Two-Dimensional Be2C with Octacoordinate Carbons and Negative

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C: Physical Processes in Nanomaterials and Nanostructures 2

Two Dimensional BeC with Octacoordinate Carbons and Negative Poisson's Ratio Shifeng Qian, Xiaowei Sheng, Yong Zhou, Xiaozhen Yan, Yangmei Chen, Yucheng Huang, Xiaofen Huang, Eryin Feng, and Wuying Huang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12758 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 31, 2018

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The Journal of Physical Chemistry

Two Dimensional Be2 C with Octacoordinate Carbons and Negative Poisson's Ratio †

Shifeng Qian,

∗,†,‡

Xiaowei Sheng,

Yucheng Huang,

†Department ‡Anhui

§

Yong Zhou,

k

Xiaofen Huang,

†,‡

Xiaozhen Yan,

Eryin Feng,

†,‡

¶

Yangmei Chen,

and Wuying Huang

¶

†,‡

of Physics, Anhui Normal University, Anhui, Wuhu 241000, China

Province Key Laboratory of Optoelectric Materials Science and Technology, Wuhu 241000, China

¶School

of Science, Jiangxi University of Science and Technology, Jiangxi, Ganzhou 341000, China

§College

of Chemistry and Material Science, Anhui Normal University, Anhui, Wuhu 241000, China

kDepartment

of Physics, Sichuan Normal University, Sichuan, Chengdu 610068, China

E-mail: [email protected]

Abstract In this work, we predicted three new two dimensional (2D) Be2 C structures, namely α-Be2 C, β -Be2 C and γ -Be2 C based on density functional theory (DFT) computations

and particle-swarm optimization (PSO) method. In α-Be2 C, a carbon atom binds to eight Be atoms forming an octacoordinate carbon moiety. This is the rst example of an octacoordinate carbon-containing material. The other two structures, β -Be2 C and γ -Be2 C, are quasi planar hexacoordinate-carbon (phC) containing 2D materials. Good stability with these three phases is revealed by their lower cohesive energy and positive phonon modes. More interestingly, these predicted new phases of Be2 C are all 1

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semiconductors and have unusual negative Poisson's ratios (NPRs). If synthesized, 2D Be2 C materials will have a broad range of applications in electronics and mechanics.

INTRODUCTION The researches of novel structures containing hypercoordinate carbons have attracted great attention in theoretical and experimental studies, due to the potentially unique properties of these structures, as well as the importance of fundamental research. 1 The rst pentacoordinate carbon species CH5 + was isolated in 1952, 2 which possess a highly uxional threedimensional (3D) structure. After that, a great deal of 3D hypercoordinate carbon species were predicted theoretically 36 and exemplied experimentally. 712 For example, Gao

et al.

show ab initio computational evidence of the possible existence of a rst global minimum heptacoordinate carbon motif, CTi7 2+ . 13 On the other hand, the notion of planer tetracoordinate carbon (ptC) was proposed by Homann

et al.

in 1970. 14,15 Later, Schleyer

and co-workers theoretically designed the rst ptC molecule (1, 1-dilithiocyclopropane) in 1976. 16 Since then, ptC chemistry has attracted extensive studies. 1719 A large number of ptC species have been proposed theoretically 2026 and some global minimum structures, such as CAl4 − , 27 CAl4 2− , 28 and CAl3 Si− 29 have been observed experimentally. More interestingly, in addition to ptC, many molecules containing planar pentacoordinate carbon (ppC) 30,31 and hexacoordinate carbon (phC) 3236 have been predicted theoretically. Recent years, there has been growing interest in designing hypercoordinate carbon containing systems. 13,3742 Motivated by graphene 43 and its inorganic analogues, 44 many 2D materials with rule-breaking chemical bonding have been designed computationally. 4552 For example, Wu

. 45 designed the rst ptC-containing 2D materials on the basis of ptC

et al.

molecule CB4 . Li

et al.

46

showed that one C atom binding to six beryllium (Be) atoms

yields a phC-featuring 2D materials with a Be2 C stoichiometry. More recently, Wang et

al.

