄ cluster loaded CNTs are observed to be negative for all the CNTs (e.g. −2.37 eV for (8,8) CNT), whereas this value is positive for all lithiated clusters (see Fig. S2, ESI†). This result clearly indicates that in the absence of Li ions, the Sn cluster will not bind strongly with CNT. Our calculations on the preferential radius for inserting clusters into CNT show that (8,8) CNT is apt for clusters with n = 0, 2, 4, and 6, while (9,9) CNT is apt for the Li₈Sn₄ cluster. Then, the calculated E_ad values for Sn₄, Li₂Sn₄, Li₄Sn₄, Li₆Sn₄, and Li₈Sn₄ clusters are −2.37, 0.41, 0.52, 3.02, and 2.44 eV, respectively. Thus, our results revealed that the E_ad value is drastically increased for n > 4 (after the formation of the Zintl cluster). In addition, we have also studied the insertion of clusters into larger sized CNT, in which the Li_nSn₄ cluster prefers to interact with one side of the CNT's wall. (see Fig. S3, ESI†). As the result of lesser interactions, the E_ad values are lowered to 0.32 and 2.19 eV for n = 4 and 6, respectively. Thus, we concluded that the interactions between Sn clusters and carbon nanostructures are mediated only through Li ions, whose absence destabilizes the Sn–C composite. Of (10,10) CNT's wall (see Fig. S3, ESI†). As the result of lesser interactions, the E_ad values are lowered to 0.32.

To demonstrate the interaction of these clusters with other types of CNTs, we also inserted the Li₈Sn₄ cluster into (12,6) chiral and (15,0) zigzag CNTs which have a similar radius to the (9,9) armchair CNT (see Fig. S4, ESI†). The calculated E_ad values are 2.02 and 2.56 eV, respectively, which are less than that of the armchair CNT. The lowering in interaction is due to the semiconducting nature of the chiral and zigzag CNTs (see Fig. S5, ESI†). Hence, it is concluded that the size and electronic properties of the cluster and CNTs play vital roles in the stability of Sn–Li–CNT composites. These results induced us to study the interaction between a planar honeycomb network (graphene) and the lithiated Sn₄ clusters. The calculated E_ad of Li_nSn₄/Gr (n = 0, 2, 4, 6 and 8) systems (optimized structures are shown in Fig. S6† in the ESI) follow the same trend with smaller values (see Table 1), owing to the planar geometry of the graphene sheet. As stronger interactions are observed between the CNTs and clusters with n > 4, it is also expected that structural changes in clusters and/or CNTs will be observed. For instance, in the Li₆Sn₄/(8,8) CNT system, the butterfly like structure of cluster reverts back to tetrahedral as it transfers two excess electrons to the CNT. Note that among the Li–Sn clusters, the Li₄Sn₄ tetrahedron cluster is highly stable. On the other hand, for the Li₈Sn₄/(9,9) CNT case, the geometry of the cluster is not affected much as all four electrons (compared to the Li₄Sn₄ cluster) could not be accepted by the CNT. In addition, it was also observed that the Li clusterization decreased when Li_nSn₄ with n > 4 clusters were inserted inside the CNT. Such a reduction in Li dimers/clusters will be beneficial for the electrode system.⁴⁰

For example, the Li–Li bond distances in Li₆Sn₄ and Li₈Sn₄ clusters were observed to change from 3.08 Å to 3.25 Å and 3.08 Å to 3.12 Å, respectively, when these clusters were inserted into CNT (Table 1). Thus, our study shows that if the cluster has more Li ions, the shape of the cluster does not change much when it is inserted inside the CNT. As expected, the shape of the CNT also changes when the Li₈Sn₄ cluster is inserted into the (9,9) CNT which is transformed from a regular to an elliptic cylinder shape, with a major to minor axis ratio (a/b) of 1.07 and deformation (|a − b|) of 0.82 Å. However, to understand the structural changes in the cluster loaded multiwalled CNTs, we also studied double walled CNT (DWCNT) with inter wall distance of ≈3.47 Å, loaded with a Li₈Sn₄ cluster (the details are given in Fig. S7, ESI†). Our results show that the a/b ratio and |a − b| of the inner wall are only 1.02 and 0.26 Å, respectively. Hence, we conclude that the outer walls resist the deformation of the inner wall during the cluster loading in the case of multiwalled CNT.

