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Structure and stability of bilayer borophene: The roles of hexagonal holes and interlayer bonding
FlatChem 7 (2018) 48–54
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FlatChem j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl a t c
Structure and stability of bilayer borophene: The roles of hexagonal holes and interlayer bonding Nan Gao, Xue Wu, Xue Jiang ⇑, Yizhen Bai, Jijun Zhao ⇑ Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
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Article history: Received 7 June 2017 Revised 15 August 2017 Accepted 18 August 2017 Available online 24 August 2017
a b s t r a c t Two-dimensional (2D) boron monolayers with diversity of structures and extraordinary physical properties have been extensively investigated using first-principles calculations. A series of boron bilayer sheets with pillars and hexagonal holes have been constructed. Many of them have lower formation energy than a-sheet boron monolayer. The structural stability and chemical bonding character of these boron bilayers are analyzed by charge density, electron localization function and Bader charge, indicating that the optimal proportions of pillars and hexagonal holes can be obtained by balancing the surplus electrons. Meanwhile, the distribution and arrangement of hexagonal holes can cause ignorable effect on the stability of structures. These findings pave the way for the structural diversity of 2D boron materials. Ó 2017 Elsevier B.V. All rights reserved.
Introduction Due to its flat honeycomb structures, peculiar electronic band structure, and high specific surface areas, graphene have achieved huge success in electronic, magnetic, optical, thermoelectric, catalysis and energy storage systems [1–4]. The boom of graphene has stimulated the research of other elemental two dimensional (2D) materials [5,6]. Similar to carbon, boron also possesses a short covalent radius and flexibility to adopt sp2 hybridization, which results in planar boron clusters [7,8], cage-like boron fullerene [9–11], and one-dimensional nanotubes [12,13]. Intuitively, boron atoms are expected to form 2D graphene-like monolayer sheet (namely, borophene). However, boron has one fewer electron than carbon. The electron deficiency in boron renders hexagonal honeycomb structures being stable by accepting elections while the flat triangular structure has surplus electrons in the antibonding states [14]. Thus, the biggest challenge in borophene synthesis is how to balance the surplus electrons. In this regard, hexagonal hole incorporation [15–19] and metal substrates passivation [20–22] are demonstrated as two effective methods. Taking the advantage of the balance of two-center and three-center bonds, Tang et al. [14] proposed stable a- and b- boron sheet with holes doping in hexagonal lattice for the first time. Soon after, more stable 2D boron sheets, such as a1-sheet, b1-sheet [15], g1/8-sheet and g2/15sheet [23,24] with mixed hexagonal-triangular motifs have been predicted using a similar self-doping approach [25–27]. In those ⇑ Corresponding authors. E-mail addresses: [email protected] (X. Jiang), [email protected] (J. Zhao). http://dx.doi.org/10.1016/j.flatc.2017.08.008 2452-2627/Ó 2017 Elsevier B.V. All rights reserved.
boron sheets, hexagonal holes are served as scavengers of extra electrons from the filled hexagons [28]. Depositing borophene on metal substrates is the alternative method to balance surplus electron of boron, which was firstly suggested for synthesis of the layered MgB2 and TiB2. Using firstprinciples calculations, Yakobson’s group [20] considered the boron sheets on Cu, Ag, Au substrates and suggested that the deposition of boron atom on a Ag or Au(111) surface can result in growth of 2D boron sheets. Liu et al. [21] have demonstrated that the stability of monolayer boron sheets can be well stabilized by metal passivation of Cu (111) surface, and hexagonal holes can be easily formed via diffusion. Following these predictions, experimental fabrications of 2D boron sheets have also made a great achievement in recent years [29–32]. Mannix and co-workers [29] synthesized borophene with the character of anisotropic and out-of-plane buckling on Ag(111) surface. Feng et al. [31] fabricated b12 sheet and v3 sheet with different arrangements of periodic holes on Ag(111) substrate, which are inert to oxidization. In line with the continuous advances in the prediction and fabrication of boron sheets, their novel properties and potential device applications become a rapidly growing area [33–38]. Zhang et al. [39] found that borophene have superior flexibility and elasticity that are even comparable to graphene. In addition, the mechanical properties could be tailored by regulating hexagonal holes density, showing promise perspective in flexible devices. Intrinsic phononmediated superconductivity was predicted in 2D boron sheet at the critical temperature about 20 K [40,41]. As an anode material, borophene enhances the capacity of Li ion batteries and outperform graphite anode [42–44].
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To fulfill those applications, some issues are dispensable to be solved. Since monolayer boron sheets must be synthesized on metal substrates, how about the bilayer boron sheets? Can bilayer boron sheets be peeled off from substrates and exist freely? If so, how about the specific distributions of stable atomic structures? How to balance the surplus electrons? What interaction and charge transfer between the two layers? What are the main differences between monolayer and bilayer boron sheets and which one is more stable? How does the arrangement of hexagonal holes and pillars affect the structural stability and electronic properties? To answer these questions, herein we systematically investigate the structure, stability, chemical bonding character and electronic properties of a variety of boron bilayers. Our calculations show that the formation energy of plenty of boron bilayers composed with pillars and hexagonal holes is lower than that of the most stable g1/8-sheet boron monolayer. The formation energies for these bilayers are reduced by self-doping between different coordinated boron atoms. The structural stability of these boron sheets are closely related to the distribution and ratio of hexagonal holes and interlayer pillars. Our theoretical results demonstrate a new electron balance approach for pure 2D boron sheets arising from interlayer interaction. This undoubtedly enlarges the family of 2D boron sheets and provides guidance in designing novel boron-based materials for experiments. Computational methods Density functional theory (DFT) calculations [45] were performed by the Vienna ab initio simulation package (VASP) [46], using the planewave basis set with energy cutoff of 500 eV, the projector augmented wave (PAW) potentials [47,48], and the generalized gradient approximation (GGA) parameterized by Perdew, Burke and Ernzerhof (PBE) [49] for the exchange-correlation interaction. The Grimme’s D3 scheme of dispersion correction [50] was used to account for the long-range van der Waals interaction. A vacuum region of 18 Å was added to the vertical direction to eliminate the interactions between the neighboring layers. The Bril-
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louin zones of the supercell were sampled by uniform k point meshes with spacing of 0.03/Å. The model structures were fully optimized for both cell and ionic degrees of freedom with thresholds for the total energy of 105 eV and the forces on each atom of 0.03 eV/Å, respectively. To describe the stability of a 2D boron sheet, we define the formation energy Eform as:
Eform ¼ ðEt N EB Þ=N
ð1Þ
where Et is the total energy of boron bilayer or monolayer, EB is energy per atom in the boron solid of a phase, N is the number of boron atoms in boron monolayer or bilayer sheets. Results and discussion Bilayer boron sheets without hexagonal holes Here we explore various possible configurations of bilayer boron sheets. There are two key parameters to characterize a bilayer sheet. First, two boron atoms from the upper and lower layers form a direct chemical bond, which is named as a pillar. Second, the electron deficiency of boron atoms in triangular lattice results in different arrangements of hexagonal holes. To better characterize the structural models, pillar density g1 and hexagonal hole density g2 [12,43] are defined as:
g1 ¼ Number of atoms forming pillars= Number of atoms in the unit cell
ð2Þ
g2 ¼ Number of hexagonal holes= Number of atoms in the original sheet
ð3Þ
For the sake of simplicity, we start from constructing a variety of boron bilayer sheets without hexagonal holes to examine the effect of pillar density on stability of structural models. The structural and energetic information of these models are summarized in Fig. 1. In all these structures, boron atoms can be classified into two
Fig. 1. Atomic structures of boron bilayers with different pillar density g1 labeled by (a), (b), . . . (h). The boron atoms at top and bottom planes and stack in top and bottom planes are labeled by pink and red color, respectively. The pillar density g1 (upper) and formation energy Eform (lower) are given below each structural model. Among them, Boron bilayer structures in Fig. 1a, c, d, g and h are dynamically stable confirmed by their phonon density of states.