47

predict a pentacoordinate carbon containing materials with NPR, namely Be5 C2 monolayer.

2


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These materials not only exhibit fascinating structural properties, but also have many unique electronical and mechanical properties. To our knowledge, among all hypercoordinate carbon containing 2D materials predicted, the highest coordinate number for central carbon is six. It is worth noting that the coordination number in a cluster species predicted can be as high as seven in CTi7 2+ . 13 Moreover, the highest coordination number in metal centered boron clusters is even ten. 5356 Is it possible to develop carbon with coordinate numbers more than six in 2D materials? Herein, we show density functional theory (DFT) calculational evidence of the possible stable structures with octacoordinate carbon motif and two allotropic qusia-phC motif. Furthermore, DFT computations demonstrate that these structure have excellent electronic and mechanical properties.

Computational Details The structure optimization, total energy and electronic structure were calculated using the Vienna ab initio simulation package(VASP). 57 The projector-augmented plane wave(PAW) method was used to represent the ion-electron interaction. 58,59 The generalized gradient approximation (GGA) in the form proposed by Perdew, Burke and Ernzehof(PBE) was using to treat the electron exchange-correlation function. 60 The energy cuto of the plane wave was set to 600 eV in all calculations. To account the substantial van der Waals(vdW) contribution from Be-Be interaction, we adopted the PBE+D2 method with the Grimme vdW correction. 61 The convergence threshold was chosen 10−6 eV in energy and 10−3 in force. The brillouin zone was sampled with a 12 × 8 × 1, 3 × 12 × 1 and 12 × 7 × 1 Γ centered Monkhorst-Pack k-points grid in α-, β - and γ -Be2 C, respectively. The phonon spectrum was computed using nite displacement method as implement in CASTEP package. 62 The COHPs were obtained by using the LOBSTER code 6366 on the electronic structures obtained from VASP calculations.

3



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The thermal stability of Be2 C monolayers was evaluated by the AIMD simulations using the Nosé-Hoover method 67 in the NVT and NPT ensemble lasted for 10 ps with the time step of 1fs. In the MD simulations, the initial congurations of α-, β - and γ -Be2 C with 4 × 4,

1 × 5 and 5 × 4 supercell, respectively, were annealed at dierent temperatures. The particle-swarm optimization method within the evolutionary algorithm, as implementd in CALYPSO code, 68 was employed to search for low-energy structures of 2D Be2 C monolayers. In the PSO simulation, the number of generation was set as 20. Unit Cells containing 6, 9, 12 and 18 atoms in total were considered. The structure optimization step of the PSO simulation was carried out employing VASP package at PBE level of theory.

Results and discussion Our study began with a global searches for the structures of Be2 C in the 2D space using rst principles based PSO method implemented in CALYPSO code. These computations led to ve stable structures, two of which, Be2 C-I and Be2 C-II, were proposed previously. 46 Three new structures are named α-, β - and γ -Be2 C (Figure 1a, b, c). It worth noting that Li al.

et

used the same method to search the structures of Be2 C, however, they only found two

structures, Be2 C-I and Be2 C-II. One possible reason is that they only searched the unit cells containing total atoms of 6, 12 and 18, but the unit cells of α- and γ -Be2 C have 9 atoms.

4


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Figure 1: Top and side views of the geometric structures of 2D Be2 C. (a) α-Be2 C. (b) β -Be2 C. (c) γ -Be2 C Generally, α-Be2 C is a tri-layer 2D structure. The top and bottom layers are exactly symmetrical and the distance is 2.99 Å. Every unit cell consists of 12 tetragonums and form a cage structure. Interestingly, each carbon in the middle layer is coordinated with eight Be atoms to form a octacoordinate carbon. At the same time, each carbon in the top and

