#
Metallic B_{2}C_{3}P Monolayer as Li-Ion Battery Materials: A First-Principles Study

^{1}

^{2}

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## Abstract

**:**

_{2}C

_{3}P monolayer with honeycomb structure was identified. The stability of the B

_{2}C

_{3}P monolayer was confirmed by cohesive energy, phonon curves, and ab initio molecular dynamics calculations. Of note, the B

_{2}C

_{3}P monolayer was demonstrated to be metallic, which shows excellent performance for Li-ion batteries. For example, the B

_{2}C

_{3}P monolayer also exhibited a metallic characteristic after Li adsorption, therefore the ability to keep good electrical conductivity during battery operation. Furthermore, when a B

_{2}C

_{3}P 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 B

_{2}C

_{3}P monolayer is an appealing anode material, and has great potential in energy storage devices.

## 1. Introduction

_{3}C

_{2}P

_{3}with a tunable band gap by applying external strain. Furthermore, the designed B

_{3}C

_{2}P

_{3}monolayer shows low barriers during water or hydrogen molecule dissociation processes. Therefore, the 2D B

_{3}C

_{2}P

_{3}is believed to be promising for applications in renewable energy and optoelectronic nano-devices. The BC

_{2}P and BC

_{3}P

_{3}monolayers have also been found to be semiconductors with suitable band gaps [27]. Recently, Tang et al. [28] predicted a BC

_{6}P monolayer, which is isostructural and isoelectronic to graphene. Furthermore, BC

_{6}P 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.

_{2}C

_{3}P using a large-scale computer structure search method, which showed excellent electrode performance for Li-ion batteries (LIBs). The B

_{2}C

_{3}P monolayer exhibited an ultra-high theoretical storage capacity for lithium ions and a relatively low diffusion energy barrier. Therefore, 2D B

_{2}C

_{3}P is an appealing candidate for a super-high capacity anode of lithium ion batteries.

## 2. Computational Methods

_{2}C

_{3}P 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 B

_{2}C

_{3}P 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 B

_{2}C

_{3}P structure was predicted. To obtain stable structures of the absorbed lithium atoms on the B

_{2}C

_{3}P monolayer, we also used CALYPSO software to find the stable absorbed structures of 2D B

_{2}C

_{3}P with lithium atoms, up to 12 per unit B

_{2}C

_{3}P monolayer.

^{−5}eV and 10

^{−3}eV/atom, respectively. Monkhorst–Pack k-point grid density was set as 2$\pi $ × 0.03 Å

^{−1}.

_{2}C

_{3}P 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 B

_{2}C

_{3}P, 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 B

_{2}C

_{3}P [36]. The elastic constants were calculated using the strain-stress method as implemented in the VASDPKIT software [37].

_{2}C

_{3}P monolayer using 3 × 3 × 1 supercell were obtained from:

_{2}C

_{3}P monolayer, and one Li atom in its bulk phase.

_{x}B

_{2}C

_{3}P at a given concentration x, electrode potential V with respect charge/discharge process was defined as:

_{x}B

_{2}C

_{3}P total energies with two different concentrations, and ${E}_{Li}$ is the energy of one Li atom in its bulk metal.

_{2}C

_{3}P formula unit, F represents the Faraday constant (26,801 mAhmol

^{−1}), and M represents the molar weight of B

_{2}C

_{3}P in gmol

^{−1}.

^{−}

^{1}or the volumetric energy density (WhL

^{−}

^{1}). The gravimetric energy density was calculated by the following formula:

_{2}C

_{3}P with the maximum absorbed Li atoms, and n

_{max}represents the maximum number of the absorb lithium atoms on the B

_{2}C

_{3}P.

## 3. Results and Discussion

_{2}C

_{3}P was obtained using the CALYPSO package with first-principles calculations. As shown in Figure 1a, the optimized B

_{2}C

_{3}P crystallized in a hexagonal structure, P$\overline{6}$m2 (No. 189), with a

_{0}= 4.8073 Å. The primitive cell of B

_{2}C

_{3}P 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 $\alpha $ = 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 $\gamma $ = 120°. We noticed that the B-C bond lengths in B

_{2}C

_{3}P were shorter than in the B

_{4}C

_{3}(1.76 Å) monolayer [24], and the P-C bond lengths in B

_{2}C

_{3}P 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 B

_{2}C

_{3}P. 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 B

_{2}C

_{3}P, 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, B

_{2}C

_{3}P showed a metallic characteristic. In fact, the unit cell of B

_{2}C

_{3}P had an odd number of electrons, therefore, a half-filled band appeared, leading to the metallic characteristic of B

_{2}C

_{3}P.

