Exploring the potential of T-Graphene-like BC2N monolayer as an anode material for Na/K-Ion batteries

We conducted a thorough analysis to assess the suitability of a T-graphene-like BC2N monolayer as an electrode material for sodium-ion batteries (NIBs) and potassium-ion batteries (KIBs) using first-principles calculations. Our investigation demonstrates the chemical adsorption of Na/K atoms onto the BC2N monolayer, which exhibits metallic properties after Na/K adsorption, ensuring excellent electrode conductivity. The average open-circuit voltages for Na and K are 0.39–0.12 V and 0.87–0.14 V, respectively. Furthermore, the BC2N monolayer revealed significantly lower Na/K diffusion barriers (0.40 eV for Na and 0.22 eV for K) and higher storage capacities (1647 mAh g−1 for Na and 2196 mAh g−1 for K) compared to conventional two-dimensional anode materials. These exceptional characteristics highlight the promising potential of the T-graphene-like BC2N monolayer in advancing Na/K-ion batteries technology.


Introduction
Li-ion batteries (LIBs) are used widely in various applications, including electronics, electric vehicles, and stationary energy storage systems [1][2][3]. They offer the highest energy density among practical secondary batteries, owing to their high operating voltage and low self-discharge rate [2]. However, LIBs face several challenges, such as high cost, limited resources, safety issues, and environmental concerns [4]. The use of Li and Co as raw materials in Li-ion batteries can be hindered by their expensive and scarce nature, uneven distribution, price fluctuations, as well as the potential fire and explosion hazards associated with organic electrolytes and electrodes, along with environmental pollution and ecological damage caused by their extraction and disposal [5]. Therefore, researchers have explored alternative battery systems based on Na-ion batteries (NIBs) and K-ion batteries (KIBs) [6][7][8][9]. The Na and K are more abundant and evenly distributed than Li in the earth's crust [10]. For instance, Na and K constitute 2.6% and 2.4% of the earth's crust by mass respectively, while Li only constitutes 0.002%. The Na and K are cheaper than Li in terms of raw materials. Furthermore, Na and K do not need Co as a cathode material, which can lower the cost significantly [10]. In terms of battery performance and safety, NIBs offer a lower working voltage and a reduced risk of thermal runaway or fire explosion when compared to LIBs [6]. And Potassium has a lower reactivity with organic solvents than lithium, which can improve the stability and safety of KIBs [8]. Hence, SIBs and KIBs are anticipated to play crucial roles as components in future sustainable energy storage systems.
The application of 2D materials in metal-ion batteries brings about numerous benefits, such as a notable specific capacity, swift ion transport, advantageous mechanical flexibility, and exceptional electrical conductivity [11,12]. These advantageous traits are derived from the expansive surface area, abundant active sites, thin-layered structure, capacity to withstand significant volume changes, and influence on electron transfer and internal resistance [11,13]. Graphene, as a representative example of 2D materials, has received considerable attention as a potential electrode material in metal-ion batteries because of its exceptional properties [13,14]. Nonetheless, the elongated metal-ion transport pathways resulting from the high aspect ratio Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. of graphene nanosheets, combined with their propensity to aggregate, can impose limitations on the specific surface area, active sites available for metal-ion storage, and the overall rate performance of the electrode [13]. The atomic-scale modification of graphene, such as the introduction of defects [14] and heteroatoms nitrogen (N) [15], boron (B) [16], and phosphorus [17] doping, can effectively generate a multitude of active sites, therefore enhancing the interaction between graphene and the absorption metal ions. The co-doped N and B into graphene would result in the formation of graphene-like BC 2 N [18,19]. In recent studies, T-graphene, a carbon monolayer consisting of flat structures incorporating both C8 and C4 rings, has been predicted to be a potential candidate as alkali-ions batteries anode [20,21]. The theoretical studies propose that the incorporation of N and B atoms into T-graphene can lead to the formation of a B-C-N nanosheet that exhibits a stable T-graphene-like structure [22,23]. Recent studies suggested that T-graphene like BC 2 N is a promising material for use in lithium-ion batteries as an anode [22].