To understand the nature of the interaction qualitatively, the charge transfer between the cluster and the CNT was plotted for all cases and is shown in Fig. 3. For the lithiated clusters, a disc like isosurface was observed between the CNT and the Li_nSn₄ cluster, which explains the charge transfer from the Sn-5p orbitals to the π orbitals of the sp² hybridized carbon atoms of CNT via Li ions. A similar charge transfer diagram was observed in Fig. S5 (ESI†) for Li ions deposited on the surface of graphene⁴¹ and it closely resembles the cation–π interaction which was elaborately discussed.⁴² Although no charge transfer between the bare Sn₄ cluster and the CNT was noticed, the charge re-population in CNT as well as the cluster was observed (see Fig. 3†). Note that though the adsorption energy was found to be small for the semiconducting CNT and graphene surface, an almost similar charge transfer mechanism was obtained. Overall, this significant charge transfer from Sn–Li clusters to CNT, through cation–π interaction, is attributed to the good structural stability of the Sn–Li–CNT composites.

Fig. 3 Red and blue isosurfaces indicate excess and depletion of charge in (a) Sn₄/(8,8) CNT, (b) Li₂Sn₄/(8,8) CNT, (c) Li₄Sn₄/(8,8) CNT, (d) Li₆Sn₄/(8,8) CNT, (e) Li₈Sn₄/(9,9) CNT, and (f) Li₆Sn₄/Gr systems. Charge transfer (δρ) is calculated from: δρ = ρ_cluster + ρ_CNT − ρ_cluster+CNT where ρ_cluster,ρ_CNT and ρ_cluster+CNT are charge densities of cluster, CNT, and cluster loaded CNT, respectively.

Further, to quantify this charge transfer between the Li_nSn₄ cluster and the CNT, Bader analysis⁴³ was performed to estimate the valence charge on each atom and is reported in Table 1. It shows that there is no charge transfer between the bare Sn₄ cluster and the CNT as the valence charge on the Sn atoms remains the same before and after insertion into the CNT which is consistent with the charge transfer plotted in Fig. 3. In the case of Li₄Sn₄/(8,8) CNT, 1.0 e⁻ was transferred from Sn-5p orbitals to C-2p orbitals through Li ions, whereas for Li₆Sn₄ and Li₈Sn₄ clusters, 2.32 and 2.36 e⁻ were transferred, respectively (Table 1). Hence, the CNT is able to draw the charge from the Li_nSn₄ cluster with a maximum limit of ≈2.3 e⁻. Even though there is nearly equal charge transfer for the n = 6 and 8 clusters to CNT, we could observe more Li dimers for the latter case which reduces the E_ad values. The calculated Bader charges for the Li_nSn₄/Gr systems show that there is no charge transfer from the bare Sn₄ cluster to the graphene substrate, whereas comparatively fewer electrons are drawn from other clusters due to fewer C–Li bonds resulting from the planar geometry of the substrate.

To explore the electronic properties of Li_nSn₄/CNT systems, the density of states (DOS) for all systems are deduced and reported in Fig. 4. It is observed in all cases that the sp² hybridized states of carbon atoms are distributed in the energy range from −12 eV to −9 eV, whereas the C-2p bands are spread over the entire range (−12 eV to −1 eV). It is also noticed that the states of Sn-5s (not shown in Fig. 4) and 5p states are pronounced as narrow peaks because the electrons in these states are well localized due to the ionic character of the Sn–Li bond. The DOS of bare Sn₄/(8,8) CNT shows that the occupied states are shifted (as indicated by arrows) slightly towards Fermi energy (E_f) when compared to pristine CNT which again manifests the poor stability of the Sn–CNT composite in the absence of lithium. Conversely, the total occupied DOS of Li_nSn₄–CNT systems with n = 2, 4, 6, and 8 are shifted away from E_f by 0.07, 0.20, 0.78 and 0.73 eV, respectively, which give an obvious reason for the good stability of the Sn–Li–CNT composites (Fig. 4).