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types: the first kind of atoms (labeled by pink color) locating at the top and bottom planes and forming bonds with surrounding six boron atoms; another kind of boron atoms (labeled by red color) forming the pillars and having seven coordination. Overall speaking, the formation energies of these bilayer boron sheets with pillars range from 0.37 to 0.66 eV/atom, close to g1/8-sheet boron monolayer of 0.50 eV/atom and substantially lower than that of the bilayer boron sheets without pillar (0.75 eV/atom), implying that appropriate ratio of pillars indeed enhances the stability of bilayer systems. On the contrary, both structures in Fig. 1f and g with the continuous pillars in boron bilayer result in relatively higher formation energy (0.16 and 0.24 eV/atom higher than the average value of 0.42 eV/atom, respectively). The instability of both structures might be attributed to the excessive seven-coordinated boron atoms, which severely disturb the balance of valence electrons. The relationship of Eform and g1 is plotted in Fig. 2. The formation energies of these boron bilayers sheets with different pillar
Fig. 2. Formation energy (Eform) as a function of pillars density (g1) for boron bilayers without hexagonal holes. The black dashed line is a linear function fitting of Eform vs. g1. The black solid/hollow dots represent for boron sheets with pillars/ without pillars. The top view of three representative structures of Fig. 1a, g and h along with the corresponding g1 are shown as insets.
density show a linear correlation with g1, which can be understood as that the existence of some pillars at appropriate ratios can effectively stabilize the whole systems. Also, the top view of three representative structural models is given in the inset of Fig. 2. The boron sheet without forming pillars, i.e., g1 = 0, is less stable than the other boron bilayer sheets with pillars. The distance of neighboring boron sheet (3.46 Å) is about twice the B-B bond length of pillars (about 1.75 Å), suggesting that pillars can balance the surplus electrons and strengthen the stability of system. In particular, formation energy of structural model in Fig. 1a (g1 = 1/4) is lower than structure in Fig. 1g (g1 = 3/4) by 0.29 eV/atom. From the chemical bonding point of view, boron element with three valence electrons in the 2s and 2p orbitals leads to different bonding character with graphene. The electron deficiency of boron can be saturated by pillars, which further stabilizes boron bilayer sheets. This is similar to the passivation of metal substrates and effectively stabilizes sp2 hybridization of boron. Also, no negative frequency in density of phonon states in Fig. S1 ensure dynamic stability. Ab initio molecular dynamics (AIMD) simulations in Fig. S2 reveal that the pillars in boron sheets at appropriate ratios are thermodynamically favorable. To further explain the stability of these boron bilayers, total charge density of three representative structures are displayed in Fig. 3. In contrast to structural model of Fig. 1h in the left panel, there is evident charge distribution in the pillars for boron sheets of Fig. 1a and g, indicating a strong covalent character. This means that these pillars are crucial to strengthen the stability of the whole system. In addition, the formation energy of Fig. 1a structure reduced by 0.29 eV/atom with regard to the structure in Fig. 1g, which can be attributed to charge distributions among upper and lower boron atoms (detailed bonding analysis will be discussed in the following). Moreover, to examine whether existence of pillars can affect electronic properties, the corresponding electronic band structures are plotted in Fig. 3. Clearly, these boron bilayers retain metallic features as those monolayer boron sheets. Then we analyze the B-B bonding character by calculating the electron localization function (ELF) to understand why these boron bilayers are more energetically favorable. ELF can be viewed as a contour picture in real space with values ranging from 0 to 1.
Fig. 3. Total charge density from top and side view and electronic band structures of the three structures corresponding to Fig. 2h, a and g. Black solid box is the unit cell of these boron bilayers and the formation energy is given below the corresponding structures. The isosurface is 0.12 e/Å3.
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The region with ELF = 1 means perfect localization of electrons, zero ELF indicates a low electron density area, and 0.5 ELF region implies the probability of free electron gas. The ELF isosurfaces of the boron sheets corresponding to the structure in Fig. 1a and g are displayed in Fig. 4a and b. Fig. 4a display the isosurface of ELF = 0.8, which mainly focus on three located areas. The most evident areas are located in the middle of boron atoms at the top and bottom planes (labeled by pink). The remaining two electron localization areas are distributed around boron atom planes (labeled by red) and pillars, respectively. In contrast to the ELF in Fig. 4a, another electronic localization area among boron atoms marked by red and pink is clearly see in Fig. 4b, implying the covalent bonding interaction to some extent like pillars. To distinctly see the interaction and chemical bond character, the ELF of sliced planes of Fig. 4b is displayed in Fig. 4c. High ELF distributions (0.9 1) are located at the top and bottom atoms and pillars, corresponding to strong covalent bonding. These results are consistent with previous work [17]. In addition, electron located areas also occur among boron atoms labeled by pink and red boron with a relatively lower ELF from the middle panel. It is noteworthy that ELF with 0.5 takes up most of this sliced plane, indicating the electrons can transport freely. Such character can also be reflected by Bader charge analysis and B-B bond lengths of different types, as shown in Fig. 4d. The B-B bond lengths in this structure can be classified into four types: d1 = 1.75 (between atom 1 and 2), d2 = 1.76 (between atom 2 and 4), d3 = 2.02 (between atom 2 and 8), d4 = 1.73 (between 4 and 8 atom). Interestingly, bond lengths of d1, d2 and d4 in this structure are close to the bond length in the high-pressure ionic phase c-B28 [36], suggesting that the energetically favorable boron bilayer possess some character of ionic bonding. We also find that the boron atoms near the top and bottom planes (marked by 3 and 4) act as acceptors and gain 0.34 electrons on average, while the boron atoms (marked by 1 and 2) act as electron donors. Relatively speaking, the charge of boron atoms at top and bottom layers (marked by 5, 6, 7 and 8) almost has no change (0.08 electrons loss). Evidently, boron atoms located at different layers can promote the transfer of electrons, further balance the surplus electrons and enhance stability of the whole system. All above analysis demonstrate the formation of pillars benefit for transfer of electrons and compensate the disadvantage of unsaturated valence electrons for sp2 hybridization.
