Investigation of N₃C₅ and B₃C₅ bilayers as anode materials for Li-ion batteries by first-principles calculations

Abstract

The best choice today for a realistic method of increasing the energy density of a metal-ion battery is to find novel, effective electrode materials. In this paper, we present a theoretical investigation of the properties of hitherto unreported two-dimensional B₃C₅ and N₃C₅ bilayer systems as potential anode materials for lithium-ion batteries. The simulation results show that N₃C₅ bilayer is not suitable for anode material due to its thermal instability. On the other hand B₃C₅ is stable, has good electrical conductivity, and is intrinsically metallic before and after lithium intercalation. The low diffusion barrier (0.27 eV) of Li atoms shows a good charge and discharge rate for B₃C₅ bilayer. Moreover, the high theoretical specific capacity (579.57 mAh/g) connected with moderate volume expansion effect during charge/discharge processes indicates that B₃C₅ is a promising anode material for Li-ion batteries.

Introduction

Studies into alternative energy sources, particularly renewable energy, are being driven by the modern world’s rising energy consumption, concerns about the fossil fuel dilemma, and the need for environmental protection¹. The method of storing the generated energy is also a huge challenge. Currently, lithium-ion batteries (LIBs) are the preferred energy storage technology for various applications, including portable electronics, electric vehicles, and grid energy storage^2,3. The materials in use as electrodes have a significant impact on the properties of LIBs. In industrial LIBs, graphite is the anode material that is most frequently used^4,5. According to estimates, graphite has a theoretical capacity of 372 mAh/g⁶. Unfortunately, the main drawbacks of the graphite electrode, which restrict its use and advancement, are structural deformation, initial loss of capacity, and electrical disconnect⁷. As one of the alternatives to the commonly used graphite as an anode material, titanium dioxide (TiO₂) has been looked into. The attractive properties of TiO₂, which include low cost, high chemical stability, low volume expansion during charging/discharging, eco-friendliness, high energy density, and ease of availability, have made it one of the promising anode materials for LIBs^8,9. Unfortunately, in comparison with commercially used graphite anode materials, TiO₂ has a relatively low theoretical capacity of around 335 mAh/g¹⁰.

The continuous demand for higher energy density, improved cycling stability, and longer battery life drives extensive research on developing advanced materials for LIB electrodes. In this context, two-dimensional (2D) materials have emerged as promising candidates for enhancing the performance of LIB anodes.

The unique properties of 2D materials, such as large surface area, atomically thin structure, and tunable electronic properties, make them attractive for energy storage applications^11–16. The atomically thin nature of 2D materials allows for efficient lithium ion diffusion and accommodation during charge and discharge processes, leading to improved capacity and cycling stability. Additionally, the large surface area of 2D materials facilitates increased electrochemically active sites, enhancing the overall electrochemical performance of the anode¹⁷. Several types of 2D materials have been recently investigated as potential anode materials for LIBs. These include transition metal dichalcogenides (TMDs) such as MoS₂, graphene, MXenes, and various other 2D carbides, nitrides, and oxides. Each of these materials possesses unique properties that can influence their electrochemical behavior, capacity, and cycling stability^18–20.

In the present study, we propose that graphene bilayers substitutionally doped with B and N atoms, specifically the B₃C₅ and N₃C₅ systems, are promising as potential anode materials for LIBs. Li-ion battery swelling during the intercalation of Li into the electrodes is a major cause of battery electrode degradation and can contribute significantly to cell failure. The swelling effect can only be investigated by studying the bilayer or bulk systems, therefore, herein we take into account bilayer systems. This investigation is based on DFT computations. It has been observed that both hitherto unreported B₃C₅ and N₃C₅ exhibit metallic properties with significant conductance after the adsorption of metal ions. Additionally, these systems demonstrate a remarkable specific Li capacity, which is significantly greater than that of pure graphene. Moreover, B₃C₅ and N₃C₅ display a low diffusion barrier and moderate volume expansion effect during charge/discharge processes. These attributes suggest that the investigated B₃C₅ and N₃C₅ systems could be ideal electrode materials for Li-ion batteries. Our comprehensive analysis aims to illuminate the potential of 2D materials as anode components for LIBs, providing insights into their distinctive properties and their contribution to the overall performance of lithium-ion batteries. The outcomes of this study have the potential to guide the design and development of advanced 2D anode materials, enhancing their electrochemical characteristics and elevating their energy storage capabilities.