Fig. 4 Total DOS (black solid line) of (a) Sn₄/(8,8) CNT, (b) Li₂Sn₄/(8,8) CNT, (c) Li₄Sn₄/(8,8) CNT, (d) Li₆Sn₄/(8,8) CNT, and (e) Li₈Sn₄/(9,9) CNT systems. C-2s, C-2p, and Sn-5p states are represented by red, blue, and green solid lines, respectively. The total DOS of bare CNT is given in the background and the direction of arrows depicts the shifting of energy levels, referenced to bare CNT.

Fig. 5 Electronic band structure of (a) Sn₄/(8,8) CNT, (b) Li₂Sn₄/(8,8) CNT, (c) Li₄Sn₄/(8,8) CNT, (d) Li₆Sn₄/(8,8) CNT, and (e) Li₈Sn₄/(9,9) CNT systems. Solid dots represent electron occupancies in the Sn-5p levels.

The band structure calculations were performed for cluster inserted CNT systems to understand the electron occupancy in the Sn-5p levels and the filling of the C-2p bands (Fig. 5). In the Sn₄/(8,8) CNT system, two bands originated from C-2p_z orbitals cross the E_f and form a Dirac cone like feature at E_f + 0.5 eV. The singly and triply degenerated localized Sn-5p states are completely occupied and observed at E_f −0.5 eV and E_f, respectively, whereas two unoccupied bonding Sn-5p states lie closer to E_f +0.5 eV. These empty states get filled when the bare Sn₄ cluster is lithiated. For instance, five Sn-5p states are occupied for the Li₂Sn₄/(8,8) CNT system and the C-2p bands are further filled, but not completely, due to the limited charge transfer from the Li ions. Conversely, the Li₄Sn₄/(8,8) CNT and Li₆Sn₄/(8,8) CNT systems have the same number of occupied Sn-5p states, because two electrons in the antibonding states of the latter system are transferred to fill the C-2p bands completely which were partially filled in the former case. Because of this charge transfer, the Li₆Sn₄ cluster changes both the geometry and the electronic structure to similar to that of the Li₄Sn₄ Zintl cluster owing to having a large HOMO–LUMO gap. Note that the C-2p bands are completely filled in this case. Hence, the Li₈Sn₄ cluster is not able to transfer all four excess electrons (compared to Li₄Sn₄ cluster) to CNT's C-2p bands; instead only two electrons are transferred, similar to the Li₆Sn₄ case. As the result of this lower charge transfer, the cluster is not able to attain a stable state. Moreover, in this case, the Sn-5p level of the cluster is well separated which indicates that the cluster reduces its symmetry due to having a planar structure. Hence, we conclude that the CNT is not able to draw all the electrons from the Li_nSn₄ with (n > 6) cluster that is electronically limited by the completely filled C-2p bands of CNT.

The results of the cluster filled CNTs motivated us to form a hexagonal assembly to study the Li-ion intercalation properties (see Fig. S7, ESI†). Generally, Li ions prefer to occupy the voids of the assembly. Here, Li ions are added one by one in well separated sites to reduce the columbic repulsion between them. The average intercalation voltage (AIV)⁴⁴ is calculated using the Nernst equation:

where E(Li_x1@Li_nSn₄) and E(Li_x2@Li_nSn₄) are the total energies of x1 and x2 Li ions intercalated in the Li_nSn₄ cluster inserted into (m,m) CNT, respectively. E(Li) and F are the total energy per atom of the Li-metal and the Faraday constant (= 1), respectively. The calculated AIV for Sn₄/(8,8) CNT, Li₂Sn₄/(8,8) CNT, Li₄Sn₄/(8,8) CNT, Li₆Sn₄/(8,8) CNT, and Li₈Sn₄/(9,9) CNT systems are ≈0.49, 0.22, 0.19, 0.07, and −0.11 V, respectively. Thus, our results show that the Li–Sn–CNT composite can potentially be used as the anode of Li-ion batteries. Moreover, the volume change during lithiation is observed to be minimal (only 0.33%).