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Bilayer boron sheets with hexagonal holes Incorporation of hexagonal hole in boron sheets has been generally regarded as an effective method to achieve the balance of valence electrons [17–20]. Wu et al. [15] have demonstrated that monolayers a1 and b1 boron sheet are more stable than boron sheets without hexagonal holes. Since monolayer boron sheets with hexagonal holes are energetically favorable, it raises an interesting question whether boron bilayers still prefer hexagonal holes. To clarify this issue, we consider bilayer structures with different hexagonal holes density and classify them into four types: (I) isolated hexagonal holes separated by boron sheets including structural models of Fig. 5i–l; (II) a series of hexagonal holes separated by boron sheets including structural models of Fig. 5m–p; (III) hexagonal holes fill the entire 2D boron sheets including structural models of Fig. 5q and r; (IV) isolated hexagonal holes separated by boron sheets with lower pillars density g1 (0.13 0.14) compared with former three types g1 (0.27 0.33) including structural models of Fig. 5s and t. The relation of Eform versus g2 is plotted in Fig. 6. Generally speaking, the formation energies of these boron bilayers range from 0.35 eV/atom to 0.93 eV/atom and decrease in the order of Eform (0.35 0.44 eV/atom for type I) < Eform (0.45 eV/atom for type IV) < Eform (0.43 0.55 eV/atom for type II) < Eform (0.80 0.93 eV/atom for type III). For type I bilayers, we can clearly see that those two structures only with one isolated hexagonal hole (Eform = 0.35 eV/atom) have lower formation energy than other two structures with two or four neighboring holes (Eform = 0.39, 0.44 eV/atom, respectively), implying that continuous hexagonal holes is detrimental to the thermodynamic stability of boron sheets. Similarly, type II boron bilayer with one series of hexagonal holes (in Fig. 5m and n) is more stable than two continuous series of holes (in Fig. 5o and p). Also, the hole density of 0.13 0.14 in type II results in relatively higher formation energy with respect to type I of 0.05 0.06 hole density by 0.11 eV/atom on average. Once the holes distribute in the whole boron sheets, the balance of electrons are awfully destroyed and the formation energy of type III can even reach 0.93 eV/atom for the structure in Fig. 5r. For type IV structures, smaller g1 and g2 can also stabilize boron bilayers, resulting in formation energy of 0.45 eV/atom. We also find the formation energy of most stable boron bilayer (with 1/16 hole density) is about 0.02 eV/atom lower than the most
Fig. 4. (a) (b) Top view and side view of the electronic localization function with isovalue of 0.8 for two representative structures in Fig. 1a and g. (c) Slabs model in Fig. 4b cut along (001) direction and their ELF. (d) Bader analysis and bond length for the system in Fig. 4b. The value labeled by blue color stand for bond length (Å).
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Fig. 5. Atomic structures of boron bilayer with different hexagonal holes density g2 labeled by (i), (j), . . .(t) The boron atoms at top and bottom planes and stacked in top and bottom planes are labeled by pink and red color, respectively. The pillar density g1, hexagonal hole density g2 and formation energy are given below the structures. Among them, Boron bilayer structures in Fig. 5i, s and t are dynamically stable confirmed by their phonon density of states.
Fig. 6. Formation energy (Eform) as a function of hexagonal holes density (g2) for boron bilayers with hexagonal holes. The black dashed line is a linear fitting of Eform vs. g2.
stable boron bilayer without hexagonal holes, implying the combination of hexagonal holes and pillars at appropriate ratio can further balance the excess electrons and enhance the stability. These results are similar to previous finding by Tang et al. [14] that mixture of three-center bonding and two-center hexagonal regions at an appropriate ratio is beneficial to the stability of monolayer systems. Therefore, we conclude that the stability of boron bilayer is closely related to the densities of pillars and hexagonal holes, as well as the arrangement of holes.
Likewise, ELF, electronic band structure and phonon spectrum of one representative boron bilayer (in Fig. 5i) with the lowest formation energy is shown in Fig. 7. Similar to Fig. 4b, ELF with 0.85 isovalue in this boron bilayer concentrate on three areas: the middle of boron atoms at top and bottom planes (labeled by pink color) around the hexagonal holes, among boron atoms labeled by red and pink around hexagonal holes and pillars. The main differences between this structure and those without holes are the coordination number. Boron atoms around the holes form 5 and 6 coordination, compared with former 6 and 7 coordination in boron bilayer without holes. To clearly see the character of chemical bonding, the sliced planes of ELF cut along the side view in Fig. 7a is plotted in Fig. 7b. Evidently, a high ELF distribution (about 0.9) locates on the middle of boron atoms labeled by red and pink around the holes. Bader charge analysis also demonstrate that each boron atom slightly below top layer boron atoms gains about 0.34 electrons from the surrounding atoms and saturate outermost valence electrons. Furthermore, the calculated phonon spectrum shows the dynamical stability (no negative frequencies) and the electronic band structure indicates metallic properties in Fig. 7c. In addition to the structure in Fig. 5i, lattice dynamic properties of some other boron bilayer sheets with holes are also studied by calculating their phonon density of states, which are displayed in Fig. S1. The absence of imaginary modes has confirmed their dynamic stabilities. Moreover, AIMD simulations were performed for boron bilayers in Fig. 5i to further examine the thermal stability. The temperature was set as 300 K and the time step was 1 fs within the
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Fig. 7. (a) Top view and side view of the electronic localization function (with isovalue = 0.85) of structural model in Fig. 5i. (b) Slabs model in Fig. 7a cut along (001) direction and the corresponding ELF. (c) The phonon spectra and electronic band structure of the structure in Fig. 7a.
canonical NVT ensemble. Boron bilayers can almost keep initial configuration after 5 ps as shown in Fig. S2. The result indicates that B-B bond is enough strong and boron bilayer sheets can exist stably at room temperature. Again, the existence of hexagonal holes in boron bilayers has significant impact on the electronic band structures. All structures in Fig. 5 exhibit metallic behaviors with bands crossing the Fermi level like other boron allotrope. In contrast to the effect of pillars on electronic band structures in Fig. 3, the bands become more flat due to hexagonal holes introduction as shown in Fig. S3, suggesting the deterioration to the carrier mobility.
