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Metallic B2C3P Monolayer as Li-Ion Battery Materials: A First-Principles Study

He-Nan International Joint Laboratory of MXene Materials Microstructure, College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China
College of Mechanical and Electrical Engineering, Nanyang Normal University, Nanyang 473061, China
Authors to whom correspondence should be addressed.
Processes 2022, 10(9), 1809;
Received: 19 August 2022 / Revised: 2 September 2022 / Accepted: 4 September 2022 / Published: 7 September 2022
(This article belongs to the Special Issue Materials and Processing for Lithium-Ion Batteries and Beyond)


The search for and design of high-performance electrode materials is always an important topic in rechargeable batteries. Using a global structure prediction method together with first-principles calculations, a free-standing two-dimensional B2C3P monolayer with honeycomb structure was identified. The stability of the B2C3P monolayer was confirmed by cohesive energy, phonon curves, and ab initio molecular dynamics calculations. Of note, the B2C3P monolayer was demonstrated to be metallic, which shows excellent performance for Li-ion batteries. For example, the B2C3P monolayer also exhibited a metallic characteristic after Li adsorption, therefore the ability to keep good electrical conductivity during battery operation. Furthermore, when a B2C3P monolayer is used as a lithium-ion battery anode, it shows an ultra-high theoretical capacity of 3024 mAh/g, and a comparatively low diffusion barrier of 0.33 eV. All calculated results showed that the B2C3P monolayer is an appealing anode material, and has great potential in energy storage devices.

1. Introduction

After the successful synthesis of graphene in 2004 [1], two-dimensional (2D) materials have attracted broad interest for their unique physical and chemical properties. They can be applied to various fields including catalysis, sensors, electronics, optoelectronics, and electrode materials [2,3]. Some typical 2D materials such as silicene, borophene, phosphorene, transition-metal dichalcogenides (TMDCs), and hexagonal boron nitride, have been fabricated experimentally [4,5,6,7,8,9,10,11,12,13,14]. Among these reported materials, graphene and phosphorene are two important and representative materials. Unfortunately, graphene is limited in widespread application due to zero band-gap. By contrast, phosphorene shows excellent electronic properties. It has a tunable direct band gap with changes of thickness, and also shows good performance in phosphorene-related field-effect transistors [15]. Furthermore, phosphorene has been proved as a good anode material with high theoretical capacity in some metal-ion batteries [16,17]. However, phosphorene tends to react with oxygen in air and become unstable, restricting the application of phosphorene in practical equipment. Due to the disadvantages of graphene and phosphorene, various other 2D carbides and phosphides with good stability and good performance for electronic devices [18,19,20,21,22] have been investigated. Most notably, 2D materials composed of phosphorus and carbide elements combine the advantages of phosphorene and graphene, and exhibit excellent electrical and optical properties [23,24].
Ternary two-dimensional materials typically consist of carbide, and boron with group V elements attract much attentions. For example, Zhao et al. designed a semiconducting 2D penta-BCN with a direct band-gap (2.81 eV), which shows intrinsic piezoelectric properties [25]. Kistanov et al. [26] theoretically predicted a 2D B3C2P3 with a tunable band gap by applying external strain. Furthermore, the designed B3C2P3 monolayer shows low barriers during water or hydrogen molecule dissociation processes. Therefore, the 2D B3C2P3 is believed to be promising for applications in renewable energy and optoelectronic nano-devices. The BC2P and BC3P3 monolayers have also been found to be semiconductors with suitable band gaps [27]. Recently, Tang et al. [28] predicted a BC6P monolayer, which is isostructural and isoelectronic to graphene. Furthermore, BC6P monolayer possesses high capacity (1410 mAh/g) as an anode in K-ion batteries. Based on the above results, we believe that for two-dimensional materials composed of boron and carbon with group V elements, there are still many unknown structures with interesting functional properties to be explored.
Although many two-dimensional materials have been experimentally synthesized, discovering and designing new two-dimensional materials with excellent physical and chemical properties are still a challenge, and remain highly needed. In this paper, we predicted as stable 2D planar B2C3P using a large-scale computer structure search method, which showed excellent electrode performance for Li-ion batteries (LIBs). The B2C3P monolayer exhibited an ultra-high theoretical storage capacity for lithium ions and a relatively low diffusion energy barrier. Therefore, 2D B2C3P is an appealing candidate for a super-high capacity anode of lithium ion batteries.

