Dong
Fan‡
^{a},
Shaohua
Lu‡
*^{a},
Yundong
Guo
^{b} and
Xiaojun
Hu
*^{a}
^{a}College of Materials Science and Engineering, Zhejiang University of Technology, Hangzhou 310014, China. E-mail: lsh@zjut.edu.cn; huxj@zjut.edu.cn; Fax: +86-571-88871522; Tel: +86-571-88871522
^{b}School of Engineering and Technology, Neijiang Normal University, Neijiang, 641000, China

Received
3rd October 2017
, Accepted 27th November 2017

First published on 28th November 2017

Exploring new two-dimensional materials with novel properties is becoming a particularly important task due to their potential applications in future nano-mechanics, electronics, and optoelectronics. In the present study, the hitherto unknown stable two-dimensional boron carbides with various stoichiometries are revealed via the structure swarm optimization method combined with first-principles calculations. The predicted new compounds are energetically more favorable compared with the previously proposed counterparts. Counterintuitively, we identify two B–C bonding patterns: pyramidal-geometry tetra-coordinated and hexa-coordinated sp^{2} carbon moiety. The intriguing covalent bonding modes create distinct and fascinating physical and chemical properties. For instance, we discover that the predicted B_{4}C_{3} has an ultrahigh Young's modulus that can even outperform graphene; the B_{2}C sheet is metallic with a relatively high superconducting transition temperature (T_{c} ≈ 21.20 K). On the other hand, the well-located band edge makes β-B_{3}C_{2} a potentially promising metal-free optoelectronic material for visible-light water splitting.

In this work, by virtual of structure swarm optimization and first-principles calculations, we perform an extensive theoretical investigation on the ground state structure of 2D B–C compounds with both finite atomic thickness and variable stoichiometry. The energetically stable 2D B–C allotropes featured by hitherto unknown chemical bonding are proposed. The dynamic stability of the proposed structures is confirmed by phonon dispersion spectra and ab initio molecular dynamics (AIMD) simulations. Five of the proposed structures are energetically competitive and might be synthesized under well-controlled experimental conditions. More importantly, we identify 3 new boron-stabilized tetra-coordinate pyramidal, hexa-coordinated sp^{2} (HC-sp^{2}) hybridized carbon, and two-fold coordinated B in extended B–C systems. Furthermore, the metallic B_{2}C is identified and discussed, which exhibits superconductivity with a high T_{c} of 21.20 K. Due to the ideal electronic band gaps and band edge alignments at pH = 0, β-B_{3}C_{2} is an excellent candidate material for visible-light water splitting. To the best of our knowledge, this is the first finding of the potential water splitting catalyst in the B–C system.

in which E

Method | B_{4}C_{3} |
α-B_{3}C_{2} |
β-B_{3}C_{2} |
B_{2}C |
B_{4}C |
---|---|---|---|---|---|

PBE | −0.08 | −0.114 | −0.073 | −0.134 | −0.107 |

HSE | −0.162 | −0.169 | −0.137 | −0.187 | −0.156 |

The calculated relative formation energy of β-B_{3}C_{2} is higher than that of α-B_{3}C_{2} by 0.2 eV per formula. Subsequently, the phase transition from β-B_{3}C_{2} to α-B_{3}C_{2} was investigated by using the nudged elastic band method.^{34} Fig. S1 (ESI†) presents the calculated energy profile relative to the β-B_{3}C_{2} phase. There exists a relatively high energy barrier of 0.80 eV per formula for the phase transition from β-B_{3}C_{2} to α-B_{3}C_{2}, indicating that the β-B_{3}C_{2} phase can be preserved once formed in experiments. On the other hand, further AIMD and phonon calculations demonstrate that these B–C allotropes are dynamically stable (vide infra). Therefore, although the β-B_{3}C_{2} is a metastable configuration compared with α-B_{3}C_{2}, under experimental conditions, one may observe both of these structures. The formation energies of other compounds, including the experimentally synthesized BC_{3} sheet, located above the convex hull. These metastable structures might also exist due to the kinetic limitation or lattice confinement from the growing substrate. As shown in Table S1 (ESI†), the cohesive energy of the predicted structures is also presented at the different levels (PBE, DFT-D3, and HSE06). For comparison, the cohesive energies of graphene and borophene are listed under the same conditions. The cohesive energies of all proposed structures are lower than that of graphene, but still higher than that of experimentally realized borophene (5.75 eV per atom), silicene (4.57 eV per atom), and phosphorene (3.30 eV per atom).^{35–37} The relatively high cohesive energies indicate that these structures are bound together strongly and could be synthesized.