Conclusion In summary, the structures, energetic stabilities, electronic properties of boron bilayer with various combinations of pillars and hexagonal holes are systematically investigated by firstprinciples calculations. The stability of these boron bilayer sheets outperforms the most stable boron monolayer g1/8-sheet. Such lower formation energy can be attributed to the balance of excess electrons by forming pillars or introducing hexagonal holes. Analyses of total charge density, ELF and Bader charge show that boron atoms can bond well with each other by in-plane covalent interactions or transferring electrons out of plane. The electronic band structures show that all boron bilayer are metallic and might be used as electrode materials in batteries. We provide a new method to decorate boron sheets by introducing pillars and hexagonal holes to design a series of stable boron bilayer sheets, expanding the scope of 2D boron materials and devices. Acknowledgements This work is supported by the National Natural Science Foundation of China (11404050) and the Fundamental Research Funds for the Central Universities of China (DUT16RC(4)50, DUT16JJ(G)05, DUT16LAB01). We acknowledge the Supercomputing Center of Dalian University of Technology for providing the computing resources.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.flatc.2017.08.008. References [1] K.S. Novoselov, V.I. Fal’ko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, Nature 490 (2012) 192–200. [2] M.J. Allen, V.C. Tung, R.B. Kaner, Chem. Rev. 110 (2010) 132–145. [3] F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Nat. Photonics 4 (2010) 611–622. [4] A.C. Ferrari, F. Bonaccorso, V. Fal’ko, K.S. Novoselov, S. Roche, P. Boggild, S. Borini, F.H. Koppens, V. Palermo, N. Pugno, et al., Nanoscale 7 (2015) 4598– 4810. [5] A. Molle, J. Goldberger, M. Houssa, Y. Xu, S.C. Zhang, D. Akinwande, Nat. Mater. 16 (2017) 163–169. [6] A.J. Mannix, B. Kiraly, M.C. Hersam, N.P. Guisinger, Nat. Rev. Chem. 1 (2017) 0014. [7] Z.A. Piazza, H.S. Hu, W.L. Li, Y.F. Zhao, J. Li, L.S. Wang, Nat. Commun. 5 (2014) 3113. [8] H.J. Zhai, B. Kiran, J. Li, L.S. Wang, Nat. Mater. 2 (2003) 827–833. [9] N. Gonzalez Szwacki, A. Sadrzadeh, B.I. Yakobson, Phys. Rev. Lett. 98 (2007) 166804. [10] H.J. Zhai, Y.F. Zhao, W.L. Li, Q. Chen, H. Bai, H.S. Hu, Z.A. Piazza, W.J. Tian, H.G. Lu, Y.B. Wu, et al., Nat. Chem. 6 (2014) 727–731. [11] J. Zhao, X. Huang, R. Shi, H. Liu, Y. Su, R.B. King, Nanoscale 7 (2015) 15086– 15090. [12] F. Liu, C. Shen, Z. Su, X. Ding, S. Deng, J. Chen, N. Xu, H. Gao, J. Mater. Chem. 20 (2010) 2197–2205. [13] D. Ciuparu, R.F. Klie, Y. Zhu, L. Pfefferle, J. Phys. Chem. B 35 (2004) 3967–3969. [14] H. Tang, S. Ismail-Beigi, Phys. Rev. Lett. 99 (2007) 115501. [15] X. Wu, J. Dai, Y. Zhao, Z. Zhuo, J. Yang, X.C. Zeng, ACS Nano. 6 (2012) 7443– 7453. [16] X.-F. Zhou, X. Dong, A.R. Oganov, Q. Zhu, Y. Tian, H.-T. Wang, Phys. Rev. Lett. 112 (2014) 085502. [17] F. Ma, Y. Jiao, G. Gao, Y. Gu, A. Bilic, Z. Chen, A. Du, Nano Lett. 16 (2016) 3022– 3028. [18] N. Karmodak, E.D. Jemmis, Angew. Chem.-Int. Ed. 56 (2017) 10093–10097. [19] W.L. Li, Q. Chen, W.J. Tian, H. Bai, Y.F. Zhao, H.S. Hu, J. Li, H.J. Zhai, S.D. Li, L.S. Wang, J. Am. Chem. Soc. 136 (2014) 12257–12260. [20] Y. Liu, E.S. Penev, B.I. Yakobson, Angew. Chem.-Int. Ed. 52 (2013) 3156–3159. [21] H. Liu, J. Gao, J. Zhao, Sci. Rep. 3 (2013) 3238. [22] L.Z. Zhang, Q.B. Yan, S.X. Du, G. Su, H.J. Gao, J. Phys. Chem. C 116 (2012) 18202– 18206. [23] E.S. Penev, S. Bhowmick, A. Sadrzadeh, B.I. Yakobson, Nano Lett. 12 (2012) 2441–2445. [24] X. Yu, L. Li, X.-W. Xu, C.-C. Tang, J. Phys. Chem. C 116 (2012) 20075–20079. [25] J. Kunstmann, A. Quandt, Phys. Rev. B 74 (2006) 035413. [26] K.C. Lau, R. Pati, R. Pandey, A.C. Pineda, Chem. Phys. Lett. 418 (2006) 549–554.
54
N. Gao et al. / FlatChem 7 (2018) 48–54
[27] K.C. Lau, R. Pandey, J. Phys. Chem. C 111 (2007) 2906–2912. [28] T.R. Galeev, Q. Chen, J.C. Guo, H. Bai, C.Q. Miao, H.G. Lu, A.P. Sergeeva, S.D. Li, A. I. Boldyrev, Phys. Chem. Chem. Phys. 13 (2011) 11575–11578. [29] A.J. Mannix, X.-F. Zhou, B. Kiraly, J.D. Wood, D. Alducin, B.D. Myers, X. Liu, B.L. Fisher, U. Santiago, J.R. Guest, et al., Science 350 (2015) 1513–1516. [30] G. Tai, T. Hu, Y. Zhou, X. Wang, J. Kong, T. Zeng, Y. You, Q. Wang, Angew. Chem. 127 (2015) 15693–15697. [31] B. Feng, J. Zhang, Q. Zhong, W. Li, S. Li, H. Li, P. Cheng, S. Meng, L. Chen, K. Wu, Nat. Chem. 8 (2016) 563–568. [32] H.S. Tsai, C.H. Hsiao, Y.P. Lin, C.W. Chen, H. Ouyang, J.H. Liang, Small 12 (2016) 5251–5255. [33] B. Albert, H. Hillebrecht, Angew. Chem.-Int. Ed. 48 (2009) 8640–8668. [34] J. Tian, Z. Xu, C. Shen, F. Liu, N. Xu, H.J. Gao, Nanoscale 2 (2010) 1375–1389. [35] A.P. Sergeeva, I.A. Popov, Z.A. Piazza, W.L. Li, C. Romanescu, L.S. Wang, A.I. Boldyrev, Acc. Chem. Res. 47 (2014) 1349–1358. [36] A.R. Oganov, J. Chen, C. Gatti, Y. Ma, Y. Ma, C.W. Glass, Z. Liu, T. Yu, O.O. Kurakevych, V.L. Solozhenko, Nature 457 (2009) 863–867.
[37] B. Peng, H. Zhang, H. Shao, Y. Xu, R. Zhang, H. Zhu, J. Mater. Chem. C 4 (2016) 3592–3598. [38] Y. Jiao, F. Ma, J. Bell, A. Bilic, A. Du, Angew. Chem. 55 (2016) 10292–10295. [39] Z. Zhang, Y. Yang, E.S. Penev, B.I. Yakobson, Adv. Funct. Mater. 27 (2017) 1605059. [40] E.S. Penev, A. Kutana, B.I. Yakobson, Nano Lett. 16 (2016) 2522–2526. [41] M. Gao, Q.-Z. Li, X.-W. Yan, J. Wang, Phys. Rev. B 95 (2017) 024505. [42] H.R. Jiang, Z. Lu, M.C. Wu, F. Ciucci, T.S. Zhao, Nano Energy 23 (2016) 97–104. [43] L. Shi, T. Zhao, A. Xu, J. Xu, Sci. Bull. 61 (2016) 1138–1144. [44] Y. Zhang, Z.F. Wu, P.F. Gao, S.L. Zhang, Y.H. Wen, ACS Appl. Mater. Interfaces 8 (2016) 22175–22181. [45] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133–A1138. [46] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169–11186. [47] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953–17979. [48] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. [49] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [50] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 132 (2010) 154104.
