First-principles investigations of vanadium disulfide for lithium and sodium ion battery applications

Abstract

Recently, two-dimensional (2D) layered transition metal dichalcogenides (LTMDs) have attracted great scientific interest for ion battery applications. Because of its remarkable metallic property, vanadium disulfide (VS₂) as a typical family member of LTMDs, can be an alternative anode material for ion battery applications. In this paper, we systematically investigate the adsorption energy and diffusion coefficient of the lithium and sodium ions in monolayer and bulk VS₂ for lithium and sodium ion batteries by a density functional theory method. Our calculations show that the VS₂ capacity can reach up to 466 mA h g⁻¹. It exhibits a low output voltage of 0.72 and 0.48 V for lithium and sodium ion batteries in the monolayer VS₂ as well as an output voltage of 0.88 and 0.6 V in the bulk VS₂, respectively. The calculated lithium and sodium ion diffusion coefficients in the bulk VS₂ are enhanced by five and seven orders of magnitude compared to the reported bulk MoS₂, respectively. Our investigations also reveal that VS₂ exhibits better electrochemical performance as an anode in the sodium ion battery than in the lithium ion battery.

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Introduction

Ion batteries (IBs) are one of the most important rechargeable energy storage devices. Motivated by the requirements for economical and sustainable electrochemical storage devices, IBs with better specific capacity, cyclic stability, high-rate capability, and safety are strongly desired, stimulating electrode material research.^1–3 Recently, a wide range of layered transition-metal dichalcogenides (LTMDs) have been considered as new functional materials and promising potential candidates for battery applications.⁴ MoS₂, a typical transition-metal sulfide, is a very promising electrode material for ion batteries.^5–7 Theoretical studies have revealed that lithium ions can easily diffuse between the adjacent layers of the MoS₂.^8,9 It has also been experimentally demonstrated that MoS₂ exhibits good electrochemical performance in the ion batteries.^5,10,11 However, the semiconducting behavior of MoS₂ would limit its electrochemical performance due to its poor electron transport efficiency. Finding LTMDs with metallic properties might be a solution to improve the performance. Semi-metallic vanadium disulfide (VS₂), a typical family member of LTMDs, is expected to enhance the electron transport during the cycling processes as anode in the ion batteries.^12–14 The bulk VS₂ are formed by numbers of monolayer VS₂ stacked with each other. Monolayer vanadium disulfide (VS₂) consists of a layer of vanadium atoms sandwiched by two layers of sulfur atoms. The neighboring monolayer VS₂ is bonded to each other with a distance of 0.64 nm by a van der Waals force. Because of the large interlayer distance, it facilitates the ion diffusions during the insertion and de-insertion processes.

In this paper, we systematically investigate the electrochemical performance of the VS₂ in both monolayer and bulk forms as anode for the applications of lithium and sodium ion batteries. By utilizing the first-principle calculations, we have probed the activation energy barriers encountered as well as the diffusion coefficient in the VS₂ as anode material. The output voltage and the theoretical capacity of VS₂ are also evaluated.

Computational details

All the first-principle calculations were carried out by the density functional theory (DFT) code Vienna ab initio Simulation Package (VASP).^15,16 The exchange and correlation terms were treated with Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA).¹⁷ The ion–electron interactions were described using projector-augmented waves (PAW).¹⁸ The plane wave cutoff energy of 500 eV was employed; a conjugate gradient scheme was used to relax the atomic positions until all the forces on every atom is less than 1 meV Å⁻¹.

For monolayer VS₂, more than 20 Å of vacuum spaces in the lateral directions are used to avoid interactions between neighboring ions. To provide adequate accuracy for geometry optimizations, atomic positions, unit cell shape, and volume were relaxed by a Monkhorst–Pack mesh with 6 × 6 × 1 k-point sampling mesh. The bulk VS₂ structures were sampled with 6 × 6 × 3 k-points.

The diffusion barriers for Li⁺ and Na⁺ ions from one low-energy adsorption site to another on the monolayer or bulk VS₂ were calculated using the Climbing Image-Nudged Elastic Band (CI-NEB) method.^19,20 The linear interpolation was applied between the initial and final states of the ion diffusion path with nine and eight intermediate images for hexagonal (H) monolayer and trigonal (T) bulk VS₂, respectively. Regarding the optimization, each image searches its lowest potential along the diffusion pathway. The image with the highest energy is driven up to the saddle point. The energy difference between this image (saddle point) and the initial image was defined as the diffusion barrier. The force convergence criterion for the optimization was set as 0.01 eV Å⁻¹.