As shown in Fig. 2 and Fig. S2 (ESI†), all the predicted 2D BC compounds tend to form structures with finite atomic thickness, and the energetically favorable structures can be seen as sandwich structures with an outer B–C hexagonal lattice and an inner boron and/or carbon moiety. The details of the structural parameters are given in Table S2 (ESI†). B_{4}C_{3} consists of 8 B atoms and 6 C atoms per unit cell with the calculated lattice parameters being a = 2.69 Å and b = 4.67 Å at the GGA level. Furthermore, the length of B–C bonds in the outer hexagonal pattern (1.56 Å) is shorter than that of B–C bonds in its inner moiety (1.76 and 1.77 Å). For α-B_{3}C_{2}, it also contains an outer planar hexagonal B–C lattice. This unique structure can be considered as that the two B atoms are implanted into the bilayer graphene-like BC in each unit cell. For the stable 2D B_{2}C sheet, it is also organized in a hexagonal lattice consisting of a B layer sandwiched between two planar honeycomb B–C layers with C2/m symmetry. The side view shows that B_{2}C is composed of tetrahedral coordinated boron atoms, surrounded by carbon atoms with the trigonal pyramidal shape. The B_{4}C structure has a Cm symmetry with two formula units per unit cell. Similar to recently reported P6/mmm boron,^{38} this structure contains three types of bond lengths in boron atoms: 1.62 Å (to connect two neighboring B atoms in the same plane), 1.88 Å (to link two B atoms with a hexa-coordination), and 1.62 Å (to connect two neighboring B and C atoms). The newly predicted metastable 2D BC compounds are plotted in Fig. S2 (ESI†). Concerning β-B_{3}C_{2} and B_{4}C_{5}, their structures correspond to the carbon-doped 2D boron sheets, having Pm2m and Pm symmetries, respectively. B_{5}C exhibits a graphene-like hexagonal B–B lattice from the top view, similar to previously reported C2/m boron in the geometrical structure.^{38}

Besides the dynamic stability, the mechanical stability is also indispensable for new materials applications in the real world. For a mechanically stable 2D free-standing structure, the calculated elastic constants should satisfy C_{11}C_{22} − C_{12}C_{21} > 0 and C_{66} > 0.^{20,40} As listed in Table S2 (ESI†), all the calculated elastic constants of the proposed structures satisfy the above mentioned criteria, indicating that these 2D BC compounds have favorable mechanical stability. For B_{4}C_{3}, the in-plane Young's modulus reaches 431 GPa·nm, which even exceeds that of graphene (340 GPa nm).^{41} This exceedingly high Young's modulus could be explained by the existence of the extraordinary hexa-coordinated B–C covalent bonds (vide infra).

However, in the interlayer domains, each centered C atom bonded with 6 B atoms (Fig. 3a and e). In significant contrast with previously reported planar hexagonal-coordinated B–C bonds in negatively charged clusters,^{42} the proposed motif is composed of three equally distributed B–C–B bonds. As can be seen from Fig. 3e, this new motif can be considered as trigonal planar sp^{2} geometry, but with each far-end atom replaced by two B atoms. The bond angle between the thereby formed two B–C bonds is atypically less than 60°, and the ELF isosurface remains connected up to a relatively high level of 0.84. To understand the unique chemical bonding of the predicted motif, we have utilized the Solid State Adaptive Natural Density Partitioning (SSAdNDP) method.^{43} As shown in Fig. 3f, the SSAdNDP analysis identifies three delocalized three-center two-electron (3c–2e) σ bonds, with the occupation number (ON) 1.83, 1.85, and 1.90 |e|. This intriguing, elongated bonding configuration is stabilized due to the formation of centered sp^{2} C and 3c-2e σ bonds caused by the deficiency of electrons.

It should be noted that the proposed intriguing HC-sp^{2} moiety itself is stable. Both structural relaxation and phonon calculations were conducted for the inner HC-sp^{2} sheet having the outer truncated bonds passivated with pseudo-hydrogens (exfoliated-B_{4}C_{3}, see the optimized geometric structure in Fig. S6, ESI†). The optimized HC-sp^{2} motif remains nearly invariant, and, there are also no imaginary phonon modes in the whole Brillouin zone. These calculations indicate that the HC-sp^{2} motif is critical for the stabilization of the proposed B_{4}C_{3} sheet; moreover, this motif can be further used as a building block for the construction of other new materials.

Besides the predicted HC-sp^{2} moiety, we also identify an intriguing 2-coordinate B moiety in α-B_{3}C_{2}. As seen from Fig. 3b, the electrons are well localized around the B–C bonds. All these localized electrons lead to a robust bonding between the B and C atoms, which is vital to electronically stabilize the 2-coordinate B moiety in extended B–C systems. It should be noted that 2-coordinate B has been synthesized by using chemically stable and weakly nucleophilic counter anions in isolated molecular in Mes_{2}B^{+} (Mes(mesityl) = 2,4,6-trimethylphenyl).^{44,45} Compared with Mes_{2}B^{+}, the geometry of the B–C bond in the interlayer is slightly distorted (∠C–B–C = 158.4°, Fig. S7, ESI†), as expected for sp-hybridization. Bader charge analysis shows a charge transfer of 1.28 electrons from interlayer B to adjacent C atoms. B_{2}C is composed of four-coordinated boron atoms (arranged in a tetrahedral shape) surrounded by carbon atoms (trigonal pyramidal shape) with the same coordination number. The DED and ELF maps indicate that strong B–C covalent bonds and slightly weak B–B covalent bonds have been formed, as represented in Fig. S8 and S9 (ESI†).