Contents lists available at ScienceDirect
FlatChem j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl a t c
Structure and stability of bilayer borophene: The roles of hexagonal holes and interlayer bonding Nan Gao, Xue Wu, Xue Jiang ⇑, Yizhen Bai, Jijun Zhao ⇑ Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
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Article history: Received 7 June 2017 Revised 15 August 2017 Accepted 18 August 2017 Available online 24 August 2017
a b s t r a c t Two-dimensional (2D) boron monolayers with diversity of structures and extraordinary physical properties have been extensively investigated using first-principles calculations. A series of boron bilayer sheets with pillars and hexagonal holes have been constructed. Many of them have lower formation energy than a-sheet boron monolayer. The structural stability and chemical bonding character of these boron bilayers are analyzed by charge density, electron localization function and Bader charge, indicating that the optimal proportions of pillars and hexagonal holes can be obtained by balancing the surplus electrons. Meanwhile, the distribution and arrangement of hexagonal holes can cause ignorable effect on the stability of structures. These findings pave the way for the structural diversity of 2D boron materials. Ó 2017 Elsevier B.V. All rights reserved.
Introduction Due to its flat honeycomb structures, peculiar electronic band structure, and high specific surface areas, graphene have achieved huge success in electronic, magnetic, optical, thermoelectric, catalysis and energy storage systems [1–4]. The boom of graphene has stimulated the research of other elemental two dimensional (2D) materials [5,6]. Similar to carbon, boron also possesses a short covalent radius and flexibility to adopt sp2 hybridization, which results in planar boron clusters [7,8], cage-like boron fullerene [9–11], and one-dimensional nanotubes [12,13]. Intuitively, boron atoms are expected to form 2D graphene-like monolayer sheet (namely, borophene). However, boron has one fewer electron than carbon. The electron deficiency in boron renders hexagonal honeycomb structures being stable by accepting elections while the flat triangular structure has surplus electrons in the antibonding states [14]. Thus, the biggest challenge in borophene synthesis is how to balance the surplus electrons. In this regard, hexagonal hole incorporation [15–19] and metal substrates passivation [20–22] are demonstrated as two effective methods. Taking the advantage of the balance of two-center and three-center bonds, Tang et al. [14] proposed stable a- and b- boron sheet with holes doping in hexagonal lattice for the first time. Soon after, more stable 2D boron sheets, such as a1-sheet, b1-sheet [15], g1/8-sheet and g2/15sheet [23,24] with mixed hexagonal-triangular motifs have been predicted using a similar self-doping approach [25–27]. In those ⇑ Corresponding authors. E-mail addresses: [email protected] (X. Jiang), [email protected] (J. Zhao). http://dx.doi.org/10.1016/j.flatc.2017.08.008 2452-2627/Ó 2017 Elsevier B.V. All rights reserved.
boron sheets, hexagonal holes are served as scavengers of extra electrons from the filled hexagons [28]. Depositing borophene on metal substrates is the alternative method to balance surplus electron of boron, which was firstly suggested for synthesis of the layered MgB2 and TiB2. Using firstprinciples calculations, Yakobson’s group [20] considered the boron sheets on Cu, Ag, Au substrates and suggested that the deposition of boron atom on a Ag or Au(111) surface can result in growth of 2D boron sheets. Liu et al. [21] have demonstrated that the stability of monolayer boron sheets can be well stabilized by metal passivation of Cu (111) surface, and hexagonal holes can be easily formed via diffusion. Following these predictions, experimental fabrications of 2D boron sheets have also made a great achievement in recent years [29–32]. Mannix and co-workers [29] synthesized borophene with the character of anisotropic and out-of-plane buckling on Ag(111) surface. Feng et al. [31] fabricated b12 sheet and v3 sheet with different arrangements of periodic holes on Ag(111) substrate, which are inert to oxidization. In line with the continuous advances in the prediction and fabrication of boron sheets, their novel properties and potential device applications become a rapidly growing area [33–38]. Zhang et al. [39] found that borophene have superior flexibility and elasticity that are even comparable to graphene. In addition, the mechanical properties could be tailored by regulating hexagonal holes density, showing promise perspective in flexible devices. Intrinsic phononmediated superconductivity was predicted in 2D boron sheet at the critical temperature about 20 K [40,41]. As an anode material, borophene enhances the capacity of Li ion batteries and outperform graphite anode [42–44].
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To fulfill those applications, some issues are dispensable to be solved. Since monolayer boron sheets must be synthesized on metal substrates, how about the bilayer boron sheets? Can bilayer boron sheets be peeled off from substrates and exist freely? If so, how about the specific distributions of stable atomic structures? How to balance the surplus electrons? What interaction and charge transfer between the two layers? What are the main differences between monolayer and bilayer boron sheets and which one is more stable? How does the arrangement of hexagonal holes and pillars affect the structural stability and electronic properties? To answer these questions, herein we systematically investigate the structure, stability, chemical bonding character and electronic properties of a variety of boron bilayers. Our calculations show that the formation energy of plenty of boron bilayers composed with pillars and hexagonal holes is lower than that of the most stable g1/8-sheet boron monolayer. The formation energies for these bilayers are reduced by self-doping between different coordinated boron atoms. The structural stability of these boron sheets are closely related to the distribution and ratio of hexagonal holes and interlayer pillars. Our theoretical results demonstrate a new electron balance approach for pure 2D boron sheets arising from interlayer interaction. This undoubtedly enlarges the family of 2D boron sheets and provides guidance in designing novel boron-based materials for experiments. Computational methods Density functional theory (DFT) calculations [45] were performed by the Vienna ab initio simulation package (VASP) [46], using the planewave basis set with energy cutoff of 500 eV, the projector augmented wave (PAW) potentials [47,48], and the generalized gradient approximation (GGA) parameterized by Perdew, Burke and Ernzerhof (PBE) [49] for the exchange-correlation interaction. The Grimme’s D3 scheme of dispersion correction [50] was used to account for the long-range van der Waals interaction. A vacuum region of 18 Å was added to the vertical direction to eliminate the interactions between the neighboring layers. The Bril-
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louin zones of the supercell were sampled by uniform k point meshes with spacing of 0.03/Å. The model structures were fully optimized for both cell and ionic degrees of freedom with thresholds for the total energy of 105 eV and the forces on each atom of 0.03 eV/Å, respectively. To describe the stability of a 2D boron sheet, we define the formation energy Eform as:
Eform ¼ ðEt N EB Þ=N
ð1Þ
where Et is the total energy of boron bilayer or monolayer, EB is energy per atom in the boron solid of a phase, N is the number of boron atoms in boron monolayer or bilayer sheets. Results and discussion Bilayer boron sheets without hexagonal holes Here we explore various possible configurations of bilayer boron sheets. There are two key parameters to characterize a bilayer sheet. First, two boron atoms from the upper and lower layers form a direct chemical bond, which is named as a pillar. Second, the electron deficiency of boron atoms in triangular lattice results in different arrangements of hexagonal holes. To better characterize the structural models, pillar density g1 and hexagonal hole density g2 [12,43] are defined as:
g1 ¼ Number of atoms forming pillars= Number of atoms in the unit cell
ð2Þ
g2 ¼ Number of hexagonal holes= Number of atoms in the original sheet
ð3Þ
For the sake of simplicity, we start from constructing a variety of boron bilayer sheets without hexagonal holes to examine the effect of pillar density on stability of structural models. The structural and energetic information of these models are summarized in Fig. 1. In all these structures, boron atoms can be classified into two
Fig. 1. Atomic structures of boron bilayers with different pillar density g1 labeled by (a), (b), . . . (h). The boron atoms at top and bottom planes and stack in top and bottom planes are labeled by pink and red color, respectively. The pillar density g1 (upper) and formation energy Eform (lower) are given below each structural model. Among them, Boron bilayer structures in Fig. 1a, c, d, g and h are dynamically stable confirmed by their phonon density of states.