To date, there has been rarely reported research on the utilization of T-graphene-like BC 2 N as an anode material for NIBs and KIBs. In this study, we investigate the potential use of T-graphene like BC 2 N as an anode for NIBs and KIBs. Our findings reveal that BC 2 N exhibits remarkable potential as an anode for NIBs, with a theoretical capacity of up to 1647 mAh g −1 . Furthermore, as an anode for KIBs, T-graphene like BC 2 N exhibits a specific capacity of 2196 mAh g −1 . Additionally, we analyze the diffusion of sodium and potassium on the T-graphene like BC 2 N, observing exceptionally low diffusion barriers of approximately 0.4 eV for Na and 0.22 eV for K. Overall, our study suggests that T-graphene-like BC 2 N holds great promise as a highly attractive anode material for NIBs and KIBs.

Computational methods
We employed the VASP code [24] to conduct density functional theory (DFT) calculations, aiming to investigate the energy storage properties of BC 2 N. The exchange-correlation functional was modeled using the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) [25,26] and the electron-ion interaction was modeled using the projector-augmented wave (PAW) technique [27]. Our calculations utilized a plane-wave energy cutoff of 500 eV to ensure accuracy. We incorporated the D2-Grimme dispersion correction [28] to account for van der Waals interactions. We implemented a sizable vacuum slab (∼26 Å) along the z-direction to minimize artificial interactions between adjacent layers. Gaussian smearing with a small SIGMA value of 0.05 was applied throughout the calculations. For geometric optimization, we employed a 12 × 12 × 1 Γ-centered k-mesh and carefully relaxed the cell volume, shape, and atomic positions until the residual force reached below 0.01 eV Å. To gain insights into the diffusion behavior of Na/K in BC 2 N, we utilized the climbing image nudged elastic band (CI-NEB) method [29], which allowed us to explore the diffusion pathways and energy barriers, shedding light on the underlying diffusion mechanism and kinetics in BC 2 N.

Results and discussions
Adsorption of Na/K on BC 2 N monolayer Our analysis on T-graphene like BC 2 N revealed the presence of 16 distinct Na/K adsorption sites. These sites (figures 1 and S1) include 9 bridge sites, 4 top sites (N, B, C1, and C2 top sites), 3 hollow sites (4-membered C ring, 4-membered B-N ring and B-C-N octagonal ring). To examine the adsorption of metal atoms on these sites, we computed the Na/K adsorption energy. As shown in the following equation, the adsorption energy calculation for one Na/K atom on the different sites of BC 2 N involves comparing the total energies of the system with and without the adsorbed atom.
Where E(BC 2 N) represents the energy of the pristine BC 2 N, E(M) denotes the energy of one Na/K atom in its bulk state and E(M-BC 2 N) denotes the energy of adsorption of one Na/K on the BC 2 N. Initially, we conducted structure optimization of BC 2 N with the adsorption of Na/K on 16 different sites. Following the optimization, the Na atom relocated to the nearby hollow site of the B-C-N octagonal ring (h1), the hollow site of the 4-membered C ring (h2), the hollow site of the 4-membered B3N ring (h3), or the B top site (t1). Similarly, the K atom migrated to the nearby h1, h2, t1, or the C top site (t2). A summary of the adsorption energies for Na/K on these BC 2 N sites can be found in table 1. Our analysis demonstrated that the hollow sites h1 and h2 (refer to figure 1) exhibit negative adsorption energies for Na, with site h1 displaying the lowest Na adsorption energy of −0.39, indicating its stability as an adsorption site. In the case of K adsorption, h1, h2, t1 and t2 exhibit negative adsorption energies, with site h1 displaying the lowest K adsorption energy of −0.88 eV. Figures 2(a) and (c) illustrate the adsorption configurations of Na/K atoms on site h1, where the Na/K atoms attach directly above the center of the B-C-N octagonal ring, forming a total coordination of eight. The distances between Na and C1, C2, N, and B are 2.73, 2.62, 2.72, and 2.72 Å, respectively. And the distances between K and C1, C2, N, and B are 3.05, 2.98, 3.05, and 3.05 Å, respectively. These findings suggest that alkali-metal atoms tend to prefer