2. Computational Methods

The stable structure of two-dimensional B2C3P was predicted using the swarm-intelligence structure search method, together with first-principle calculations, as implemented in CALYPSO software [29,30]. One to four formula units (f.u.) of B2C3P were used to perform structure searching. To ensure the convergence, the population size was set to 40, while the number of generations was set to 30. To remove the interactions among atoms along the vacuum layer direction, a vacuum layer with a length of 20 Å was used when the 2D B2C3P structure was predicted. To obtain stable structures of the absorbed lithium atoms on the B2C3P monolayer, we also used CALYPSO software to find the stable absorbed structures of 2D B2C3P with lithium atoms, up to 12 per unit B2C3P monolayer.
Structural relaxation and total energy simulations were investigated using Vienna ab initio simulation package (VASP) [31]. In order to describe the ion-electron interactions, the projected–augmented wave (PAW) method was used [32,33]. The Perdew–Burke–Ernzerhof (PBE) and generalized gradient approximation (GGA) methods [34] were used for the electronic exchange correlation function. The energy cut-off, precision energy and precision force were set as 520 eV, 10−5 eV and 10−3 eV/atom, respectively. Monkhorst–Pack k-point grid density was set as 2 π × 0.03 Å−1.
The phonon dispersion curves of B2C3P were performed with the density-functional response method using Quantum-ESPRESSO software [35]. Ab initio molecular dynamics (AIMD) simulations were used to test thermal stability of B2C3P, and a large 3 × 3 × 1 supercell was constructed during the AIMD calculations. We used a climbing-image nudged elastic band (CI-NEB) method in order to determine the diffusion pathways of Li atoms on the surface of B2C3P [36]. The elastic constants were calculated using the strain-stress method as implemented in the VASDPKIT software [37].
The adsorption energy of lithium atoms on the B2C3P monolayer using 3 × 3 × 1 supercell were obtained from:
E a d = ( E t o t a l E B 2 C 3 P n E L i ) / n
where E t o t a l , E B 2 C 3 P , and E L i are the corresponding total energies of the Li-ion adsorbed monolayer, B2C3P monolayer, and one Li atom in its bulk phase.
The formation energy was estimated using the following formula:
E f ( x ) = ( E B 2 C 3 P L i x E B 2 C 3 P x E L i ) / ( x + 1 )
where E B 2 C 3 P L i x and E B 2 C 3 P are the energies for E B 2 C 3 P L i x and pure E B 2 C 3 P monolayer, respectively.
For LixB2C3P at a given concentration x, electrode potential V with respect charge/discharge process was defined as:
V = E ( x 2 ) E ( x 1 ) ( x 2 x 1 ) E L i e ( x 2 x 1 )
where E ( x 2 ) and E ( x 1 ) represent LixB2C3P total energies with two different concentrations, and E L i is the energy of one Li atom in its bulk metal.
The battery capacity was further calculated by means of the following formula:
C M = n F M
where n represents the number of adsorbed Li atoms per B2C3P formula unit, F represents the Faraday constant (26,801 mAhmol−1), and M represents the molar weight of B2C3P in gmol−1.
Energy density is usually defined either by the gravimetric energy density Wh kg1 or the volumetric energy density (WhL1). The gravimetric energy density was calculated by the following formula:
ε M = E B 2 C 3 P L i n max E B 2 C 3 P n max E L i Σ M
where Σ M is the sum of the formula mole weights of the two reactants ( B 2 C 3 P monolayer and Li atoms), E B 2 C 3 P L i n m a x represents the energy of the B2C3P with the maximum absorbed Li atoms, and nmax represents the maximum number of the absorb lithium atoms on the B2C3P.