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types: the first kind of atoms (labeled by pink color) locating at the top and bottom planes and forming bonds with surrounding six boron atoms; another kind of boron atoms (labeled by red color) forming the pillars and having seven coordination. Overall speaking, the formation energies of these bilayer boron sheets with pillars range from 0.37 to 0.66 eV/atom, close to g1/8-sheet boron monolayer of 0.50 eV/atom and substantially lower than that of the bilayer boron sheets without pillar (0.75 eV/atom), implying that appropriate ratio of pillars indeed enhances the stability of bilayer systems. On the contrary, both structures in Fig. 1f and g with the continuous pillars in boron bilayer result in relatively higher formation energy (0.16 and 0.24 eV/atom higher than the average value of 0.42 eV/atom, respectively). The instability of both structures might be attributed to the excessive seven-coordinated boron atoms, which severely disturb the balance of valence electrons. The relationship of Eform and g1 is plotted in Fig. 2. The formation energies of these boron bilayers sheets with different pillar
Fig. 2. Formation energy (Eform) as a function of pillars density (g1) for boron bilayers without hexagonal holes. The black dashed line is a linear function fitting of Eform vs. g1. The black solid/hollow dots represent for boron sheets with pillars/ without pillars. The top view of three representative structures of Fig. 1a, g and h along with the corresponding g1 are shown as insets.
density show a linear correlation with g1, which can be understood as that the existence of some pillars at appropriate ratios can effectively stabilize the whole systems. Also, the top view of three representative structural models is given in the inset of Fig. 2. The boron sheet without forming pillars, i.e., g1 = 0, is less stable than the other boron bilayer sheets with pillars. The distance of neighboring boron sheet (3.46 Å) is about twice the B-B bond length of pillars (about 1.75 Å), suggesting that pillars can balance the surplus electrons and strengthen the stability of system. In particular, formation energy of structural model in Fig. 1a (g1 = 1/4) is lower than structure in Fig. 1g (g1 = 3/4) by 0.29 eV/atom. From the chemical bonding point of view, boron element with three valence electrons in the 2s and 2p orbitals leads to different bonding character with graphene. The electron deficiency of boron can be saturated by pillars, which further stabilizes boron bilayer sheets. This is similar to the passivation of metal substrates and effectively stabilizes sp2 hybridization of boron. Also, no negative frequency in density of phonon states in Fig. S1 ensure dynamic stability. Ab initio molecular dynamics (AIMD) simulations in Fig. S2 reveal that the pillars in boron sheets at appropriate ratios are thermodynamically favorable. To further explain the stability of these boron bilayers, total charge density of three representative structures are displayed in Fig. 3. In contrast to structural model of Fig. 1h in the left panel, there is evident charge distribution in the pillars for boron sheets of Fig. 1a and g, indicating a strong covalent character. This means that these pillars are crucial to strengthen the stability of the whole system. In addition, the formation energy of Fig. 1a structure reduced by 0.29 eV/atom with regard to the structure in Fig. 1g, which can be attributed to charge distributions among upper and lower boron atoms (detailed bonding analysis will be discussed in the following). Moreover, to examine whether existence of pillars can affect electronic properties, the corresponding electronic band structures are plotted in Fig. 3. Clearly, these boron bilayers retain metallic features as those monolayer boron sheets. Then we analyze the B-B bonding character by calculating the electron localization function (ELF) to understand why these boron bilayers are more energetically favorable. ELF can be viewed as a contour picture in real space with values ranging from 0 to 1.
Fig. 3. Total charge density from top and side view and electronic band structures of the three structures corresponding to Fig. 2h, a and g. Black solid box is the unit cell of these boron bilayers and the formation energy is given below the corresponding structures. The isosurface is 0.12 e/Å3.
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The region with ELF = 1 means perfect localization of electrons, zero ELF indicates a low electron density area, and 0.5 ELF region implies the probability of free electron gas. The ELF isosurfaces of the boron sheets corresponding to the structure in Fig. 1a and g are displayed in Fig. 4a and b. Fig. 4a display the isosurface of ELF = 0.8, which mainly focus on three located areas. The most evident areas are located in the middle of boron atoms at the top and bottom planes (labeled by pink). The remaining two electron localization areas are distributed around boron atom planes (labeled by red) and pillars, respectively. In contrast to the ELF in Fig. 4a, another electronic localization area among boron atoms marked by red and pink is clearly see in Fig. 4b, implying the covalent bonding interaction to some extent like pillars. To distinctly see the interaction and chemical bond character, the ELF of sliced planes of Fig. 4b is displayed in Fig. 4c. High ELF distributions (0.9 1) are located at the top and bottom atoms and pillars, corresponding to strong covalent bonding. These results are consistent with previous work [17]. In addition, electron located areas also occur among boron atoms labeled by pink and red boron with a relatively lower ELF from the middle panel. It is noteworthy that ELF with 0.5 takes up most of this sliced plane, indicating the electrons can transport freely. Such character can also be reflected by Bader charge analysis and B-B bond lengths of different types, as shown in Fig. 4d. The B-B bond lengths in this structure can be classified into four types: d1 = 1.75 (between atom 1 and 2), d2 = 1.76 (between atom 2 and 4), d3 = 2.02 (between atom 2 and 8), d4 = 1.73 (between 4 and 8 atom). Interestingly, bond lengths of d1, d2 and d4 in this structure are close to the bond length in the high-pressure ionic phase c-B28 [36], suggesting that the energetically favorable boron bilayer possess some character of ionic bonding. We also find that the boron atoms near the top and bottom planes (marked by 3 and 4) act as acceptors and gain 0.34 electrons on average, while the boron atoms (marked by 1 and 2) act as electron donors. Relatively speaking, the charge of boron atoms at top and bottom layers (marked by 5, 6, 7 and 8) almost has no change (0.08 electrons loss). Evidently, boron atoms located at different layers can promote the transfer of electrons, further balance the surplus electrons and enhance stability of the whole system. All above analysis demonstrate the formation of pillars benefit for transfer of electrons and compensate the disadvantage of unsaturated valence electrons for sp2 hybridization.