Computational methods

The first-principles calculations in this study were performed using the Quantum ESPRESSO package^21,22, employing projector augmented wave (PAW) potentials within density-functional theory (DFT). The exchange-correlation energy of the electrons was treated within the generalized gradient approximation (GGA) functional of Perdew–Burke–Erzenhoff (PBE). The charge density and kinetic energy cut-off values were set to 500 Ry and 50 Ry, respectively. To minimize interactions between neighboring slabs, a vacuum of 20 Å was included. Van der Waals (VdW) interactions between the layers were accounted for using Grimme’s DFT-D correction²³. The geometrical structure is optimized by using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm²⁴ with the convergence criterion of ${10}^{-5}$ eV for energy. The forces on all atoms are less than 0.001 eV/Å. Structural optimization and band structure computations were performed using a Monkhorst pack k-point grid of $36\times 36\times 1$. The diffusion barrier is calculated by the climbing image nudged elastic band (Cl-NEB) method²⁵. The thermal stability of the B₃C₅ and N₃C₅ bilayer systems was examined through ab initio molecular dynamics (AIMD) simulations at 300 K using the CP2K software²⁶ with a constant volume and temperature ensemble (NVT ensemble) and a time step of 1 fs and 10000 ionic steps.

The intercalation energy of Li between B₃C₅ and N₃C₅ bilayers was computed as below:

$$\begin{array}{c}\hfill E_{\text{int}}=(E_{{\text{Li}}_n{\text{X}}_3{C}_5}-E_{{\text{X}}_3{C}_5}-n{E}_{\text{Li}})/n,\end{array}$$ 1

where $E_{{\text{X}}_3{C}_5}$ is the total energy of pristine ${\text{X}}_3{C}_5$ bilayer (X = B or N), $E_{\text{Li}}$ is the energy of a single Li atom (in bulk bcc phase), $E_{{\text{Li}}_n{\text{X}}_3{C}_5}$ means the total energy of Li-intercalated ${\text{X}}_3{C}_5$ bilayer and n is the number of intercalated lithium atoms. From this definition, the more negative the value of $E_{\text{int}}$, the more it illustrates the exothermic nature of the reaction, indicating a higher likelihood of the reaction occurring. Conversely, a positive value of $E_{\text{int}}$ indicates an endothermic reaction, suggesting that the reaction is less likely to occur.

Theoretical Li capacity can be estimated as below:

$$\begin{array}{c}\hfill C=\frac{\mathit{nzF}}{{\text{M}}_{X_3{C}_5}},\end{array}$$ 2

where n is the number of intercalated Li atoms ($n=16$), z is the valence number ($z=1$ for Li), F is the Faraday constant (26801 mAh/mol), and ${\text{M}}_{X_3{C}_5}$ is the molar mass of B₃C₅ or N₃C₅ bilayer.

Results and discussion

A fully-relaxed structure of pristine B₃C₅ and N₃C₅ bilayer systems that have a hexagonal resemblance to graphene, but with a rippled surface, can be observed in Fig. 1a, b, respectively. Lattice constants a and b are both 5.22 Å for B₃C₅ and 4.81 Å for N₃C₅. The C–C and C–B bond lengths are 1.443 Å and 1.541 Å (1.592 Å) in the case of B₃C₅ and the C–C and C–N bond lengths are 1.387 Å and 1.388 Å (1.481 Å) in the case of N₃C₅.

Figure 1.

Atomic structure (top and side views) of pristine $2\times 2$ supercell of (a) B₃C₅ and (b) N₃C₅ bilayer.