Results and discussion

VS₂ has a layered structure with the vanadium atom layer sandwiched by two layers of sulfur atoms. Generally, there are two phases of crystal structures observed in VS₂ as T and H phases, respectively. Both of T and H are sensitive to the variation of temperature and layer numbers in the VS₂.¹⁴ At room temperature, monolayer VS₂ prefers to crystallize in H phase, while in the bulk form, the structure of T phase becomes more stable than H phase at room temperature.¹⁴ Therefore, we chose the T phase monolayer and H phase bulk VS₂ in our calculations for the electrochemical performance studies as anode material in the Li and Na ion batteries.

With a 20 Å vacuum layer, monolayer VS₂ has a hexagonal structure with vanadium and sulfur atoms alternatively aligned as shown in Fig. 1a. After optimizing the monolayer structure, the lattice parameter is calculated to be a = b = 3.17 Å and the V–S bond lengths are calculated to be 2.36 Å with an S–V–S bond angle of 84.43°. The bulk VS₂ structure by full geometry optimization was shown in Fig. 1b. The lattice parameter for bulk VS₂ was calculated to be a = b = 3.18 Å, c = 6.47 Å and the V–S bond lengths are calculated to be 2.35 Å with V–S–V bond angle of 85.06°, consistent with previous reports.¹⁴

Fig. 1 Electronic structure of VS₂: (a) top and side view of monolayer H-VS₂ structure. (b) Top and side view of bulk T-VS₂. The yellow and gray spheres represent S and V atoms, respectively. (c) Density of states in the monolayer H-VS₂. (d) Density of states in the bulk T-VS₂. Band structure along the high-symmetry direction in Brillouin zone of (e) monolayer H-VS₂ and (f) bulk T-VS₂, respectively.

Electrical conductivity in the battery electrodes is one of the important issues to determine the electrochemical performance. Generally material conductivity is determined by the density of states (DOS) at the Fermi level.¹² We have calculated the DOS of the VS₂ in the form of monolayer and bulk (Fig. 1c and d), respectively. At its Fermi level, the emergence of the DOS contributed by both V-3d and S-3p states reveals the metallic property in the monolayer and bulk forms of VS₂. A band crossing the Fermi level observed in the band structures of monolayer and bulk VS₂ (Fig. 1e and f) indicates a zero band gap.

To probe the stability of the Na⁺ and Li⁺ ions adsorbed on the surface of VS₂, we calculated the adsorption energy by the followed equation:¹²

E_ads = (E[VS₂ + M] − E[VS₂] − E(M))

where E[VS₂ + M] is the total energy of the geometry optimized structure with the adsorbed M⁺ (M = Na, Li) ions, E[VS₂] is the total energy of the pure monolayer or bulk. E(M) is the energy of single M atom in bulk form. According to our definition, the more negative adsorption energy indicates a more favorable reaction occurring between VS₂ and M. There are two stable sites for Li⁺ adsorbed on the surface of VS₂ monolayer: the hollow site (HS) above the center of the hexagon and the top site (TS) right above the V atom (Fig. 2a). Our calculations indicate that the adsorption energy for Li at the TS is the lowest potential energy compared to other sites, being consistent with the reported results.¹² It demonstrates that the adsorbed ions are more favorably stable on the TS of VS₂ monolayer surface. For T-bulk VS₂ structure, we calculated the lowest adsorption energy site is located at the T′ site (T′S) as shown in Fig. 2b.

Fig. 2 Schematic illustrations of (a) the top and side view of two possible Li/Na adsorption sites in the monolayer H-VS₂ and (b) top and side view of insertion sites in the bulk T-VS₂. The green sphere represents the adsorbed ion.