sites with higher coordination. Prior theoretical research also indicated that the hollow site of the C8 ring in T-graphene and BC 2 N is the most stable adsorption site for Na/K [21]. Furthermore, our results indicate that K atoms exhibit higher adsorption energies compared to Na, aligning with the previous observation of alkali-metal adsorption trends [30]. The adsorption energy of Na/K on T-graphene like BC 2 N is lower than   To examine the Na/K adsorption process on the BC 2 N monolayer, a detailed examination can be performed by studying the charge density difference utilizing the equation below: represents the total electron density of the BC 2 N monolayer, M BC N 2 ( ) r represents the total electron density of the BC 2 N monolayer with Na/K adsorbed, and M ( ) r represents the total electron density of the Na/K atom. By subtracting the electron density of the pristine BC 2 N monolayer and the electron density of the Na/K atom from the electron density of the BC 2 N monolayer with Na/K adsorbed, we obtain the charge density difference ( r D ).
Upon examining the charge density difference (figures 2(b) and (d)), it is evident that there is an electron accumulation area between the BC 2 N monolayer and Na/K, accompanied by an electron depletion area surrounding the Na/K atoms. This observation suggests that the BC 2 N monolayer accepts electrons from the adsorbed Na/K atoms. The electron accumulation area between the adsorption atoms and the BC 2 N indicates a substantial Coulombic interaction between them. This interaction enhances the binding between the Na/K and the surrounding atoms in the BC 2 N monolayer, resulting in a strong adsorption configuration. The Bader charge analysis confirms the transfer of 0.73 e-from Na to BC 2 N upon adsorption, providing additional evidence for charge donation from Na to BC 2 N. For the adsorbed potassium atom on BC 2 N, the potassium atom transfers 0.81 e-of charge to BC 2 N. Additionally, the C1 atom in close proximity to Na/K accepts more electrons compared to its state in pure BC 2 N. This finding underscores the strong ionic bonding properties between the BC 2 N system and the ionized metal.
We further examined the electronic structure of BC 2 N with one Na/K atom adsorbed at the h1-site. Figure 3 illustrates the total and partial density of states (DOS) of the BC 2 N monolayer after Na and K adsorption. In contrast to T-graphene, which exhibits metallic behavior [31], the T-graphene like BC 2 N monolayer behaves as a semiconductor. Previous theoretical work suggests that the primary contribution to the density of states in the conduction and valence bands of BC 2 N comes from the p orbitals of B and C atoms [22]. However, upon the adsorption of Na/K atoms, the electronic state of BC 2 N transitions into a metallic state. It is worth noting that no electron states of Na/K are observed in close proximity to the Fermi level. As discussed above, following the adsorption of Na/K, Na/K transfers electrons to BC 2 N, causing the electron states in the conduction band to shift downward. The adsorption of Na/K on BC 2 N leads to a transition of the material from a semiconductor to a metal, enhancing its electrical conductivity. This is highly beneficial for the charging and discharging processes of batteries, as well as overall batteries performance.

Diffusion of Na/K on BC 2 N monolayer
We employed the CI-NEB method [29] to investigate the mobility of Na/K ions on the BC 2 N monolayer. As shown in figure 4, we focused on two possible diffusion patterns, path1 and path2. The aim was to understand how Na/K atoms can move between different adsorption sites within the BC 2 N structure. In path1, Na/K atoms initially occupy the octagonal hollow site of BC 2 N. They then traverse through the top site near a carbon atom and ultimately reach the neighboring octagonal hollow site. The calculated diffusion barriers for Na and K along path1 are 0.40 eV and 0.17 eV, respectively. These values represent the energy barriers that Na/K atoms need to overcome during their movement along path1. For path2, Na/K atoms also begin at the octagonal hollow site of BC 2 N. They then follow a trajectory passing through the C4 hollow site before finally reaching the adjacent octagonal hollow site.
