- Email: [email protected]
Structural prediction for zirconium boride monolayer
Physica E: Low-dimensional Systems and Nanostructures 113 (2019) 43–46
Contents lists available at ScienceDirect
Physica E: Low-dimensional Systems and Nanostructures journal homepage: www.elsevier.com/locate/physe
Structural prediction for zirconium boride monolayer a
a,∗
Chen-Ling Li , Jing Wang , Ying Liu a b
T
a,b
Department of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang, 050024, Hebei, China National Key Laboratory for Materials Simulation and Design, Beijing, 100083, China
A B S T R A C T
A stable zirconium boride monolayer with the chemical formula of ZrB4 has been identified by using the first-principles calculations. It has a planar structure by extending the Zr-hexagon, which is formed by jointing three ZrB4 unit cells. The novel ZrB4 monolayer has sound thermodynamic, kinetic and thermal stabilities and can retain its original topological planar structure at an effective temperature of about 500 K. The analysis of electronic property reveals that it is a metallic material with high conductivity. These findings could greatly enrich the diversity of graphene-like materials, which is of great importance for nanoscale device applications.
1. Introduction Boron is a peculiar element with unique chemical and structural complexity. It can form a wide variety of metal boride materials with important industrial applications, ranging from superconductor to superhard and thermoelectric materials [1–3]. Due to the electron deficiency of boron, metal borides also exhibit a huge compositional and structural diversity [4]. In transition metal borides (TMBs), the boron sublattices can be a layered honeycomb structure, a buckled sheet, a B6 octahedra, or a B12 icosohedra [5]. As a matter of fact, various electrical behaviors has been found in metal borides systems. CaB6, SrB6, and BaB6 are semiconductors, while LaB6 and EuB6 are conductors [6]. MgB2 exhibit superconductivity [1]. YbB6 and YbB12 are reported to be non-trivial Z2 topological insulator and Kondor insulator, respectively [7]. Monoclinic MoB4 [8] and the ZrB12 [9] are predicted to be new promising superhard materials. The fascinating features displayed by these metal borides have made the research of metal boride nanomaterials as appealing as carbon nanomaterials. In the past two decades, extensive experimental and theoretical studies have been conducted on two-dimensional (2D) metal borides. By means of a particle swarm optimization method combined with density functional theory computations, three 2D FeB6 monolayers have been predicted to be stable, where α-FeB6 is metallic, and β-FeB6 and γ-FeB6 are semiconductors [10]. Some 2D metal borides, including single-layer MoB4 [11], monolayer TiB2 [12], and FeB2 sheet [13] have been predicted to be Dirac materials. Among them, the Spin-Orbit Coupling (SOC) from the interaction between transition metal (TM) atoms and light B atom open a small band gap. Recently, by using density functional theory methods, a 2D WB4 nanosheet has been reported possessing a double Dirac cone, a high Fermi velocity, and a sizable band gap of 0.27eV [14]. In addition, some borides belong to
∗
the P6/mmm space group structure with TM atoms sandwiched between the borophene-like plane have been proposed to be stable structures, such as MgB6 [15], MnB6 [16], and WB4 [14]. The 2D Li-B sheets have been reported to be high capacity electrode materials [17] and the superconducting materials [18]. Very recently, W. Li et al. reported their experimental realization of honeycomb, graphene-like borophene by using an Al(111) surface as the substrate and the molecular beam epitaxy growth in ultrahigh vacuum [19,20]. In this work, we performed the searching of possible candidates for 2D Zr borides nanostructures by means of the particle swarm optimization combined with the first-principles calculations. The results reveal a ZrB4 monolayer sheet is the energetically stable state with an atomic thin planar structure. Then, the structural, thermodynamic, and dynamical stabilities of ZrB4 monolayer are investigated, as well as the intrinsic bonding character and the electronic property. 2. Methodology The basic crystal structure of ZrB4 monolayer was identified by using the particle-swarm optimization (PSO) method as implemented in the CALYPSO code [21], which offers a fast and efficient way to predicted reliable structures with only according to the chemical composition of the materials and the given external conditions, such as pressure and temperature. In our PSO simulation, each primitive cell contains one Zr atom and four B atoms, and the number of formula units per simulation cell was set to be 1; that is, the unit cells contained a total of 5 atoms. The number of generation was set to be 50 and the population size was set to be 30. During the PSO simulation, the structural relaxations was carried out at the generalized gradient approximation (GGA) level, using the Perdew-Burke-Ernzerhof (PBE) [22] exchange correlation function implemented in Vienna ab initio
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.physe.2019.04.011 Received 26 February 2019; Received in revised form 10 April 2019; Accepted 19 April 2019 Available online 28 April 2019 1386-9477/ © 2019 Elsevier B.V. All rights reserved.