3. Results and Discussion

The most stable structure of B2C3P was obtained using the CALYPSO package with first-principles calculations. As shown in Figure 1a, the optimized B2C3P crystallized in a hexagonal structure, P 6 ¯ m2 (No. 189), with a0 = 4.8073 Å. The primitive cell of B2C3P contained two B, three C and one P atoms forming a hexagonal unit, as shown in Figure 1b. The B atom at the Wyckoff 2d site was coordinated with a B-C distance of 1.551 Å and bond angle of α = 120°. The P atom at the 1b site was also trigonally coordinated with a P-C distance of 1.711 Å, and bond angle of γ = 120°. We noticed that the B-C bond lengths in B2C3P were shorter than in the B4C3 (1.76 Å) monolayer [24], and the P-C bond lengths in B2C3P were also shorter than in the PC (1.83 Å) monolayer [38]. The C atom at the 3 g site exhibits slightly distorted trigonal coordination, with a bond angle of β = 116.5° for B-C-P, and θ = 127.0° for B-C-B. This distortion was ascribed to the radius and electronegativity differences between B and P atoms. In addition, using the total charge density minus the corresponding charge density of each atom at their specified position, we calculated its charge density difference (Figure 1c) and further assessed the chemical bonding of B2C3P. Obviously, there was a strong covalent bond between B and C. As for the P-C bond, the charges tended to shift from P to C atoms, suggesting that there was a polarized covalent bond between P and C. The Bader charge analysis [39] revealed that a 0.33 e was transferred from every P to every C. From the band structure and total density of states for B2C3P, as shown in Figure 1d, we saw that sever bands across the Fermi level, and the total density of states at Fermi level were not zero, therefore, B2C3P showed a metallic characteristic. In fact, the unit cell of B2C3P had an odd number of electrons, therefore, a half-filled band appeared, leading to the metallic characteristic of B2C3P.
The thermal stability of the B2C3P monolayer was checked by cohesive energy calculations using the formula E c o h = ( 2 E B + 3 E C + E P E B 2 C 3 P ) / 6 , where E B , E C , E P , and E B 2 C 3 P are the total energies of an isolated B atom, C atom, P atom, and one primitive cell of the B2C3P monolayer, respectively. The calculated cohesive energy value of B2C3P was 6.82 eV/atom, which is comparable to graphene, and higher than other experimentally synthesized two-dimensional materials. For example, the cohesive energy values of borophene, silicene and phosphorene are 5.99, 4.57, and 3.30 eV/atom, respectively [40,41,42], showing that the B2C3P monolayer has thermodynamic stability. The phonon dispersion curves were also calculated to check the dynamical stability, which are shown in Figure S1a. There were no negative frequencies in all the Brillouin zones, confirming that the B2C3P monolayer is dynamically stable. We also performed AIMD calculations to check the thermal stability of 2D B2C3P. The AIMD were carried out in a canonical ensemble (NVT) with a time step of 1 fs, and a total of 5 ps at a temperature of 400 K were performed. The vibration behavior of the total potential energy with increasing time is given in Figure S1b. The final structural configuration of 2D B2C3P at the end of AIMD is also illustrated in Figure S1b. It can be seen that the total potential energy was nearly invariant with increasing time, and the initial structure was generally well-kept after 5 ps, so the 2D B2C3P had good thermal stability even at 400 K temperature. The mechanical stability was checked by calculating the linear elastic constants of B2C3P. The four elastic constants were calculated to be C11 = C22 = 214.6 N/m, C12 = 61.4 N/m, and C66 = 76.6 N/m, respectively. Therefore, the 2D B2C3P met the mechanical equilibrium conditions C 11 C 22 C 12 2 > 0 and C 66 > 0 , and, therefore, the B2C3P monolayer is mechanically stable.
Due to the prominent contradiction of energy, there is an urgent need to develop new batteries with high energy density electrode materials and excellent performance. Various anode materials are being explored for batteries [43,44,45,46,47]. Among these anode materials, 2D materials generally have a large surface-area-to-volume ratio as well as a larger contact area between the electrolyte and electrode, which are believed to be promising anode materials for the next generation of metal ion batteries. Particularly in our case, the metallic characteristics of B2C3P benefit its potential application as a battery anode material. Therefore, we checked the performance of B2C3P as a lithium-ion battery anode. We first calculated the adsorption properties of Li atoms on 2D B2C3P using a 3 × 3 × 1 supercell as the substrate. According to the crystal lattice symmetry of B2C3P, there were six nonequivalent lithium-ion adsorption sites (Figure 2a). After the lattice relaxations of the adsorbed B2C3P, only S1, S4, S5 and S6 sites remained, because the Li atoms in S1, S2, and S3 were found to be optimized equivalent sites. The adsorption energies of Li atom are shown in Figure 2b. The absorbed energies were −1.82 eV (S1), −1.510 eV (S4), −1.80 eV (S5), and −1.190 (S6), respectively. The adsorption energy on S6 was larger by about 0.63 eV, than the Li atom on S1 and S5, indicating that the adsorption of the Li atom on the top site of P atom, is impossible. We also noticed that the adsorption energy on S1 and S5 was nearly the same.