The diffusion barriers calculated for path2 are 0.40 eV for Na and 0.22 eV for K. Interestingly, the diffusion barriers for K are significantly lower than those for Na, indicating faster migration of K atoms compared to Na atoms within the BC 2 N monolayer. The energy barriers for Na diffusion in both path1 and path2 are found to be 0.40 eV, indicating that the movement of Na is equally easy in both directions. However, K atoms exhibit slightly higher barriers for diffusion along path2 compared to path1. The Na diffusion barrier on the BC 2 N monolayer is comparable to that on T-graphene (0.35 eV ∼ 0.41 eV) [31] and lower than on N doped T-graphene (0.50 eV) [32]. The K diffusion barrier on the BC 2 N monolayer is lower than that on T-graphene (0.25 eV ∼ 0.29 eV) and graphene with point defects (0.49 eV) [33]. The low diffusion barriers for Na/K ions on BC 2 N suggest easy and efficient diffusion, indicating favorable charge and discharge rates. Storage-capacity of Na/K on BC 2 N monolayer Investigating the storage capacity and open-circuit voltages (OCVs) of Na/K batteries is important to assess their energy storage capabilities and overall performance, enabling the development of efficient and reliable energy storage systems. The average Na/K adsorption energies are calculated as below ( ) denotes the total energy of BC 2 N supercell with the adsorption of x 2 and x 1 number of Na/K atoms, respectively.
We calculated the average open-circuit voltages using the following equation The E(M x BC 2 N) represents the total energy of BC 2 N supercell with adsorption of x number of Na/K atoms. The maximum Na/K-ion storage capacity can be determined using the following equation: here F represents the Faraday constant, x denotes the upper limit for the adsorption of Na/K atoms on the BC 2 N and mass of BC 2 N is the molecular weight of BC 2 N supercell.
We conducted adsorption studies of Na/K atoms on BC 2 N to assess the Na/K storage capacity of BC 2 N monolayer. The adsorption was gradually increased, considering a maximum of three layers of Na/K on both sides of the BC 2 N using a 2 × 2 × 1 supercell (figures 5(c) and (d)). Figure 5(a) reveals that as the adsorbed Na atoms rise from 1 to 24 on the 2 × 2 × 1 supercell of BC 2 N, the E ads ¢ progressively rises from −0.39 eV to −0.10 eV. The increased Coulombic repulsion among the adsorbed Na atoms is most likely the cause of this pattern, which shows a decline in system stability as additional Na atoms are added. Beyond the 24th Na atom, a significant change in stability occurs, resulting in positive E . ads ¢ For K adsorption, the E ads ¢ gradually increases from −0.87 eV to −0.02 eV as the number of adsorbed K atoms increases from 1 to 34 on the 2 × 2 × 1 supercell of BC 2 N. Further adsorption of K atoms yields positive adsorption energy. Our calculations indicate that the BC 2 N monolayer within a 2 × 2 × 1 supercell can adsorb up to 24 Na atoms ( figure 5(c)), resulting in a maximum capacity of 1647 mAh g −1 . This capacity surpasses that of expanded graphite (284 mAh/g), N doped graphene (384 mAh g −1 ) [17], N doped T-graphene (754 mAh g −1 ) [34]. It has been reported that the borondoped graphene-like BC 2 N has a maximum Na storage capacity of 686 mAh g −1 [35], which is lower than that of T-graphene-like BC 2 N presented in this work. The difference in the predicted sodium atoms storage capacity between this study and the previous report [35] can be attributed primarily to the distinct BC 2 N structures. In prior studies, BC 2 N with a graphene-like structure, comprising B, C, and N six-membered rings, was investigated [35]. In this work, BC 2 N with a structure resembling T-graphene, featuring B, N four-membered rings, and B, C, N eight-membered rings, was utilized. According to earlier theoretical investigations, T-graphene has demonstrated a superior sodium ion capacity compared to graphene [21]. The BC 2 N structure similar to T-graphene is expected to offer more adsorption sites for sodium atoms, potentially leading to a