5



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bottom layer is coordinated with six Be atoms to form a hexacoordinate carbon. This nding is very inspiring because α-Be2 C is the rst octacoordinate carbon containing structure in 2D materials. Figure 1(a) presents the structure. The bond lengths of Be1-C3 and Be3-C3 are 1.824 Å and 1.90 Å respectively, and the bond angles of Be3-C3-Be4 and Be1-C3-Be2 are 80.47◦ and 71.85◦ respectively. β -Be2 C and γ -Be2 C are qusia-phC containing structures, which are similar to Be2 C-I. The only dierence of these structures is the location of the carbons. For β -Be2 C and γ -Be2 C, the carbons are in the dierent planes, while the carbons of the Be2 C-I are in the same plane. Table 1: The calculated cohesive energies per atom for the phases of α-, β - and γ -Be2 C and previously proposed Be2 C-I and Be2 C-II Method PBE (eV/atom) PBE-D2 (eV/atom) HSE06 (eV/atom)

α-Be2 C -4.9138 -5.0348 -5.2878

β -Be2 C -4.8753 -4.9514 -5.2505

γ -Be2 C -4.8629 -4.9436 -5.2115

Be2 C-I -4.8781 -4.9534 -5.2571

Be2 C-I -4.7034 -4.7420 -5.0124

Figure 2: Phonon spectrum of 2D Be2 C. (a) α-Be2 C. (b) β -Be2 C. (c) γ -Be2 C Now our rst priority is to ensure whether these three new 2D Be2 C materials are stable. We rst calculated the cohesive energy of 2D Be2 C, which is dened as: Ecoh = (nEBe + 6


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mEC − EBe2 C )/(n + m), where EBe , EC and EBe2 C are the total energies of single Be, C atom and Be2 C unit cell, respectively; n and m are the number of Be and C atoms in the unit cell, respectively. For comparison, PBE, PBE+D2 and HSE06 functionals have been used to do the calculations. As one can see that the cohesive energy of α-Be2 C is even lower than Be2 C-I (Table I). The other two structures, β - and γ -Be2 C, are higher than Be2 C-I but lower than Be2 C-II in cohesive energy. Then we evaluated the dynamical stabilities of 2D Be2 C by calculating the phonon dispersion along the high-symmetry lines in rst Brillouin zone (Figure 2). The absence of any imaginary frequency in the phonon spectra of these 2D Be2 C structures, suggesting the kinetic stabilities of these dierent phases. The highest frequencies of α-, β - and γ -Be2 C reach up to 30.10 THz, 32.72 THz, and 32.40 THz, respectively, which are similar to Be2 C-I 46 and Be5 C2 . 47 In order to further examine the thermal stability of 2D Be2 C, we carried out ab initio molecular dynamic (AIMD) simulations using 4 × 4, 1 × 5 and 5 × 4 supercell for α-, β and γ -Be2 C, respectively. The simulations were done at the temperature of 900,1200, and 1500 K respectively. The results show that structural integrity of 2D Be2 C materials can be maintained for up to 10 ps at 1200K, but is disrupted severely at 1500 K (Supplementary Figure S1). Optimizations were performed for distorted geometries through AIMD simulations. After full atomic relaxation, the distorted structures at 1200 and 900 K can recover the initial conguration. The above results demonstrate that 2D Be2 C has a good thermal stability. To understand the unique chemical bonding and the stabilizing mechanism of hexa- and octacoordinate carbons in 2D Be2 C, we cauculated the deformation electronic density, which is dened as the total electronic density of 2D Be2 C substracting the electronic density of isolated carbon and beryllium atoms (Figure 3). There is remarkable electron transfer from the 2s orbitals of beryllium atoms to carbon atoms. The transferred electrons are quite delocalized around the C-Be bonds, which is crucial for stabilizing the octacoordinate carbon 7



and illustrates multi-center bond states of C-Be bonds. The similar stabilizing mechanism also has been found in other ptC- and phC-containing 2D materials. 4649,69 According to the Hirshfeld charge popular analysis, C1, C3, Be1, and Be3 atoms in α-Be2 C possess -0.30, -0.20, 0.07, and 0.17 e charge, respectively. The charge transfer of the octacoordinate carbon is much smaller than other two carbon atoms.