In order to investigate the interaction between Li-ions and the 2D B2C3P monolayer, the charge density difference (CDD) was calculated, and is given in Figure 2c. The CDD can be expressed by the following formula:
Δ ρ = ρ L i B 2 C 3 P ρ B 2 C 3 P ρ L i
where ρ LiB 2 C 3 P , ρ B 2 C 3 P , and ρ Li are the charge densities of B2C3P with adsorbed Li atom, pure B2C3P, and the isolated Li atom, respectively. The electrons mainly accumulated between the Li atom and the adjacent B/C/P atom of B2C3P surface, resulting in strong chemical B/C/P-Li bonding. The total DOSs of LiB2C3P is plotted in Figure 2d. It was found that a great quantity of electronic states appear at the Fermi level, indicating that 2D B2C3P was a metal instead of a semiconductor, after Li atom absorption. The metal character of LiB2C3P will generally keep good electronic conduction when B2C3P is used in battery electrodes.
To quantify the diffusion barrier of the Li-ion on the B2C3P monolayer, the diffusion energy between two adjacent sites was calculated using a climbing-image nudged elastic band (CI-NEB) method. Two possible diffusion paths were explored, as illustrated by the red arrows in Figure 3. The real Li-ion diffusion trajectory for path 2 showed large changes after full relaxation (See Figure 3b), which finally, became nearly equivalent to path 1. Therefore, the diffusion barriers of path 1 and path 2 were both about 0.33 eV, which is nearly equal to graphene (0.33 eV) [48], and smaller than Si3C (0.46 eV) [49] and commercially-available graphite (0.4 eV) [50].
To obtain the intermediate states of the lithiated process, the formation energies for each concentration were calculated by Equation (2), as shown in Figure 4a. The dashed red lines connect the lowest formation energies forming convex hulls. If the structures are located on the hull, it means that the structures were thermodynamically stable after adsorption. The compounds of B2C3PLix (x/(x + 1) = 0.1, 0.2, 0.5, 0.8, and 0.91) lay on the red convex hull, meaning that B2C3PLi0.11, B2C3PLi0.25, B2C3PLi1.0, B2C3PLi4.0, and B2C3PLi10.0 were stable intermediate states. The stable configurations for Li-ion adsorption for each Li concentration of LixB2C3P, are given in Figure S2 (Supporting Information).
The open circuit voltages (OCV) of B2C3P for LIBs were calculated according to Formula (5). As seen in Figure 4b, there were five plateaus (B2C3P→B2C3PLi0.11, B2C3PLi0.11→B2C3PLi0.25, B2C3PLi0.2→B2C3PLi1.0, B2C3PLi1.0→B2C3PLi4.0, and B2C3PLi4.0→B2C3PLi10.0) in the entire process of lithium insertion. According to Equation (3), the OCV for the five plateaus were 1.99, 1.62, 1.34, 0.10, and 0.06 V, respectively. The calculated average OCV of B2C3P was 0.85 V, which implied that B2C3P is a suitable anode material for LIBs.
Storage capacity is the most important parameter of an electrode material. Based on the convex hull, the B2C3P monolayer can absorb a maximum of 10 Li-ions for each B2C3P unit cell, in theory. We checked the stability of Li10B2C3P by performing an AIMD simulation at a temperature of 300 K, up to 8 ps. It was observed that the final structure of a B2C3P unit cell with 10 Li-ions adsorption kept structural integrity, as shown in Figure S3 (Supporting Information). According to Equation (4), the stoichiometry LixB2C3P has a maximum theoretical capacity up to 3024 mAhg−1. Therefore, we can see that B2C3P has a strong ability to store lithium. We note that electrodes of Li-ion batteries are usually intercalation materials, therefore, when B2C3P is used as a lithium-ion battery anode, the real capacity might not reach such a high storage capacity. However, if only one layer of lithium atoms were to be absorbed on the B2C3P monolayer (B2C3PLi4), the theoretical capacity reached about 1210 mAhg−1. Therefore, the storage capacity of B2C3P is much higher than many other anode materials. For example, the storage capacities of Zr2B2 [51], Ti2BN [52], and graphite [50], are 526 mAhg−1, 889 mAhg−1, and 72 mAhg−1, respectively. We also calculated the gravimetric energy density according to Equation (5); on the basis that only one layer of lithium atoms were to be absorbed on the B2C3P monolayer (B2C3PLi4), then the energy density value was calculated to be 405 Whkg−1, and the total volume expansion was calculated to be as low as −0.4%, which is much smaller than graphite (10%) [53]. All the results indicated that B2C3P monolayer is an appealing anode material.