To check the energetical stability of our bilayer structures, we evaluate the cohesive energies:

$$\begin{array}{c}\hfill E_{\text{coh}}=\frac{6E_{\text{X}}+10E_{\text{C}}-E_{{\text{X}}_3{C}_5}}{16},\end{array}$$ 3

where $E_{\text{X}}$ is the energy of an isolated B or N atom, $E_{\text{C}}$ means the energy of an isolated C atom, and $E_{{\text{X}}_3{C}_5}$ represents the total energy of X₃C₅ bilayer. The calculated cohesive energies of B₃C₅ and N₃C₅ bilayers are 7.76 eV/atom and 8.26 eV/atom, respectively. The higher cohesive energy indicates a more stable structure, indicating that the N₃C₅ monolayer has a more stable structure. The values of B₃C₅ and N₃C₅ monolayers are higher than those of phosphorene (3.48 eV/atom), silicene (3.71 eV/atom), SnC (5.5 eV/atom), GeP₃ (3.34 eV/atom), P₃C (4.18 eV/atom), MoS₂ (4.98 eV/atom) and Mo₂C (6.31 eV/atom) and close to Ti₃BN monolayer (7.46 eV/atom) and graphene (7.95 eV/atom)^27–33.

To investigate the dynamical stability of studied structures, phonon calculations were performed along $\mathrm{\Gamma }$–M–K–$\mathrm{\Gamma }$ symmetry points. As we can see in Fig. 2, no imaginary frequencies are observed in the entire Brillouin zone, confirming the dynamical stability of both investigated systems, which is an important result, especially from the energy storage point of view.

Figure 2.

Calculated phonon spectra of (a) B₃C₅ bilayer and (b) N₃C₅ bilayer.

We also used AIMD simulations to investigate the thermal stability of the B₃C₅ and N₃C₅ bilayers. Our structures retain their integrity after being heated to 300 K (see insert of Fig. 3). Simultaneously, the energy fluctuation is quite small, with a variation of around 0.003 Ry, indicating that both systems are thermally stable.

Figure 3.

Fluctuation graphs of the total energy of $2\times 2$ (a) B₃C₅ and (b) N₃C₅ bilayers supercells as a function of time at 300 K. The embedded figures show the corresponding top views of the initial configurations and configurations after 10 ps of simulation.

The intercalation energy ($E_{\text{int}}$) of B₃C₅ and N₃C₅ bilayers was estimated using Eq. (4). To denote the concentration of Li per unit bilayer cell, we use the notation of Li_n(X₃C₅)₂. The calculated $E_{\text{int}}$ of the single lithium atom (1:17 ratio) equals $-3.96$ eV and $-1.75$ eV for B₃C₅ and N₃C₅ bilayers, respectively. With further increase of Li number, the intercalation energy almost linearly decreases in the case of B₃C₅ and nonlinearly changes in the case of N₃C₅, as shown in Table 1. The obtained results showed that from the energy storage point of view, the B₃C₅ has better properties than the N₃C₅ due to the enhancement of intercalation energy. In the case of N₃C₅, the most energetically favorable is Li₃(N₃C₅)₂ configuration with the intercalation energy of $-2.46$ eV. The bilayer B₃C₅ exhibits an intercalation energy of $-4.43$ eV in the fully lithiated case, Li₄(X₃C₅)₂, illustrating that it is most promising and worth considering for the study of new anode materials for LIBs.

Table 1.

Intercalation energy per lithium atoms (in eV) for the Li-intercalation between B₃C₅ and N₃C₅ bilayers as a function of Li atoms concentration in the unit cell.

n	Lin(B3C5)2	Lin(N3C5)2
1	$-3.96$	$-1.75$
2	$-4.12$	$-2.30$
3	$-4.35$	$-2.46$
4	$-4.43$	$-2.06$

The formation energy relative to stable reference materials is crucial for assessing the stability of various phases at 0 K. The formation energy of structure with intermediate lithium content can be delineated as follows³⁴:

$$\begin{array}{c}\hfill E_{\text{f}}=\frac{E_{{\text{Li}}_n{\text{X}}_3{C}_5}-E_{{\text{X}}_3{C}_5}-n{E}_{\text{Li}}}{n+1},\end{array}$$ 4

The convex hulls obtained from the formation energies are presented in Fig. 4. The minimum value of $E_{\text{f}}$ corresponds to the most thermodynamically stable adsorption concentrations. The corresponding structures are illustrated in Fig. 4 insets.