Figure 3: Top and side views of deformation charge density of 2D Be2 C. Blue and Yellow refer to electron depletion and accumulation regions, respectively. (a) α-Be2 C. (b) β -Be2 C. (c) γ -Be2 C. The isovalue is 0.01 e/au. . To detect the bonds of octacoordinate carbon in the α-Be2 C, the crystal orbit Hamiltonian population (COHP) can be used, which counts the population of wavefunctions on two atomic orbitals of a pair of selected atoms. The calculated COHP (Figure 4 (a, b)) shows two dierent orbitals overlap of octacoordinate C and Be. The covalent bond between Be1 and C3 stems from the overlap of the 2s-2s, 2s-2px , and 2s-2py of Be and C, respectively, while the bond between Be3 and C3 stems from the overlap of the 2s-2s and 2s-2pz of Be and C, respectively. The integrated COHP (ICOHP) below the Fermi level is -1.2324 and -1.0019 eV/pair for Be1-C3 and Be3-C3, respectively, which means the strong bond states between the octacoordinated C and the nearest eight Be atoms. We also notice that the charges around C are quite delocalized as it is shown in the Figure 3. Therefore, it is a 8


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multi-center bond between the octacoordinated C and the nearest eight Be atom.

Figure 4: Crystal orbital Hamilton population (COHP) analysis for the 2s-2s, 2s-2px , 2s-2py and 2s-2pz orbitals of the nearest-neighbor Be-C interactions. (a) Be1-C3. (b) Be3-C3 (The COHPs of the Be2-C3 is same with Be1-C3, and Be4-C3, Be5-C3 and Be6-C3 are same with Be3-C3.) With such unique bonding states, will the 2D Be2 C sheets possess interesting properties? To address this question, we calculated the band structures and density of states (DOS) of the lowest-energy 2D Be2 C. A indirect gap of about 0.23 eV appears in the band structures, with the valence band maximum (VBM) located at the S point and the conduction band minimum (CBM) located at Y point. It means that α-Be2 C is an indirect narrow-gap semiconductor. This is dierent from Be2 C-I and Be5 C2 -I which are direct wild-gap semiconductor and semi-metal respectively. In order to get a more accurate band gap, we re-computed the band structure and DOS of α-Be2 C by using the hybrid HSE06 functional, as shown in Figure 9



5. HSE06 predicted a 0.75 eV indirect band gap (S → − Y ) and a 1.27 eV direct band gap (Γ) with similar dispersion of energy bands to that of PBE functional. Band structures of

β -Be2 C and γ -Be2 C were also computed (Figure S2). It shows that these two phases have direct band gap located at the Γ point, which is same with Be2 C-I. HSE06 predicted 2.16 and 1.97 eV band gap for β -Be2 C and γ -Be2 C, respectively. The DOS analysis shows in gure 5a. From the energy region around Fermi level of

α-Be2 C, the VBM is contributed by Be-2p and C-2p states, while the CBM is mainly contributed by Be-2p states. For more information of the orbital states, we also computed the partial charge density corresponding to the VBM and CBM of α-Be2 C (Figure 5 b,c). The VBM is mainly localized at the multicenter σ -bonding between C2/C3 and Be atoms while the CBM corresponds solely to the 2p orbitals of Be atoms, which are consistent with the DOS analysis. The DOS analysis shows that the VBM of Be2 C monolayer is contributed by C-2p and Be-2p states while the CBM is mainly contributed by Be-2p states. To get more information, we also computed the partial charge density corresponding to the VBM and CBM of α-Be2 C (Figure 5 b,c). The VBM is mainly localized at the multicenter σ -bonding between C2/C3 and Be atoms while the CBM corresponds solely to the 2p orbitals of Be atoms, consistent with the DOS analysis.

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Figure 5: (a) Band structure and DOS of α-Be2 C. The Fermi level is assigned 0 eV. The isosurfaces of partial charge densities for the top and side views of (b) VBM and (c) CBM of α-Be2 C. The isovalue is 0.01 eA−3

11



Figure 6: The Poisson's ratio as a function of uniaxial deformation of 2D Be2 C in the x and y direction. (a, b) α-Be2 C. The liner Poisson's ratios are -0.00318 in x direction and -0.0151 or -0.0074 in y direction. (c, d) β -Be2 C. The liner Poisson's ratios are -0.5660 in x direction and -0.0151 in y direction. (e, f) γ -Be2 C. The liner Poisson's ratios are -0.2326 in x direction and -0.302 in y direction.