_{2}C

_{3}P monolayer was checked by cohesive energy calculations using the formula ${E}_{coh}=(2{E}_{\mathrm{B}}+3{E}_{\mathrm{C}}+{E}_{\mathrm{P}}-{E}_{{\mathrm{B}}_{2}{\mathrm{C}}_{3}\mathrm{P}})/6$, where ${E}_{\mathrm{B}}$, ${E}_{\mathrm{C}}$, ${E}_{\mathrm{P}}$, and ${E}_{{\mathrm{B}}_{2}{\mathrm{C}}_{3}\mathrm{P}}$ are the total energies of an isolated B atom, C atom, P atom, and one primitive cell of the B

_{2}C

_{3}P monolayer, respectively. The calculated cohesive energy value of B

_{2}C

_{3}P 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 B

_{2}C

_{3}P 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 B

_{2}C

_{3}P monolayer is dynamically stable. We also performed AIMD calculations to check the thermal stability of 2D B

_{2}C

_{3}P. 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 B

_{2}C

_{3}P 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 B

_{2}C

_{3}P had good thermal stability even at 400 K temperature. The mechanical stability was checked by calculating the linear elastic constants of B

_{2}C

_{3}P. The four elastic constants were calculated to be C

_{11}= C

_{22}= 214.6 N/m, C

_{12}= 61.4 N/m, and C

_{66}= 76.6 N/m, respectively. Therefore, the 2D B

_{2}C

_{3}P met the mechanical equilibrium conditions ${\mathrm{C}}_{11}{\mathrm{C}}_{22}{-\mathrm{C}}_{12}^{2}>0$ and ${\mathrm{C}}_{66}>0$, and, therefore, the B

_{2}C

_{3}P monolayer is mechanically stable.

_{2}C

_{3}P benefit its potential application as a battery anode material. Therefore, we checked the performance of B

_{2}C

_{3}P as a lithium-ion battery anode. We first calculated the adsorption properties of Li atoms on 2D B

_{2}C

_{3}P using a 3 × 3 × 1 supercell as the substrate. According to the crystal lattice symmetry of B

_{2}C

_{3}P, there were six nonequivalent lithium-ion adsorption sites (Figure 2a). After the lattice relaxations of the adsorbed B

_{2}C

_{3}P, 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.

_{2}C

_{3}P monolayer, the charge density difference (CDD) was calculated, and is given in Figure 2c. The CDD can be expressed by the following formula:

_{2}C

_{3}P with adsorbed Li atom, pure B

_{2}C

_{3}P, and the isolated Li atom, respectively. The electrons mainly accumulated between the Li atom and the adjacent B/C/P atom of B

_{2}C

_{3}P surface, resulting in strong chemical B/C/P-Li bonding. The total DOSs of LiB

_{2}C

_{3}P is plotted in Figure 2d. It was found that a great quantity of electronic states appear at the Fermi level, indicating that 2D B

_{2}C

_{3}P was a metal instead of a semiconductor, after Li atom absorption. The metal character of LiB

_{2}C

_{3}P will generally keep good electronic conduction when B

_{2}C

_{3}P is used in battery electrodes.

_{2}C

_{3}P 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 Si

_{3}C (0.46 eV) [49] and commercially-available graphite (0.4 eV) [50].

_{2}C

_{3}PLi

_{x}(x/(x + 1) = 0.1, 0.2, 0.5, 0.8, and 0.91) lay on the red convex hull, meaning that B

_{2}C

_{3}PLi

_{0.11}, B

_{2}C

_{3}PLi

_{0.25}, B

_{2}C

_{3}PLi

_{1.0}, B

_{2}C

_{3}PLi

_{4.0}, and B

_{2}C

_{3}PLi

_{10.0}were stable intermediate states. The stable configurations for Li-ion adsorption for each Li concentration of Li

_{x}B

_{2}C

_{3}P, are given in Figure S2 (Supporting Information).

_{2}C

_{3}P for LIBs were calculated according to Formula (5). As seen in Figure 4b, there were five plateaus (B

_{2}C

_{3}P→B

_{2}C

_{3}PLi

_{0.11}, B

_{2}C

_{3}PLi

_{0.11}→B

_{2}C

_{3}PLi

_{0.25}, B

_{2}C

_{3}PLi

_{0.2}→B

_{2}C

_{3}PLi

_{1.0}, B

_{2}C

_{3}PLi

_{1.0}→B

_{2}C

_{3}PLi

_{4.0}, and B

_{2}C

_{3}PLi

_{4.0}→B

_{2}C

_{3}PLi

_{10.0}) 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 B

_{2}C

_{3}P was 0.85 V, which implied that B

_{2}C

_{3}P is a suitable anode material for LIBs.