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Bilayer boron sheets with hexagonal holes Incorporation of hexagonal hole in boron sheets has been generally regarded as an effective method to achieve the balance of valence electrons [17–20]. Wu et al. [15] have demonstrated that monolayers a1 and b1 boron sheet are more stable than boron sheets without hexagonal holes. Since monolayer boron sheets with hexagonal holes are energetically favorable, it raises an interesting question whether boron bilayers still prefer hexagonal holes. To clarify this issue, we consider bilayer structures with different hexagonal holes density and classify them into four types: (I) isolated hexagonal holes separated by boron sheets including structural models of Fig. 5i–l; (II) a series of hexagonal holes separated by boron sheets including structural models of Fig. 5m–p; (III) hexagonal holes fill the entire 2D boron sheets including structural models of Fig. 5q and r; (IV) isolated hexagonal holes separated by boron sheets with lower pillars density g1 (0.13 0.14) compared with former three types g1 (0.27 0.33) including structural models of Fig. 5s and t. The relation of Eform versus g2 is plotted in Fig. 6. Generally speaking, the formation energies of these boron bilayers range from 0.35 eV/atom to 0.93 eV/atom and decrease in the order of Eform (0.35 0.44 eV/atom for type I) < Eform (0.45 eV/atom for type IV) < Eform (0.43 0.55 eV/atom for type II) < Eform (0.80 0.93 eV/atom for type III). For type I bilayers, we can clearly see that those two structures only with one isolated hexagonal hole (Eform = 0.35 eV/atom) have lower formation energy than other two structures with two or four neighboring holes (Eform = 0.39, 0.44 eV/atom, respectively), implying that continuous hexagonal holes is detrimental to the thermodynamic stability of boron sheets. Similarly, type II boron bilayer with one series of hexagonal holes (in Fig. 5m and n) is more stable than two continuous series of holes (in Fig. 5o and p). Also, the hole density of 0.13 0.14 in type II results in relatively higher formation energy with respect to type I of 0.05 0.06 hole density by 0.11 eV/atom on average. Once the holes distribute in the whole boron sheets, the balance of electrons are awfully destroyed and the formation energy of type III can even reach 0.93 eV/atom for the structure in Fig. 5r. For type IV structures, smaller g1 and g2 can also stabilize boron bilayers, resulting in formation energy of 0.45 eV/atom. We also find the formation energy of most stable boron bilayer (with 1/16 hole density) is about 0.02 eV/atom lower than the most
Fig. 4. (a) (b) Top view and side view of the electronic localization function with isovalue of 0.8 for two representative structures in Fig. 1a and g. (c) Slabs model in Fig. 4b cut along (001) direction and their ELF. (d) Bader analysis and bond length for the system in Fig. 4b. The value labeled by blue color stand for bond length (Å).
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Fig. 5. Atomic structures of boron bilayer with different hexagonal holes density g2 labeled by (i), (j), . . .(t) The boron atoms at top and bottom planes and stacked in top and bottom planes are labeled by pink and red color, respectively. The pillar density g1, hexagonal hole density g2 and formation energy are given below the structures. Among them, Boron bilayer structures in Fig. 5i, s and t are dynamically stable confirmed by their phonon density of states.
Fig. 6. Formation energy (Eform) as a function of hexagonal holes density (g2) for boron bilayers with hexagonal holes. The black dashed line is a linear fitting of Eform vs. g2.
stable boron bilayer without hexagonal holes, implying the combination of hexagonal holes and pillars at appropriate ratio can further balance the excess electrons and enhance the stability. These results are similar to previous finding by Tang et al. [14] that mixture of three-center bonding and two-center hexagonal regions at an appropriate ratio is beneficial to the stability of monolayer systems. Therefore, we conclude that the stability of boron bilayer is closely related to the densities of pillars and hexagonal holes, as well as the arrangement of holes.
Likewise, ELF, electronic band structure and phonon spectrum of one representative boron bilayer (in Fig. 5i) with the lowest formation energy is shown in Fig. 7. Similar to Fig. 4b, ELF with 0.85 isovalue in this boron bilayer concentrate on three areas: the middle of boron atoms at top and bottom planes (labeled by pink color) around the hexagonal holes, among boron atoms labeled by red and pink around hexagonal holes and pillars. The main differences between this structure and those without holes are the coordination number. Boron atoms around the holes form 5 and 6 coordination, compared with former 6 and 7 coordination in boron bilayer without holes. To clearly see the character of chemical bonding, the sliced planes of ELF cut along the side view in Fig. 7a is plotted in Fig. 7b. Evidently, a high ELF distribution (about 0.9) locates on the middle of boron atoms labeled by red and pink around the holes. Bader charge analysis also demonstrate that each boron atom slightly below top layer boron atoms gains about 0.34 electrons from the surrounding atoms and saturate outermost valence electrons. Furthermore, the calculated phonon spectrum shows the dynamical stability (no negative frequencies) and the electronic band structure indicates metallic properties in Fig. 7c. In addition to the structure in Fig. 5i, lattice dynamic properties of some other boron bilayer sheets with holes are also studied by calculating their phonon density of states, which are displayed in Fig. S1. The absence of imaginary modes has confirmed their dynamic stabilities. Moreover, AIMD simulations were performed for boron bilayers in Fig. 5i to further examine the thermal stability. The temperature was set as 300 K and the time step was 1 fs within the
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Fig. 7. (a) Top view and side view of the electronic localization function (with isovalue = 0.85) of structural model in Fig. 5i. (b) Slabs model in Fig. 7a cut along (001) direction and the corresponding ELF. (c) The phonon spectra and electronic band structure of the structure in Fig. 7a.
canonical NVT ensemble. Boron bilayers can almost keep initial configuration after 5 ps as shown in Fig. S2. The result indicates that B-B bond is enough strong and boron bilayer sheets can exist stably at room temperature. Again, the existence of hexagonal holes in boron bilayers has significant impact on the electronic band structures. All structures in Fig. 5 exhibit metallic behaviors with bands crossing the Fermi level like other boron allotrope. In contrast to the effect of pillars on electronic band structures in Fig. 3, the bands become more flat due to hexagonal holes introduction as shown in Fig. S3, suggesting the deterioration to the carrier mobility.