Physica E: Low-dimensional Systems and Nanostructures 113 (2019) 43–46
C.-L. Li, et al.
Fig. 1. (a) Configuration and (b) Phonon dispersion spectrum of the ZrB4 monolayer sheet.
Fig. 3. Deformation electron density of the ZrB4 monolayer sheet. (a) the 2D slice with the atom configurations and (b) the 3D isosurface. The iso-value is set to be 0.02 e/Å3.
simulation package (VASP). The structure relaxation and total energy calculations for the ZrB4 monolayer obtained by CALYPSO were further refined by using DFT with higher accuracy as implemented in VASP. The projector-augmented wave (PAW) [23,24] method was used for the core region, and the kinetic energy cutoff of 500 eV was used in all calculations. In selfconsistent field, the convergence criteria was set to be 10−5 eV/Å for the energy and 10−4 eV/Å for the force. The Brillouin zone was sampled by Monkhorst-Pack (MP) [25] method with a 9 × 9 × 1. The vacuum space was set to larger than 15 Å in order to avoid interactions between adjacent layers. The phonon dispersion was calculated by using density functional perturbation theory (DFPT) [26] with the phonopy package [27]. To further study of thermodynamic stability, Born-Oppenheimer Molecular dynamics simulations were conducted by using NVT ensembles. A double numerical basis set including polarization (DNP) [28] and the PBE exchange correlation functional were used. The total simulation time was set to be 10.0 ps with a step of 2.0 fs at four different initial temperatures of 300 K, 1000 K, 1500 K and 2000 K.
structures were generated and then our search yields a highly stable ZrB4 monolayer sheet. In this sheet, the Zr atoms and the B atoms are all on the same plane and each Zr atom is surrounded by nine B atoms. Among them, there are six nearest-neighbored B and three secondary-neighbored B atoms. The lattice parameters are a = b = 4.628 Å, γ = 120.0°, and the ZrB4 monolayer sheet has a Pm(6) symmetry. Fig. 1(a) shows the configuration of the ZrB4 monolayer. It may be viewed as constructed by motifs of equilateral Zr-trigons. In this structure, there are two kinds of Zr-trigons, one with only a B atom at the center (ZrB-trigon), and the other with a B-trigon inside (ZrB3-trigon). These two Zr-trigons just make up the unit cell of this ZrB4 monolayer sheet. Every group of three unit cells joins together forming a Zr-hexagon, which are extended to a completely planar structure in a periodic arrangement. The distance between Zr atoms is 4.628 Å. For the B-trigons inside the Zr-trigons, the lengths of the BeB bonds are 1.650 Å, which is about the same as in the pure boron sheet (1.67 Å) [29]. Along with a slightly larger BeB bond (1.719 Å) connects the neighboring B atom lying at the center of the adjacent ZrB-trigon. There are two 2.345 Å bond lengths between Zr atom and the nearest-neighbored B, and one 2.672 Å distance between the Zr and the second-neighbored B atom in one primitive cell, resulting in an average of 2.454 Å ZreB bond length. To access the experimental feasibility of the newly predicted ZrB4
3. Results and discussions The ground state structures of ZrB4 were obtained through a comprehensive PSO search, which was followed by the full relaxation of random structures with VASP code. Overall, 1500 initial ZrB4 sheet
Fig. 2. Snapshots for the equilibrium structures of ZrB4 monolayer at the temperatures of (a) 300 K, (b) 1000 K, (c) 1500 K, and (d) 2000 K, at the end of 10 ps ab initio dynamic simulations. 44
Physica E: Low-dimensional Systems and Nanostructures 113 (2019) 43–46
C.-L. Li, et al.