higher sodium storage capacity in comparison to BC 2 N with a graphene-like structure. Additionally, the supercell has the capability to accommodate up to 32 K atoms ( figure 5(d)), corresponding to a maximum capacity of 2196 mAh g −1 , which surpasses that of B doped graphene (546 mAh g −1 ) [36], T-graphene ( 1116 mAh g −1 ) [21] and pentadiamond monolayer (743.86 mAh g −1 ) [37]. The observed higher potassium storage capacity compared to sodium can be attributed to the following factors. The potassium atoms exhibit a stronger adsorption tendency on T-graphene-like BC 2 N relative to sodium atoms. Subsequent analysis of the adsorbed structures (figures 5(c)-(d)) reveals that potassium atoms can be accommodated in three atomic layers on BC 2 N, while sodium atoms are confined to two atomic layers. Specifically, the adsorption of two atomic layers of sodium atoms adopts an AA stacking configuration, whereas the adsorption of three atomic layers of potassium atoms follows a similar ABA stacking arrangement. As a result, the enhanced adsorption energy and distinct adsorption configurations of potassium atoms contribute to their superior storage capacity in comparison to sodium atoms. To assess the stability of the adsorbed structures, we performed molecular dynamics simulations (AIMD). In figure S2, we present the structures obtained after the AIMD simulation. During the AIMD simulations, we observed oscillations of B, C, and N atoms around their equilibrium positions. Notably, the C-N, C-B, and C-N bonds remained well-preserved after the 10 ps AIMD simulation at 300 K. Additionally, both sodium and potassium atoms remained close to their respective adsorption sites throughout the simulation period. These findings indicate the stability of the adsorption of Na and K atoms on BC 2 N.
To assess the electrochemical behavior and energy delivery capabilities, we investigated the OCVs. As the adsorbed Na atoms grow from 1 to 24 on the BC 2 N monolayer, the OCVs decrease from 0.39 to 0.12 V ( figure 5(a)). According to a previous report, the OCVs (Open Circuit Voltages) of T-graphene were observed to decrease from 0.95 to 0.12 V as the amount of adsorbed Na increased. Compared to T-graphene, the OCVs of BC 2 N exhibited a relatively narrow range, suggesting that BC 2 N may possess a more consistent and stable electrochemical performance. The OCVs for K atoms behave similarly, falling from 0.87 to 0.14 V as the adsorbed K atoms rise from 1 to 32 ( figure 5(a)). The overall OCVs is lower than that of T-graphene (0.37 V), indicating that BC 2 N may have a lower electrochemical potential or a less favorable redox behavior compared to T-graphene. These outcomes, characterized by high Na/K storage capacities and low open-circuit voltages, indicate the potential of BC 2 N as a promising anode material for NIBs and KIBs. However, it is crucial to remember that additional experimental studies are required to validate these results and assess the viability of using BC 2 N as an anode material in NIBs and KIBs.

Conclusion
Based on our comprehensive first-principles calculations, we have conducted a systematic investigation into the suitability of a T-graphene-like BC 2 N as a promising electrode material for NIBs and KIBs. Our findings demonstrate that the BC 2 N monolayer can effectively undergo chemical adsorption of Na/K atoms, resulting in a transition to metallic behavior, which enhances the monolayer's conductivity. The average open-circuit voltages for Na and K are within the ranges of 0.39-0.12 V and 0.87-0.14 V, respectively, indicating the exceptional potential of the BC 2 N monolayer as an anode material. Furthermore, the BC 2 N monolayer possesses a lower diffusion barrier (0.40 eV for Na and 0.22 eV for K) and a higher storage capacity (1647 mAh g −1 for Na and 2196 mAh g −1 for K) compared to most conventional two-dimensional anode materials. These exceptional characteristics strongly suggest that the BC 2 N monolayer exhibits significant promise as an electrode material for NIBs and KIBs.