Conclusion In summary, the structures, energetic stabilities, electronic properties of boron bilayer with various combinations of pillars and hexagonal holes are systematically investigated by firstprinciples calculations. The stability of these boron bilayer sheets outperforms the most stable boron monolayer g1/8-sheet. Such lower formation energy can be attributed to the balance of excess electrons by forming pillars or introducing hexagonal holes. Analyses of total charge density, ELF and Bader charge show that boron atoms can bond well with each other by in-plane covalent interactions or transferring electrons out of plane. The electronic band structures show that all boron bilayer are metallic and might be used as electrode materials in batteries. We provide a new method to decorate boron sheets by introducing pillars and hexagonal holes to design a series of stable boron bilayer sheets, expanding the scope of 2D boron materials and devices. Acknowledgements This work is supported by the National Natural Science Foundation of China (11404050) and the Fundamental Research Funds for the Central Universities of China (DUT16RC(4)50, DUT16JJ(G)05, DUT16LAB01). We acknowledge the Supercomputing Center of Dalian University of Technology for providing the computing resources.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.flatc.2017.08.008. References [1] K.S. Novoselov, V.I. Fal’ko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, Nature 490 (2012) 192–200. [2] M.J. Allen, V.C. Tung, R.B. Kaner, Chem. Rev. 110 (2010) 132–145. [3] F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Nat. Photonics 4 (2010) 611–622. [4] A.C. Ferrari, F. Bonaccorso, V. Fal’ko, K.S. Novoselov, S. Roche, P. Boggild, S. Borini, F.H. Koppens, V. Palermo, N. Pugno, et al., Nanoscale 7 (2015) 4598– 4810. [5] A. Molle, J. Goldberger, M. Houssa, Y. Xu, S.C. Zhang, D. Akinwande, Nat. Mater. 16 (2017) 163–169. [6] A.J. Mannix, B. Kiraly, M.C. Hersam, N.P. Guisinger, Nat. Rev. Chem. 1 (2017) 0014. [7] Z.A. Piazza, H.S. Hu, W.L. Li, Y.F. Zhao, J. Li, L.S. Wang, Nat. Commun. 5 (2014) 3113. [8] H.J. Zhai, B. Kiran, J. Li, L.S. Wang, Nat. Mater. 2 (2003) 827–833. [9] N. Gonzalez Szwacki, A. Sadrzadeh, B.I. Yakobson, Phys. Rev. Lett. 98 (2007) 166804. [10] H.J. Zhai, Y.F. Zhao, W.L. Li, Q. Chen, H. Bai, H.S. Hu, Z.A. Piazza, W.J. Tian, H.G. Lu, Y.B. Wu, et al., Nat. Chem. 6 (2014) 727–731. [11] J. Zhao, X. Huang, R. Shi, H. Liu, Y. Su, R.B. King, Nanoscale 7 (2015) 15086– 15090. [12] F. Liu, C. Shen, Z. Su, X. Ding, S. Deng, J. Chen, N. Xu, H. Gao, J. Mater. Chem. 20 (2010) 2197–2205. [13] D. Ciuparu, R.F. Klie, Y. Zhu, L. Pfefferle, J. Phys. Chem. B 35 (2004) 3967–3969. [14] H. Tang, S. Ismail-Beigi, Phys. Rev. Lett. 99 (2007) 115501. [15] X. Wu, J. Dai, Y. Zhao, Z. Zhuo, J. Yang, X.C. Zeng, ACS Nano. 6 (2012) 7443– 7453. [16] X.-F. Zhou, X. Dong, A.R. Oganov, Q. Zhu, Y. Tian, H.-T. Wang, Phys. Rev. Lett. 112 (2014) 085502. [17] F. Ma, Y. Jiao, G. Gao, Y. Gu, A. Bilic, Z. Chen, A. Du, Nano Lett. 16 (2016) 3022– 3028. [18] N. Karmodak, E.D. Jemmis, Angew. Chem.-Int. Ed. 56 (2017) 10093–10097. [19] W.L. Li, Q. Chen, W.J. Tian, H. Bai, Y.F. Zhao, H.S. Hu, J. Li, H.J. Zhai, S.D. Li, L.S. Wang, J. Am. Chem. Soc. 136 (2014) 12257–12260. [20] Y. Liu, E.S. Penev, B.I. Yakobson, Angew. Chem.-Int. Ed. 52 (2013) 3156–3159. [21] H. Liu, J. Gao, J. Zhao, Sci. Rep. 3 (2013) 3238. [22] L.Z. Zhang, Q.B. Yan, S.X. Du, G. Su, H.J. Gao, J. Phys. Chem. C 116 (2012) 18202– 18206. [23] E.S. Penev, S. Bhowmick, A. Sadrzadeh, B.I. Yakobson, Nano Lett. 12 (2012) 2441–2445. [24] X. Yu, L. Li, X.-W. Xu, C.-C. Tang, J. Phys. Chem. C 116 (2012) 20075–20079. [25] J. Kunstmann, A. Quandt, Phys. Rev. B 74 (2006) 035413. [26] K.C. Lau, R. Pati, R. Pandey, A.C. Pineda, Chem. Phys. Lett. 418 (2006) 549–554.
54
N. Gao et al. / FlatChem 7 (2018) 48–54
[27] K.C. Lau, R. Pandey, J. Phys. Chem. C 111 (2007) 2906–2912. [28] T.R. Galeev, Q. Chen, J.C. Guo, H. Bai, C.Q. Miao, H.G. Lu, A.P. Sergeeva, S.D. Li, A. I. Boldyrev, Phys. Chem. Chem. Phys. 13 (2011) 11575–11578. [29] A.J. Mannix, X.-F. Zhou, B. Kiraly, J.D. Wood, D. Alducin, B.D. Myers, X. Liu, B.L. Fisher, U. Santiago, J.R. Guest, et al., Science 350 (2015) 1513–1516. [30] G. Tai, T. Hu, Y. Zhou, X. Wang, J. Kong, T. Zeng, Y. You, Q. Wang, Angew. Chem. 127 (2015) 15693–15697. [31] B. Feng, J. Zhang, Q. Zhong, W. Li, S. Li, H. Li, P. Cheng, S. Meng, L. Chen, K. Wu, Nat. Chem. 8 (2016) 563–568. [32] H.S. Tsai, C.H. Hsiao, Y.P. Lin, C.W. Chen, H. Ouyang, J.H. Liang, Small 12 (2016) 5251–5255. [33] B. Albert, H. Hillebrecht, Angew. Chem.-Int. Ed. 48 (2009) 8640–8668. [34] J. Tian, Z. Xu, C. Shen, F. Liu, N. Xu, H.J. Gao, Nanoscale 2 (2010) 1375–1389. [35] A.P. Sergeeva, I.A. Popov, Z.A. Piazza, W.L. Li, C. Romanescu, L.S. Wang, A.I. Boldyrev, Acc. Chem. Res. 47 (2014) 1349–1358. [36] A.R. Oganov, J. Chen, C. Gatti, Y. Ma, Y. Ma, C.W. Glass, Z. Liu, T. Yu, O.O. Kurakevych, V.L. Solozhenko, Nature 457 (2009) 863–867.
[37] B. Peng, H. Zhang, H. Shao, Y. Xu, R. Zhang, H. Zhu, J. Mater. Chem. C 4 (2016) 3592–3598. [38] Y. Jiao, F. Ma, J. Bell, A. Bilic, A. Du, Angew. Chem. 55 (2016) 10292–10295. [39] Z. Zhang, Y. Yang, E.S. Penev, B.I. Yakobson, Adv. Funct. Mater. 27 (2017) 1605059. [40] E.S. Penev, A. Kutana, B.I. Yakobson, Nano Lett. 16 (2016) 2522–2526. [41] M. Gao, Q.-Z. Li, X.-W. Yan, J. Wang, Phys. Rev. B 95 (2017) 024505. [42] H.R. Jiang, Z. Lu, M.C. Wu, F. Ciucci, T.S. Zhao, Nano Energy 23 (2016) 97–104. [43] L. Shi, T. Zhao, A. Xu, J. Xu, Sci. Bull. 61 (2016) 1138–1144. [44] Y. Zhang, Z.F. Wu, P.F. Gao, S.L. Zhang, Y.H. Wen, ACS Appl. Mater. Interfaces 8 (2016) 22175–22181. [45] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133–A1138. [46] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169–11186. [47] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953–17979. [48] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. [49] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [50] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 132 (2010) 154104.