Fig. 4. The NBO analysis for ZrB4 monolayer. (a)–(c) The σ bonds for B-B and ZreB. The natural atomic hybrids are σ1 = 0.705(sp2.77)B+0.710 (sp2.96)B, σ2 = 0.760(sp2.09)B+0.650(sp0.59)B, and σ3 = 0.771(d)Zr+0.636(p)B, respectively. (d)–(h) The five d orbitals of Zr atom.
We further evaluate the thermodynamic stability of ZrB4 monolayer by performing the ab initio molecular dynamic simulation. We used relatively large 3 × 3 supercell and carried out the Born-Oppenheimer simulations with the NVT ensemble. Four different initial temperatures of 300 K, 1000 K, 1500 K, and 2000 K were used in the calculations. Snapshots of the geometries at the end of 10 ps simulations (Fig. 2) show that the ZrB4 monolayer can maintain its original topological structures at the temperature up to 1000 K, corresponding to an effective temperature of about 500 K, but it will collapse at extremely high temperatures of 1500 K and 2000 K. The results show that ZrB4 monolayer has a relatively high thermodynamic stability. To gain deep insight into the unique bonding nature and stabilizing mechanism in 2D ZrB4 monolayer sheet, the bonding characteristics were analyzed by calculating the deformation electron density, as shown in Fig. 3. It can be seen from Fig. 3(a) that there exist strong covalent bonds between B atoms. In one primitive cell, there are six BeB bonds, which just correspond to the twelve valence electrons of the four B atoms. They are 2c-2e BeB bonds. Furthermore, the Mülliken atomic charge analysis [31] also indicates few electron transfer. In general, a total of 0.190e transferred from a Zr atom to the six neighboring B atoms. As shown in Fig. 3(b), it is mainly the d-orbital characteristics on Zr atoms. For B atoms, there are obvious sp2-like hybridization, which is crucial for stabilizing the planar structure. The Natural bonding orbital (NBO) analysis [32] also confirm these bonding characteristics, as shown in Fig. 4. The analysis results indicate that the occupation number of the 2c2e BeB bonds are 1.601–1.804e. The ZreB bonds are mainly composed of Zr d orbital and B p orbital. In addition, the five d orbitals of Zr are given in Fig. 4(d–h). The Zr atom with relatively large atom radium, embedded into the networks of B atoms, and further reinforced the stability of this ZrB4 monolayer. Then, we investigated the electronic properties, including the band structure and corresponding projected density of states (PDOS) of the ZrB4 monolayer, as shown in Fig. 5. In the band structure, there are two band lines across the Fermi level. Thus, the ZrB4 monolayer is metallic. The high peaks of the PDOS around the Fermi level, which are predominantly composed of Zr-d states. It indicates high density of carriers
Fig. 5. Electronic structure of ZrB4 monolayer sheet. (a) Band structure and (b) PDOS. The Fermi energy is taken to be the zero energy.
monolayer, the stability was first evaluated by calculating its cohesive energy (Eb). Here, Eb=(EZr +4EB-EZrB4)/5, where EZr, EB, and EZrB4 are the total energies of a single Zr atom, a single B atom, and one unit cell of the ZrB4 monolayer, respectively. The computed cohesive energy of ZrB4 monolayer sheet is 6.152 eV/atom, which is higher than those of FeB6 (5.79–5.56 eV/atom) [10], FeB2 (4.87 eV/atom) [13], and Be2C (4.86 eV/atom) [30]. The large cohesive energy suggests that the ZrB4 monolayer is a strongly bonded network and a stable phase of ZreB system. Then, the dynamical stability of ZrB4 monolayer was evaluated by computing the phonon dispersion along the high-symmetry lines in first Brillouin zone, as shown in Fig. 1(b). The absence of imaginary frequencies suggests the kinetic stability of the ZrB4 monolayer. The highest frequency reaches up to 37.280 THz, indicating the robust ZreB and BeB interactions in this novel ZrB4 monolayer. 45
Physica E: Low-dimensional Systems and Nanostructures 113 (2019) 43–46
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at Fermi level and accordingly, outstanding electric conductivity of the ZrB4 monolayer. Considering the relativistic effect of Zr atom, the band structures with spin orbit coupling (SOC) was calculated and discussed in Section I of the Supplementary Information. Finally, the magnetic moment and the elastic constants were evaluated as shown in the Supplementary Information (Sections II and III).