Figure 4.

Formation energy convex hull of Li_n(B₃C₅)₂ and Li_n(N₃C₅)₂ systems.

It’s worth noting that a geometry optimization was conducted for different intercalation sites. The most energetically favorable position is found to be the hole position, where atoms from the initial bridge and top positions migrate during the optimization process. This indicates that the hole position is indeed the most energetically favorable configuration. Crystal structures of all Li-intercalated stages for Li_n(B₃C₅)₂ and Li_n(N₃C₅)₂ are included in Supplementary Information.

After full lithiation (Li atoms intercalation between monolayers at all hole positions, Li₄(B₃C₅)₂), the monolayers in pristine B₃C₅ bilayer transforms from the initial structure with a rippled surface into a graphene-like plane structure, as shown in Fig. 5a. In the case of N₃C₅ bilayer (Li₃(N₃C₅)₂), the Li-intercalation contributes to the increase of rippling of the surface and changes ideal AA stacking where atoms of both layers have identical lateral coordinates into degenerate AA stacking where the one layer is slightly shifted relative to the other one (see Fig. 5b). Moreover, in both systems, the Li-intercalation increases the interlayer distance from 2.53 Å to 3.63 Å for B₃C₅ and from 2.78 Å to 4.69 Å in the case of N₃C₅. The practical application of new 2D anode materials is strongly impeded by large volume expansion during lithiation/delithiation processes which can result in loss of electrical contact with the conductive additive or the current collector and even peeling off from the current collector³⁵. The results obtained for B₃C₅ and N₃C₅ clearly show a low volume expansion of about $43-69$%, compared to 2D Si/C composite (54%), commercial Si (183%) and pure Si nanosheets (95%)^36,37.

Figure 5.

Atomic structure (top and side views) of Li-intercalated $2\times 2$ supercell of (a) B₃C₅ and (b) N₃C₅ bilayer.

Structural stability during the charging and discharging process at finite temperatures is an important factor in the performance of LIBs. An AIMD simulation is used to investigate the thermal stability of the Li₄(B₃C₅)₂ and Li₃(N₃C₅)₂ structures. Figure 6 show the calculated total energy of the fully lithiated bilayers during the AIMD simulation time of 10 ps at 300 K. As expected, the total energy of Li₄(B₃C₅)₂ does not change much during the AIMD steps. Such a slight change in energy indicates good thermal stability of a fully Li-intercalated B₃C₅ bilayer. In the case of Li₃(N₃C₅)₂ we observed structural deformation and energy drift, indicating that N₃C₅ bilayer is thermally unstable. Due to the above, we eliminated it from further analysis and we focused our attention only on the B₃C₅ bilayer.

Figure 6.

Fluctuation graphs of the total energy of $2\times 2$ (a) Li₄(B₃C₅)₂ and (b) Li₃(N₃C₅)₂ supercells as a function of time at 300 K. The embedded figures show the corresponding top views of the initial configurations and configurations after 10 ps of simulation.

Figure 7 represents the electronic band structure of pristine B₃C₅ and alterations in its electronic structure after Li intercalation. Both materials show a metallic character as indicated by the electronic states crossing the Fermi level. The metallic properties of the B₃C₅ bilayer offer an intrinsic profit in high electrical conductivity and a satisfying electrochemical property for better battery cycling.

Figure 7.

The electronic band structure along the $\mathrm{\Gamma }$–K–M–$\mathrm{\Gamma }$ high-symmetry line, together with the total and partial density of states for (a) pristine B₃C₅ bilayer and (b) Li-intercalated B₃C₅ bilayer.

To determine the diffusion and mobility features, we calculated the energy barrier for Li-ion diffusion with three main diffusion pathways as shown in Fig. 8. Path 1 is shown by the red color. The Li atom diffuses in the interlayer space from the hole of the B₂C₄ ring to the hole of the B₂C₄ ring through the C–B bridge. Path 2 is shown by the green color. The Li atom diffuses from the B₂C₄ ring position to the B₃C₃ ring also through the C–B bridge. In the case of path 3, which is shown by the black color, the Li atom migrates between two adjacent B₂C₄ rings through the C–C bridge. Data illustrating the diffusion stages of Li atom between two B₃C₅ layers are included in Supplementary Information.