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In addition to the electronic properties, we also investigated the mechanical properties of 2D Be2 C. Take the graphene for an example, the calculated C11 , C22 and C12 are 1051.44, 1051.44,191.47 Gpa, respectively, which achieve good agreements with experimental measurements 70 and previous computations. 71 For α-Be2 C, it belongs to orthorhombic 2D sheet, which have four independent elastic constants: C11 , C22 , C12 and C66 . Elastic constants of

α-Be2 C were calculated to be C11 = 495 GPa, C22 = 307 GPa, C12 = C21 = -5 GPa, and C66 = 130 GPa, in line with the mechanical stability criteria (C11 C22 -C12 2 > 0, C66 > 0). 72 The in-plane Young's modules along x (Yx ) and y (Yy ) directions, which can be deduced from the elastic constants by Yx = (C11 C22 -C12 C21 )/C22 and Yy = (C11 C22 -C12 C21 )/C11 , were computed to be 495 GPa and 308 GPa, respectively (Table S1). Therefore, α-Be2 C is mechanically anisotropic, due to the Yx is not equal to Yy . Moreover, at the same theory level, the in-plane Young's modules of α-Be2 C are less than those of graphene (Yx = Yy = 1051 GPa) but much higher than those of BP (Yx = 165 GPa and Yy = 39 GPa), suggesting that α-Be2 C has good mechanical properties. Remarkably, we noted that three phases of 2D-Be2 C have negative C12 , which means these three structures all have NPRs. We quantitatively calculated the Poisson's ratio ν with the following equations:

νxy = −

dεx dεy , νyx = − , dεx dεy

(1)

Where νxy is the Poisson's ratio of the x direction which is induced by a strain in the x axis, and νyx is the y direction. Figure 6(a, c, e) display the strain response in the y direction when applying stretch in the y direction of 2D Be2 C. Similarly, the Poisson's ratio of the x directions are shown in Figure 6(b, d, f). The strain method and elastic solid theory have the similar results, which means that both methods conrm that the NPR property of these three Be2 C structures. Another interesting nding is that the Poisson's ratio in the y direction of α-Be2 C becomes positive when ε < −0.1. α-Be2 C has diametrically opposed

13



Poisson's ratios in the y direction when we stretch and compress in the x direction (Fig. 6 (a)), which means no matter we stretch or compress in the x direction, α-Be2 C will expand in the y direction.

Figure 7: The evolution of local structure in 2D Be2 C during uniaxial tension in y direction. (a) α-Be2 C is stretch in the y direction, that is, atoms moved in the directions of the attached arrows (red online). To accomodate the tension in the y direction, α-Be2 C contracts in the z direction, that is atoms Be3, Be4, Be5 and Be6 move inward along the attached arrows (blue online). The Be1 and Be2, therefore, was pushed outward along the attached arrows (purple arrows). (b) γ -Be2 C is stretch in the y direction. Atoms moved in the directions of the attached arrows. (c) The variations of d1 and d2 under a strain of deformation along x-direction of α-Be2 C. We oer an explanation to explain the origin of the NPR. Figure 7 illustrates the relationship between the structures and the NPRs, where the motion of atoms for a representative strain increment in the y direction is illustrated. When α-Be2 C is stretched in the y direction, that is, the two surrounding atoms are moved along the attached arrows (blue online) in gure 7a. Normally, the angles θBe5C3Be4 and θBe2C3Be2 (or θBe3C3Be6 and θBe1C3Be1 ) all 14