Based on the energetics obtained from the first principles calculations, it was found that the lithiation of the anode during the first cycle of charging happens in three stages. First, the Li ion prefers to alloy with Sn to form the Zintl cluster; second, it forms a composite via cation–π interaction; and third, it intercalates in the pores of the CNT assembly. Now, the composite formation energy of Li–Sn–CNT system is defined as E_c = E_al + E_ad. The first term, E_al is estimated from:

E_al = E(Sn₄) + nμ(Li) − E(Li_nSn₄) (4)

where μ(Li) is the chemical potential of the Li metal, and E(Sn₄) and E(Li_nSn₄) are the total energies of the Sn₄ and Li_nSn₄ clusters, respectively. Here, we used the chemical potential of Li to calculate E_al as alloying occurs between the Sn₄ cluster and the Li metal. The calculated E_c values are shown in Fig. 6 and it can be inferred that up to n = 4, the alloying process dominates, whereas for n > 4, E_ad is found to be larger than E_al. Hence, the Sn–Li–carbon composite is formed in this region. To determine the feasibility of the intercalation process, we also plotted the intercalation energy (shown as dotted lines in Fig. 6) of Li_nSn₄ (n = 0, 2, 4, 6) clusters by considering the respective E_c as the origin. From this, it is clearly observed that the value of E_c is always higher than that of the intercalation energy until n = 6; so, the intercalation in the pores of the CNTs assembly dominates only after this limit. Since the E_al and E_ad values are comparatively larger than the energetics of the intercalation process, it is very difficult to gain back all the Li ions from the composites for n ≤ 6. Thus, the capacity of the material is expected to fade as observed experimentally.²⁰ However, a constant capacity will be retained afterwards as E_c is saturated beyond n = 6.

Fig. 6 The composition energy of Li–Sn–CNT (total) versus number of Li ions (n) is shown along with the Sn–Li alloying energy (E_al), adsorption energy (E_ad) and intercalation energy (dotted line).

4. Conclusions

By employing the first principles density functional calculations, the structural stability and electronic properties of Li_nSn₄ (n = 0–10) clusters and cluster loaded CNTs were studied. Among the clusters, the Li₄Sn₄ Zintl cluster was found to be the most stable as it has tetrahedral symmetry and largest HOMO–LUMO gap. Our calculations revealed that the insertion of the non-lithiated Sn₄ cluster into CNT was shown to be unstable due to the negative adsorption energy which is reflected as charge polarization on the CNT as well as the cluster. On the other hand, the lithiated Sn cluster is preferred for insertion into CNT as significant charge transfer occurs from Sn-5p states to C-2p states through Li ions by cation–π interaction, which was confirmed by electronic density of states and band structure calculations. A similar study was repeated for the deposition of clusters onto graphene and the results were almost reproduced with a smaller effect owing to its planar nature. As a result of the strong interaction between the CNT and the lithiated cluster, the number of Li dimers is reduced, as well as, in certain cases, the geometry of SWCNT being deformed from regular circular to elliptic cylinder shape. We also demonstrated that this deformation is controlled by introducing MWCNT. In addition, we also showed that this composite could be used as the anode of Li-ion batteries as the maximum intercalation potential was observed to be ≈0.5 V.

Acknowledgements

We acknowledge T. Prem Kumar for initiating this work. This work is supported by CSIR, India through TAPSUN (NWP-56) project. We also extend it for CSIR – CECRI, CSIR – NCL and CSIR – CMMACS for sharing their HPC facilities.

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Footnote

† Electronic supplementary information (ESI) available: [1] Kohn–Sham energy levels of various clusters, [2] adsorption energies (E_ad) of Li_nSn₄ clusters with various sized armchair CNT, [3] optimized structure of Li₆Sn₄/(10,10) CNT system, [4] charge transfer diagram of Li₈Sn₄/(12,6) and Li₈Sn₄/(15,0) systems, [5] electronic density of states of Li₈Sn₄/(12,6) and Li₈Sn₄/(15,0) systems, [6] charge transfer diagram of Li₄Sn₄/Gr, Li₆Sn₄/Gr and Li₈Sn₄/Gr systems, [7] optimized structures of Li₈Sn₄/(9,9) CNT and Li₈Sn₄/double walled CNTs (DWCNT) systems and [8] Li ion intercalation in hexagonal assembly of Li₆Sn₄/(8,8) CNT and Li₈Sn₄/(9,9) CNT systems. See DOI: 10.1039/c4ra11187g

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