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

Abstract

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$\pi$ × 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:

$$E_{ad}=(E_{total}-E_{B_2{C}_{3}P}-n{E}_{Li})/n$$

(1)

where $E_{total}$, $E_{B_2{C}_{3}P}$, and $E_{Li}$ 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:

$$E_f(x)=(E_{B_2{C}_{3}PL{i}_x}-E_{B_2{C}_{3}P}-x{E}_{Li})/(x+1)$$

(2)

where $E_{B_2{C}_{3}PL{i}_x}$ and $E_{B_2{C}_{3}P}$ are the energies for $E_{B_2{C}_{3}PL{i}_x}$ and pure $E_{B_2{C}_{3}P}$ monolayer, respectively.

For Li_xB₂C₃P at a given concentration x, electrode potential V with respect charge/discharge process was defined as:

$$V=\frac{E(x_2)-E(x_1)-(x_2-x_1)E_{Li}}{e(x_2-x_1)}$$

(3)

where $E(x_2)$ and $E(x_1)$ represent Li_xB₂C₃P total energies with two different concentrations, and $E_{Li}$ is the energy of one Li atom in its bulk metal.

The battery capacity was further calculated by means of the following formula:

$$C_M=\frac{n\mathrm{F}}{M}$$

(4)

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 kg⁻¹ or the volumetric energy density (WhL⁻¹). The gravimetric energy density was calculated by the following formula:

$${\epsilon }_M=\frac{E_{B_2{C}_{3}PL{i}_{n_{\max }}}-E_{B_2{C}_{3}P}-n_{\max }{E}_{Li}}{\Sigma M}$$

(5)

where $\Sigma M$ is the sum of the formula mole weights of the two reactants ($B_2{C}_{3}P$ monolayer and Li atoms), $E_{B_2{C}_{3}PL{i}_{n_{max}}}$ represents the energy of the B₂C₃P with the maximum absorbed Li atoms, and n_max 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$\overline{6}$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 $\alpha$ = 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 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 $E_{coh}=(2E_{\mathrm{B}}+3E_{\mathrm{C}}+E_{\mathrm{P}}-E_{{\mathrm{B}}_2{\mathrm{C}}_3\mathrm{P}})/6$, 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 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 ${\mathrm{C}}_{11}{\mathrm{C}}_{22}{-\mathrm{C}}_{12}^2>0$ and ${\mathrm{C}}_{66}>0$, 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:

$$\Delta \rho ={\rho }_{Li{B}_2{C}_{3}P}-{\rho }_{B_2{C}_{3}P}-{\rho }_{Li}$$

(6)

where ${\rho }_{{\mathrm{LiB}}_2{\mathrm{C}}_3\mathrm{P}}$, ${\rho }_{{\mathrm{B}}_2{\mathrm{C}}_3\mathrm{P}}$, and ${\rho }_{\mathrm{Li}}$ 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 B₂C₃PLi_x (x/(x + 1) = 0.1, 0.2, 0.5, 0.8, and 0.91) lay on the red convex hull, meaning that B₂C₃PLi_0.11, B₂C₃PLi_0.25, B₂C₃PLi_1.0, B₂C₃PLi_4.0, and B₂C₃PLi_10.0 were stable intermediate states. The stable configurations for Li-ion adsorption for each Li concentration of Li_xB₂C₃P, 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→B₂C₃PLi_0.11, B₂C₃PLi_0.11→B₂C₃PLi_0.25, B₂C₃PLi_0.2→B₂C₃PLi_1.0, B₂C₃PLi_1.0→B₂C₃PLi_4.0, and B₂C₃PLi_4.0→B₂C₃PLi_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 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 Li_xB₂C₃P 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.