B_{4}C, as shown in Fig. 3c, exists as a unique multilayer structure, which consists of a monolayer graphene-like B–C layer and borophene,^{33} connected by strong B–C covalent bonds. Obviously, this structure exhibits two main ELF domains: for the first region, the electrons are mainly localized between B–B atoms in the uppermost borophene layer; another charge localization region is distributed around the C atoms, reflecting a strong covalent bonding state within the graphene-like lattice. Interestingly, the partially ionic bond can be verified by Bader charge analysis.^{34,43} We find that there is an average of 0.44 electrons around one B atom at the B_{2}-plane (Fig. 3c) transferred to its neighboring graphene-like B_{1}-plane and planar hexagonal B–C lattice. The detailed ELF and DED analyses of the other metastable structures, such as β-B_{3}C_{2}, B_{4}C_{5}, B_{5}C, and Bi-BC, are also given in Fig. S8 and S9 (ESI†).

For B_{2}C, as shown in Fig. 4d, there are two bands crossing the Fermi level, indicating the metallic nature of the structure. The metallic property with covalent bonding of this unique configuration is satisfied with the requirements of conventional Bardeen–Cooper–Schrieffer (BCS) type superconductor. We then performed electron–phonon coupling (EPC) calculations to probe its potential superconductivity. The calculated EPC parameters (λ), Eliashberg spectral function α^{2}F(ω) and projected phonon DOS are presented in Fig. 5a. The main contributor to the EPC is derived from the low-frequency B–B translational vibration (5–15 THz). This result highlights that low-frequency vibrations from the B–B bonding structure and high-frequency (28–36 THz) vibrations from B–C bonding derived phonons are mainly responsible for the strong EPC in the B_{2}C sheet. As shown in Fig. 5b and d, there are two bands crossing the Fermi level along the high symmetry directions of the Brillouin zone. The nesting feature is not found in all Fermi surfaces. The number of three-dimensional Fermi surfaces correspond to the bands shown in Fig. 4d. The Fermi surface of B_{2}C is formed by cylindrical-like quasi-2D sheets parallel to the z direction, and all the Fermi surfaces are hole-like (a wide hole pocket is seen around the Γ point).

Superconducting T_{c} of B_{2}C is estimated through the Allen–Dynes modified McMillan formula by using the calculated logarithmic average frequency (ω_{log}) and a series of Coulomb pseudopotential parameters (μ*) from 0.10 to 0.13, as shown in Table S3 (ESI†). At μ* = 0.10, the highest T_{c} value of B_{2}C is 21.20 K originating from its strong EPC (λ = 0.73) and high logarithmic average frequency (ω_{log} = 549.62 K). Thus, the evaluated T_{c} is in the range of 21.20 K (μ* = 0.10) to 16.56 K (μ* = 0.13), indicating that the B_{2}C is an intrinsic BCS-type superconductor.

Band structure calculations indicate that the band gap of β-B_{3}C_{2} ranges from 2.27 to 1.93 eV using the HSE06 functional under uniaxial compression (0–5%) along the zigzag chain direction (Fig. 2c), exceeding the free energy of water splitting of 1.23 eV. Such suitable band gaps are located in the visible light region (1.62–3.11 eV), making it an effective 2D material for use in visible light-harvesting applications. The calculated work functions of strained β-B_{3}C_{2} are presented in Table S4 (ESI†). As can be seen in Fig. 6a, the band alignment was obtained by using the vacuum potential as a common reference. The standard water reduction and oxidation potential levels (pH = 0) are also plotted for comparison. For all the cases of the unstrained and strained β-B_{3}C_{2}, the VBM and CBM location is more positive and more negative than the hydrogen reduction potential of H^{+}/H_{2} and the water oxidation potential of H_{2}O/O_{2}, respectively. Thus, the band gap and band edge alignment provide persuasive evidence that β-B_{3}C_{2} is a potentially promising material for hydrogen generation from water splitting.

The in- and out-of-plane optical absorption spectra of the proposed 2D semiconducting B–C allotropes are further inspected with the HSE06 hybrid functional. As shown in Fig. 6b, the in-plane absorption coefficient is always larger, indicating that these sheets should be aligned on the surface of the photovoltaic cells for most efficient utilization of energy. We can see that all the optical adsorption is reasonably robust over a wide range between 1 and 5 eV, a range important for light-driven water splitting devices. Therefore, the β-B_{3}C_{2} structure can be considered as a promising photocatalyst.

Fig. 7 The calculated Raman and IR spectra of B_{4}C_{3}, B_{4}C, and β-B_{3}C_{2}. The structural motifs are also plotted. Arrows represent the directions of the corresponding oscillation. |

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## Footnotes |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7tc04505k |

‡ D. Fan and S. H. Lu contributed equally. |

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