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4. Conclusions In summary, we performed comprehensive DFT computations to check the possibility to obtain graphene-like materials containing planar hypercoordinate transition metal atoms. The calculations identified a 2D ZrB4 monolayer. It has a planar structure by extending the Zr-hexagon, which is formed by jointing three ZrB4 unit cells. This ZrB4 monolayer has sound thermodynamic, kinetic and thermal stabilities. It can retain its original topological planar structure at an effective temperature of about 500 K. The newly predicted ZrB4 monolayer is a metallic material with high conductivity, due to the high density of electronic states around the Fermi Level. These results has provided some promising strategy to stabilize the 2D boron networks and to design boron related 2D materials, which could greatly enrich the diversity of graphene-like materials. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 11274089 and 11304076), the Natural Science Foundation of Hebei Province for Distinguished Young Scholars (Grant No. A2018205174), and the Program for High-level Talents of Hebei Province (Grant No. A201500118). We also acknowledge partially financial support from the 973 Project in China under Grant No. 2011CB606401. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.physe.2019.04.011. References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Superconductivity at 39 K in magnesium diboride, Nature 410 (2001) 63–64. [2] H.Y. Chung, M. Weinberger, J.B. Levine, A. Kavner, J.M. Yang, S.H. Tolbert, R.B. Kaner, Response to comment on “Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure”, Science 316 (2007) 436–439. [3] A. Sussardi, T. Tanaka, A.U. Khan, L. Schlapbach, T. Mori, Enhanced thermoelectric properties of samarium boride, J. Materiomics 1 (2015) 196–204. [4] T. Mori, K.A. Gschneidner, J.C. Bunzli Jr., V. Pecharsky, Handbook on the Physics and Chemistry of Rare Earths, vol. 38, Elsevier, Amsterdam, 2008, pp. 105–173. [5] J.K. Burdett, E. Canadell, G.J. Miller, Electronic structure of transition-metal borides with the AlB2 structure, J. Am. Chem. Soc. 108 (1986) 6561–6568. [6] N.N. Greenwood, R.V. Parish, P. Thornton, Metal borides, Q. Rev. Chem. Soc. 20 (1966) 441–464.
46
Contents lists available at ScienceDirect
Physica E: Low-dimensional Systems and Nanostructures journal homepage: www.elsevier.com/locate/physe
Structural prediction for zirconium boride monolayer a
a,∗
Chen-Ling Li , Jing Wang , Ying Liu a b
T
a,b
Department of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang, 050024, Hebei, China National Key Laboratory for Materials Simulation and Design, Beijing, 100083, China
A B S T R A C T
A stable zirconium boride monolayer with the chemical formula of ZrB4 has been identified by using the first-principles calculations. It has a planar structure by extending the Zr-hexagon, which is formed by jointing three ZrB4 unit cells. The novel ZrB4 monolayer has sound thermodynamic, kinetic and thermal stabilities and can retain its original topological planar structure at an effective temperature of about 500 K. The analysis of electronic property reveals that it is a metallic material with high conductivity. These findings could greatly enrich the diversity of graphene-like materials, which is of great importance for nanoscale device applications.