_{2}C

_{3}P monolayer can absorb a maximum of 10 Li-ions for each B

_{2}C

_{3}P unit cell, in theory. We checked the stability of Li

_{10}B

_{2}C

_{3}P by performing an AIMD simulation at a temperature of 300 K, up to 8 ps. It was observed that the final structure of a B

_{2}C

_{3}P unit cell with 10 Li-ions adsorption kept structural integrity, as shown in Figure S3 (Supporting Information). According to Equation (4), the stoichiometry Li

_{x}B

_{2}C

_{3}P has a maximum theoretical capacity up to 3024 mAhg

^{−1}. Therefore, we can see that B

_{2}C

_{3}P has a strong ability to store lithium. We note that electrodes of Li-ion batteries are usually intercalation materials, therefore, when B

_{2}C

_{3}P 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 B

_{2}C

_{3}P monolayer (B

_{2}C

_{3}PLi

_{4}), the theoretical capacity reached about 1210 mAhg

^{−1}. Therefore, the storage capacity of B

_{2}C

_{3}P is much higher than many other anode materials. For example, the storage capacities of Zr

_{2}B

_{2}[51], Ti

_{2}BN [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 B

_{2}C

_{3}P monolayer (B

_{2}C

_{3}PLi

_{4}), 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 B

_{2}C

_{3}P monolayer is an appealing anode material.

## 4. Conclusions

_{2}C

_{3}P using the swarm-intelligence structure prediction method combined with first-principles calculations. The phonon curves without negative frequency and molecular dynamic simulations showed that B

_{2}C

_{3}P exhibits dynamic stability. We further investigated its electronic and lithium battery properties based on ab initio methods. B

_{2}C

_{3}P shows metallic characteristic. More importantly, B

_{2}C

_{3}P 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 B

_{2}C

_{3}P shows that it might be an excellent energy-storage device, so we hope our work can encourage experimental research on the B

_{2}C

_{3}P monolayer in the future.

## Supplementary Materials

_{2}C

_{3}P. (b)Variations of temperature in the AIMD simulations of the B

_{2}C

_{3}P at 400 K. The insets are the structure of B

_{2}C

_{3}P at the end of the AIMD simulation; Figure S2: Top and side views of the lithiated structures of (a) Li

_{0.25}B

_{2}C

_{3}P, (b) Li

_{1.0}B

_{2}C

_{3}P, (c) Li

_{4.0}B

_{2}C

_{3}P, (d) Li

_{10.0}B

_{2}C

_{3}P. 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 Li

_{10.0}B

_{2}C

_{3}P at 300 K. Li

_{10.0}B

_{2}C

_{3}P with Li-ions adsorbed on the surface of 2D B

_{2}C

_{3}P monolayer before the AIMD simulation (c), and the structure of Li

_{10.0}B

_{2}C

_{3}P at the end of the AIMD simulation (d).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Top and side view illustration of B

_{2}C

_{3}P, and the solid line frame represents the unit cell of B

_{2}C

_{3}P. (

**b**) B

_{2}C

_{3}P hexagonal geometry. B, C and P atoms are colored green, brown, and grey, respectively. (

**c**) Charge density difference of B

_{2}C

_{3}P. 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 B

_{2}C

_{3}P.

**Figure 2.**(

**a**) The various sites for Li adsorption on the surface of the B

_{2}C

_{3}P. (

**b**) Adsorption energies for Li on the surface of 2D B

_{2}C

_{3}P. (

**c**) The charge density difference of the Li-adsorbed B

_{2}C

_{3}P. 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 B

_{18}C

_{27}P

_{9}Li.

**Figure 3.**Diffusion barriers of Li-ion on the surface of B

_{2}C

_{3}P along (

**a**) path 1, and (

**b**) path 2. The insets are the corresponding trajectories of Li-ion diffusion over the surface of B

_{2}C

_{3}P, while the red arrows indicate the settled artificially-initial paths.

**Figure 4.**(

**a**) Formation energies of B

_{2}C

_{3}PLi

_{x}related to 2D B

_{2}C

_{3}P and bulk Li metal. Data points on the convex hull (red squares) are the stable adsorptions against decomposition. (

**b**) Electrode potential of Li-intercalated B

_{2}C

_{3}P.

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**MDPI and ACS Style**

Zhou, D.; Wang, Z.; Cheng, J.; Pu, C.
Metallic B_{2}C_{3}P Monolayer as Li-Ion Battery Materials: A First-Principles Study. *Processes* **2022**, *10*, 1809.
https://doi.org/10.3390/pr10091809

**AMA Style**

Zhou D, Wang Z, Cheng J, Pu C.
Metallic B_{2}C_{3}P Monolayer as Li-Ion Battery Materials: A First-Principles Study. *Processes*. 2022; 10(9):1809.
https://doi.org/10.3390/pr10091809

**Chicago/Turabian Style**

Zhou, Dawei, Zhuo Wang, Jinbing Cheng, and Chunying Pu.
2022. "Metallic B_{2}C_{3}P Monolayer as Li-Ion Battery Materials: A First-Principles Study" *Processes* 10, no. 9: 1809.
https://doi.org/10.3390/pr10091809