To evaluate the energy storage capacity of VS₂ as anode material, we calculated the amount of ions that can stably adsorbed on the surface of VS₂. In the monolayer VS₂, there are x ions which can be stably adsorbed at each TS with the x value of 2, 1, 0.667, 0.5, 0.22, 0.125 (Fig. 3a). The negative energy value observed in the adsorption energy profile as a function of the adsorbed ion concentration indicates that two ions can be stably adsorbed at each TS in the monolayer VS₂. The adsorption energy becomes positive as long as the amount of the adsorbed ions at TS is larger than two ions. It reveals that the maximum ions adsorbed at each TS are no more than two ions. Regarding the T-bulk VS₂, we achieved the stably adsorbed ions on the surface at each T′S with x value of 2, 1, 0.75, 0.5, 0.25, 0.11 (Fig. 3b). It can be seen that two ions can be stably adsorbed at each T′S in the bulk VS₂. As each T′S adsorbs more than two ions, the adsorbed ions become unstable which is similar to the adsorption behavior obtained in the monolayer VS₂. The calculated maximum capacity for Li⁺ and Na⁺ storage by utilizing VS₂ as anode material is 466 mA h g⁻¹, larger than the reported capacity of 335 mA h g⁻¹ in the MoS₂.¹² We attribute it to the lighter molecular weight in the VS₂. Compared to the Li adsorption energy profile, the Na adsorption energy is higher at a relatively high adsorbed ion concentration. At a relatively low adsorbed ion concentration, adsorption energy of Na is similar to that of Li. Because of the larger radius in the sodium ion, there is a larger electrostatic repulsion interaction between the adsorb Na⁺–Na⁺ at a relatively high adsorbed ion concentration. Consequently, the continuing adsorbed Na⁺ needs to overcome an extra electrostatic barrier induced from the repulsion Coulomb effect to reach its stable site on the VS₂ surface.²¹ Therefore, the Na adsorption energy is larger than that of the Li at a relatively high adsorbed ion concentration. However, there is less effect from the electrostatic repulsion interactions at a low adsorbed ion concentration. It explains that the Na adsorption energy is similar to the Li adsorption energy at a relative low adsorbed ion concentration. In the H monolayer structure, each adsorbed ion on the surface is surrounded with three neighboring S atoms, while the inserted adsorbed ion into the interlayer is surrounded by six neighboring S atoms in the T-bulk VS₂. Compared to the H-monolayer structure, larger coordination number makes the adsorbed ions more stable in the T-bulk structure. Therefore, more negative adsorption energy is observed in the bulk VS₂ than that of in the monolayer VS₂.²²

Fig. 3 Adsorption energy profiles for (a) Li and Na adsorption on the surface of H-monolayer VS₂. (b) Li and Na adsorption in T-bulk VS₂. Voltage versus adsorbed ion concentration plots for (c) Li and Na adsorption in the H-monolayer VS₂ and (d) T-bulk VS₂.

The output voltage is a key parameter to evaluate the ion battery performance. We calculated the output voltage V̄ for Li⁺ and Na⁺ intercalation in the VS₂ anode material by the following equation:²³

where ΔG is the change of Gibbs free energy, n is the number of Li and Na atoms inserted, e is the absolute electron charge. ΔG can be obtained from the adsorption energy E_ads: ΔG = nE_ads. Regarding the maximum theoretical capacity, the calculated absolute average voltage (Fig. 3c) is 0.72 and 0.48 V to drive Li⁺ and Na⁺ intercalation in the monolayer VS₂, respectively. For the T-phase bulk VS₂, the voltage (Fig. 3d) is 0.82 V (Li⁺) and 0.6 V (Na⁺) to drive the intercalation, respectively. Based on our results, we safely conclude that as anode material in the lithium ion battery application, VS₂ has a better electrochemical performance than that of reported MoS₂.²⁴