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have the trend of decrease. However, the decrease of the angle θBe5C3Be4 (or θBe3C3Be6 ) forces the θBe2C3Be2 (or θBe1C3Be1 ) increase , as shown in Figure 7a. Thus, α-Be2 C has a NPR. It is worthwhile to note that the structures of β -Be2 C and γ -Be2 C are similar to Be2 C-I, however Be2 C-I has a PPR. Therefore, The NPRs of β -Be2 C and γ -Be2 C originate from the puckered structure. Take the γ -Be2 C for an example, uniaxial tension in the y direction let to the angle θBe1C2Be2 increase (Figure 7b), which result in the auxetic in x direction. To probe the origin of the opposite sign of Poisson's ratio in the y-direction of α-Be2 C, we further analyze the related structural response(i.e., variations of bonding lengths, bonding angles), as shown in gure 7c. The stress-induced changes in y-direction was decoupled into three parts, that is, the bond length d1 between Be4 and Be6 and the length of d2 and d3 which can be determined by the bond angle of Be4-Be6-C1. Therefore, the lattice constant of y-direction is given by dy =d1 +2d2 . When compress lattice along the x-direction, d1 would increase, whereas d2 vary in an inverse way. Consequently, the variation of lattice distant of y-direction depends on the competition of bond change of Be4 and Be6 and angle change of Be4-Be6-C1. For example, when εx < -0.1 Å, although d2 decrease, d1 increase rapidly. Therefore, Poisson's ratio would be positive. The NPR may endow 2D Be2 C with enhanced toughness and shear resistance, along with enhanced sound and vibration adsorption. Three phases of 2D Be2 C, therefore, could nd some important applications in the elds of medicine, fasteners, tougher composites, national security and defense, and many other potential applications. Recently, Jiang

et al.

73

predicted that single layer black phosphorus (BP) has NPR due to the unique puckered conguration. However, the NPR of BP was observed in out-of-plane direction, which is dierent from 2D Be2 C. Remarkably, the Poisson's ratios of β -Be2 C and γ -Be2 C in the x direction are much higher than that of BP and other 2D NPR materials recently reported, 47,71,7375 especially the β -Be2 C (νxy = -0.5660). The Poisson's ratio of α-Be2 C is also interesting. In y direction, it has a NPR in tension and a PPR in compression. These unique Poisson's ratio make 2D Be2 C a promising candidate for specic application. The puckered structure 15



of β -Be2 C and γ -Be2 C can also give us a new guideline for designing materials with a NPR.

CONCLUSION In summary, we performed comprehensive DFT computations and global minimum search to check the possibility to obtain hypercoordinate carbon containing 2D materials. Our computations identied three 2D Be2 C , namely α-Be2 C, β -Be2 C and γ -Be2 C, which possess hypercoordinate carbon and dierently arranged beryllium. In α-Be2 C, a carbon atom binds to eight beryllium atoms to form a octacoordinate carbon moiety, representing the rst example of a octacoordinate carbon in 2D structure. α-Be2 C has a strong chemical bonding and a high in-plane stiness, positive phonon modes and high thermal stability. Most importantly, the PSO method conrmed that the octacoordinate carbon containing 2D Be2 C has the lowest cohesive energy in ve 2D Be2 C materials, which endows α-Be2 C great possibility to be realized experimentally. The other two structures, β -Be2 C and γ -Be2 C, are quasi phC containing 2D materials. Unique chemical bonds also generate excellent electronic and mechanical properties. Our computation demonstrated that α-Be2 C have a 0.75 eV indirect band gap (S → − Y ) and other two phases have 2.16 and 1.97 eV direct band gap, respectively. More interestingly, three phases of 2D Be2 C all have rather intriguing mechanical properties featured with a NPR. Therefore, 2D Be2 C structures are expected to have wide applications in electronics and mechanics. We hope our theoretical studies will stimulate future experimental studies on the synthesis of beryllium carbide to probe their mechanic and electronic properties and attract more attentions on investigating nano materials with novel chemical bonding.

Supporting Information Figure S1 and Figure S2 show the snapshots of the nal frame of each molecular dynamics simulation using NVT and NPT, and Figure S3 shows the band structures of β -Be2 C and 16


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γ -Be2 C. Table S1 shows the calculated valus for elastic modulus tensor Cij and in-plane Young's modulus.

Acknowledgements This work has been supported by the National Natural Science Foundation of China (No. 11404006, No. 21503001 and No. 11704163), the Anhui Provincial Natural Science Foundation (No.1708085QB41) and China Postdoctoral Science Foundation (No. 2017M623064). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

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Two-Dimensional Be2C with Octacoordinate Carbons and Negative

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