Figure 8.

The comparison diffusion barriers in different paths of Li atom between two B₃C₅ layers.

The calculations reveal that the diffusion energy barriers corresponding to path 1, path 2 and path 3 are 1.16 eV, 1.22 eV and 0.27 eV, respectively. The diffusion energy barrier through the C–C bridge is lower than the C–B bridge, indicating that Li atoms are more inclined to spread in an anisotropic way across the C–C bridge. We also note that the lowest diffusion barrier obtained for the Li atom is superior to the graphene bilayer (0.34 eV)³⁸, therefore, B₃C₅ shows great potential to serve as a LIB electrode.

The maximum theoretical storage capacity (C) is an important parameter to evaluate the performance of the LIB. It depends on the concentration of the Li ions intercalated between B₃C₅ layers and can be calculated using Eq. (2). The capacity of a fully lithiated B₃C₅ bilayer is as high as 579.57 mAh/g for LIBs (1159.15 mAh/g if we take into calculations only one layer of B₃C₅). The obtained result is much larger compared to the storage capacities of commercially used graphite (372 mAh/g)⁶ or TiO₂ (335 mAh/g)¹⁰ and other typical 2D anode materials for LIBs like VS₂ (466 mAh/g)³⁹, Zr₂B₂ (526 mAh/g)⁴⁰, NbSe₂ (203 mAh/g)⁴¹, Nb₂C (542 mAh/g)⁴², TaC₂ (523 mAh/g)⁴³ or W₂C (259 mAh/g)⁴⁴.

Open circuit voltage (OCV) is another crucial parameter to characterize the performance of metal-ion batteries which can be calculated using the following equation:

$$\begin{array}{c}\hfill V\approx \frac{-E_{{\text{Li}}_{x_2}{X}_3{C}_5}+E_{{\text{Li}}_{x_1}{X}_3{C}_5}+({\mathrm{x}}_2-{\mathrm{x}}_1)E_{\text{Li}}}{z({\mathrm{x}}_2-{\mathrm{x}}_1)e},\end{array}$$ 5

where, $E_{{\text{Li}}_{x_2}{B}_3{C}_5}$ and $E_{{\text{Li}}_{x_1}{B}_3{C}_5}$ are the total energies of Li-intercalated B₃C₅ supercell with the Li concentration of ${\mathrm{x}}_2$ and ${\mathrm{x}}_1$, respectively. The symbol e denotes the fundamental charge. The calculated average OCV of Li-intercalated B₃C₅ bilayer is 2.47 V, which is comparable to those of the commercial anode materials such as TiO₂ with an open circuit voltage of 1.5–1.8 V⁴⁵ and lower than OCV obtained for 2D phosphorene (2.9 V)⁴⁶ or black arsenic (4.31 V)⁴⁷.

Conclusions

Lithium-ion batteries have brought about a significant transformation in the realm of energy storage, playing an indispensable role in both portable electronic devices and electric vehicles. To cater to the ever-growing demand for high-performance batteries, the quest for advanced anode materials with augmented capacity, improved lithium ion mobility, and minimal swelling effects has taken on paramount importance. This study delves into a theoretical exploration of the characteristics exhibited by novel two-dimensional B₃C₅ and N₃C₅ bilayer systems, considering their potential as anode materials for lithium-ion batteries (LIBs). The ab initio molecular dynamics (AIMD) simulations conducted at a temperature of 300 K reveal that pristine B₃C₅ and N₃C₅ bilayer systems exhibit very good stability. However, upon the introduction of lithium atoms, the N₃C₅ bilayer loses stability, prompting its exclusion from further analysis. Furthermore, the first-principles calculations demonstrate that the B₃C₅ bilayer boasts outstanding electronic conductivity, a notably lower Li diffusion barrier (0.27 V meV), and an impressive theoretical storage capacity (579.57 mAh/g). These exceptional properties strongly indicate its suitability for use as an anode material.

Author contributions

All authors contributed equally to this work.

Data availability

The data that support the findings of this study are available in Supplementary Information.

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-61939-x.