4. Conclusions

In summary, we found a new two-dimensional structure for B2C3P using the swarm-intelligence structure prediction method combined with first-principles calculations. The phonon curves without negative frequency and molecular dynamic simulations showed that B2C3P exhibits dynamic stability. We further investigated its electronic and lithium battery properties based on ab initio methods. B2C3P shows metallic characteristic. More importantly, B2C3P has an ultra-high theoretical capacity, and a low diffusion barrier of 0.33 eV, which offers a critical reference for the discovery of new two-dimensional anode materials with ultra-high capacity. Our newly found 2D B2C3P shows that it might be an excellent energy-storage device, so we hope our work can encourage experimental research on the B2C3P monolayer in the future.

Supplementary Materials

The following supporting information can be downloaded at:, Figure S1: (a) Phonon spectra curve of B2C3P. (b)Variations of temperature in the AIMD simulations of the B2C3P at 400 K. The insets are the structure of B2C3P at the end of the AIMD simulation; Figure S2: Top and side views of the lithiated structures of (a) Li0.25 B2C3P, (b) Li1.0 B2C3P, (c) Li4.0 B2C3P, (d) Li10.0 B2C3P. The B, C, P, and Li atoms are denoted by green, brown, gray, and purple balls, respectively. When all lithiated structures are illustrated, a 2 × 2 × 1 supercell is used; Figure S3: Variations of temperature (a), and energy (b), in the AIMD simulations of the Li10.0B2C3P at 300 K. Li10.0 B2C3P with Li-ions adsorbed on the surface of 2D B2C3P monolayer before the AIMD simulation (c), and the structure of Li10.0B2C3P at the end of the AIMD simulation (d).

Author Contributions

Investigation; Methodology; Writing—original draft D.Z.; Supervision; Formal analysis; Visualization Z.W.; Resources; Funding acquisition; Writing—review & editing J.C.; Supervision; Project administration; Software; Visualization, C.P. All authors have read and agreed to the published version of the manuscript.