The rate capability, which determined by the kinetics of both electron transports and adsorbed ion diffusions, is another important index in the ion battery. The diffusion pathways were examined by investigating the ion diffusion barriers (activation energy) on the surface of VS₂. This would help us get deep insights into possible mechanism at the atomic level. With the CI-NEB method, we demonstrated a specific path by which the adsorbed ions migrate in a zigzag way between two adjacent TSs through an intermediate nearest-neighbor HS as shown in Fig. 4a. Convergence tests have shown that nine intermediate images are adequate to accurately describe the activation energy barriers. To better understand the atoms diffusion, the migration in the interlayer of bulk VS₂ is also considered. In the bulk structure, the T′ Ss are confirmed to be the lowest energy barrier sites according to our CI-NEB calculations. Therefore, the diffusion pathway is between two consecutive T′Ss in the bulk VS₂. Schematic illustration of the minimum energy pathway for the ion migrations in a VS₂ bulk structure is shown in Fig. 4b. The corresponding activation energy barrier for each diffusion path in monolayer and bulk VS₂ are plotted in Fig. 4c and d. There are two saddle points observed between two TSs in the monolayer structure, while only one saddle point observed in the bulk structure. In the H-phase monolayer structure, HS becomes another low activation energy site with slightly larger activation energy than TS. Therefore, two saddle points are observed in the monolayer VS₂ as shown in Fig. 4c. The calculated activation energy barriers for Li⁺ and Na⁺ diffusions in the monolayer VS₂ are 195 and 114 meV, respectively. It can be seen that due to its smaller adsorption energy, the activation energy barrier for Na⁺ diffusions is smaller than that of Li⁺ diffusions. We have also calculated the activation energy of monolayer MoS₂ for lithium and sodium ion batteries with a value of 240 and 170 meV, respectively (ESI†), which is consistent with the reported results.^24–26 Our calculations show that the activation energy barrier for Li⁺ and Na⁺ diffusions in monolayer VS₂ is much smaller than that of diffusions in the monolayer MoS₂. Our calculated activation energy barriers for Li⁺ and Na⁺ diffusions (240 and 300 meV) in the bulk VS₂ is much lower than that of our calculations in the bulk MoS₂ (510 and 780 meV) (ESI†). The lower activation energy barrier for both H monolayer and T bulk VS₂ structures facilitates fast charging/discharging processes in the ion batteries, and the enhanced battery rate capability can be expected. Fang et al.²⁷ have reported the experimental data about VS₂/graphene (VS₂/GNS) nanocomposites applied in lithium-ion battery. With the carbon content of 3.9 wt% in the VS₂/GNS composites, the output voltage is at 2.2 V. A reversible specific capacity of ∼180 mA h g⁻¹ is obtained at 0.2C in the VS₂/GNS composite. VS₂/GNS, as an anode material also shows stable performance with a reversible specific capacity of ∼500 mA h g⁻¹ after 100 cycles at 200 mA g⁻¹. Because of only 3.9 wt% carbon content in the nanocomposites of VS₂/GNS, the capacity contribution from graphene is negligible. In our calculation, the theoretical capacity is 466 mA h g⁻¹ in the VS₂. A specific capacity of 174.7 mA h g⁻¹ is observed as x = 0.75, and x represents the numbers of Li ion adsorbed on the bulk VS₂ with a corresponding voltage of 1.7 V. As shown in the Fig. 3d, with a decrease in the value of x, the voltage increased. As x decreased to 0.125, the voltage was up to 2.2 V. It is consistent with the reported experimental data.

Fig. 4 (a) Li⁺ and Na⁺ diffusion path on the surface of H-monolayer VS₂. (b) Li⁺ and Na⁺ diffusion path in the interlayer of T-bulk VS₂. Activation energy barrier curves along the Li⁺ and Na⁺ diffusion path in the (c) H-monolayer VS₂ and (d) T-bulk VS₂.

The diffusion coefficient is also evaluated by means of the Arrhenius' formula,²⁸ in which D is related to the activation energy barrier E_A at a temperature T in a chemical reaction of physical process. Where k_B is the Boltzmann constant and k₀ is a pre-factor often assumed to be independent of the temperature. Since the diffusion constant is proportional to , a reduction in activation energy barrier at room temperature can lead to an improvement in the ion diffusions. By applying the activation energy barriers into the Arrhenius' formula, we found that there are several orders of magnitude enhancement in the value of the lithium and sodium ion diffusion coefficient D in the VS₂ compared to MoS₂.

Summary

In summary, we have systematically investigated the electrochemical performance of H monolayer and T bulk VS₂ as anode material for the lithium and sodium ion battery applications with first-principles calculations. Our calculations reveal that a lower adsorption energy and a higher ion diffusion rate can be achieved in both monolayer and bulk VS₂, compared to other two dimensional materials. The calculated capacity can reach to 466 mA h g⁻¹. Our results show that VS₂ exhibits better electrochemical performance as anode material in the sodium ion battery than that of in the lithium ion battery. Both monolayer and bulk VS₂ are the promising candidates for the anode material in the lithium and sodium ion batteries.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21373196, 11434009), the National Program for Thousand Young Talents of China and the Fundamental Research Funds for the Central Universities (WK2340000050, WK2060140014). This work is supported by the Supercomputing Center of USTC.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra07586j

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