This research was funded by Henan Joint Funds of the National Natural Science Foundation of China (grant No. U1904612), the Natural Science Foundation of Henan Province (grant Nos. 222300420506, 222300420255), the Key Scientific and Technological Project of Technology Department of Henan Province of China (grant No. 212102210448), and the Science Fund of Educational Department of Henan Province of China (grant No. 21A140020).

Data Availability Statement

Data available on request from the authors.

Conflicts of Interest

The authors confirm having no known involvement in any organization with any financial interest in the subject and materials presented in this manuscript.


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Figure 1. (a) Top and side view illustration of B2C3P, and the solid line frame represents the unit cell of B2C3P. (b) B2C3P hexagonal geometry. B, C and P atoms are colored green, brown, and grey, respectively. (c) Charge density difference of B2C3P. The gold color (i.e., 0.025 eÅ−3) means a charge density increase, while the cyan color (i.e., 0.025 eÅ−3) means a charge density decrease. (d) Electronic band structure and total density of states of B2C3P.
Figure 1. (a) Top and side view illustration of B2C3P, and the solid line frame represents the unit cell of B2C3P. (b) B2C3P hexagonal geometry. B, C and P atoms are colored green, brown, and grey, respectively. (c) Charge density difference of B2C3P. The gold color (i.e., 0.025 eÅ−3) means a charge density increase, while the cyan color (i.e., 0.025 eÅ−3) means a charge density decrease. (d) Electronic band structure and total density of states of B2C3P.
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Figure 2. (a) The various sites for Li adsorption on the surface of the B2C3P. (b) Adsorption energies for Li on the surface of 2D B2C3P. (c) The charge density difference of the Li-adsorbed B2C3P. The yellow and blue areas denote the electron gain and loss with the iso-surface level of 0.002 eÅ−3. (d) The total density of states of B18C27P9Li.
Figure 2. (a) The various sites for Li adsorption on the surface of the B2C3P. (b) Adsorption energies for Li on the surface of 2D B2C3P. (c) The charge density difference of the Li-adsorbed B2C3P. The yellow and blue areas denote the electron gain and loss with the iso-surface level of 0.002 eÅ−3. (d) The total density of states of B18C27P9Li.
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Figure 3. Diffusion barriers of Li-ion on the surface of B2C3P along (a) path 1, and (b) path 2. The insets are the corresponding trajectories of Li-ion diffusion over the surface of B2C3P, while the red arrows indicate the settled artificially-initial paths.
Figure 3. Diffusion barriers of Li-ion on the surface of B2C3P along (a) path 1, and (b) path 2. The insets are the corresponding trajectories of Li-ion diffusion over the surface of B2C3P, while the red arrows indicate the settled artificially-initial paths.
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Figure 4. (a) Formation energies of B2C3PLix related to 2D B2C3P and bulk Li metal. Data points on the convex hull (red squares) are the stable adsorptions against decomposition. (b) Electrode potential of Li-intercalated B2C3P.
Figure 4. (a) Formation energies of B2C3PLix related to 2D B2C3P and bulk Li metal. Data points on the convex hull (red squares) are the stable adsorptions against decomposition. (b) Electrode potential of Li-intercalated B2C3P.
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Zhou, D.; Wang, Z.; Cheng, J.; Pu, C. Metallic B2C3P Monolayer as Li-Ion Battery Materials: A First-Principles Study. Processes 2022, 10, 1809.

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Zhou D, Wang Z, Cheng J, Pu C. Metallic B2C3P Monolayer as Li-Ion Battery Materials: A First-Principles Study. Processes. 2022; 10(9):1809.

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Zhou, Dawei, Zhuo Wang, Jinbing Cheng, and Chunying Pu. 2022. "Metallic B2C3P Monolayer as Li-Ion Battery Materials: A First-Principles Study" Processes 10, no. 9: 1809.

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