1. Introduction Boron is a peculiar element with unique chemical and structural complexity. It can form a wide variety of metal boride materials with important industrial applications, ranging from superconductor to superhard and thermoelectric materials [1–3]. Due to the electron deficiency of boron, metal borides also exhibit a huge compositional and structural diversity [4]. In transition metal borides (TMBs), the boron sublattices can be a layered honeycomb structure, a buckled sheet, a B6 octahedra, or a B12 icosohedra [5]. As a matter of fact, various electrical behaviors has been found in metal borides systems. CaB6, SrB6, and BaB6 are semiconductors, while LaB6 and EuB6 are conductors [6]. MgB2 exhibit superconductivity [1]. YbB6 and YbB12 are reported to be non-trivial Z2 topological insulator and Kondor insulator, respectively [7]. Monoclinic MoB4 [8] and the ZrB12 [9] are predicted to be new promising superhard materials. The fascinating features displayed by these metal borides have made the research of metal boride nanomaterials as appealing as carbon nanomaterials. In the past two decades, extensive experimental and theoretical studies have been conducted on two-dimensional (2D) metal borides. By means of a particle swarm optimization method combined with density functional theory computations, three 2D FeB6 monolayers have been predicted to be stable, where α-FeB6 is metallic, and β-FeB6 and γ-FeB6 are semiconductors [10]. Some 2D metal borides, including single-layer MoB4 [11], monolayer TiB2 [12], and FeB2 sheet [13] have been predicted to be Dirac materials. Among them, the Spin-Orbit Coupling (SOC) from the interaction between transition metal (TM) atoms and light B atom open a small band gap. Recently, by using density functional theory methods, a 2D WB4 nanosheet has been reported possessing a double Dirac cone, a high Fermi velocity, and a sizable band gap of 0.27eV [14]. In addition, some borides belong to
∗
the P6/mmm space group structure with TM atoms sandwiched between the borophene-like plane have been proposed to be stable structures, such as MgB6 [15], MnB6 [16], and WB4 [14]. The 2D Li-B sheets have been reported to be high capacity electrode materials [17] and the superconducting materials [18]. Very recently, W. Li et al. reported their experimental realization of honeycomb, graphene-like borophene by using an Al(111) surface as the substrate and the molecular beam epitaxy growth in ultrahigh vacuum [19,20]. In this work, we performed the searching of possible candidates for 2D Zr borides nanostructures by means of the particle swarm optimization combined with the first-principles calculations. The results reveal a ZrB4 monolayer sheet is the energetically stable state with an atomic thin planar structure. Then, the structural, thermodynamic, and dynamical stabilities of ZrB4 monolayer are investigated, as well as the intrinsic bonding character and the electronic property. 2. Methodology The basic crystal structure of ZrB4 monolayer was identified by using the particle-swarm optimization (PSO) method as implemented in the CALYPSO code [21], which offers a fast and efficient way to predicted reliable structures with only according to the chemical composition of the materials and the given external conditions, such as pressure and temperature. In our PSO simulation, each primitive cell contains one Zr atom and four B atoms, and the number of formula units per simulation cell was set to be 1; that is, the unit cells contained a total of 5 atoms. The number of generation was set to be 50 and the population size was set to be 30. During the PSO simulation, the structural relaxations was carried out at the generalized gradient approximation (GGA) level, using the Perdew-Burke-Ernzerhof (PBE) [22] exchange correlation function implemented in Vienna ab initio
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.physe.2019.04.011 Received 26 February 2019; Received in revised form 10 April 2019; Accepted 19 April 2019 Available online 28 April 2019 1386-9477/ © 2019 Elsevier B.V. All rights reserved.
Physica E: Low-dimensional Systems and Nanostructures 113 (2019) 43–46
C.-L. Li, et al.
Fig. 1. (a) Configuration and (b) Phonon dispersion spectrum of the ZrB4 monolayer sheet.
Fig. 3. Deformation electron density of the ZrB4 monolayer sheet. (a) the 2D slice with the atom configurations and (b) the 3D isosurface. The iso-value is set to be 0.02 e/Å3.
simulation package (VASP). The structure relaxation and total energy calculations for the ZrB4 monolayer obtained by CALYPSO were further refined by using DFT with higher accuracy as implemented in VASP. The projector-augmented wave (PAW) [23,24] method was used for the core region, and the kinetic energy cutoff of 500 eV was used in all calculations. In selfconsistent field, the convergence criteria was set to be 10−5 eV/Å for the energy and 10−4 eV/Å for the force. The Brillouin zone was sampled by Monkhorst-Pack (MP) [25] method with a 9 × 9 × 1. The vacuum space was set to larger than 15 Å in order to avoid interactions between adjacent layers. The phonon dispersion was calculated by using density functional perturbation theory (DFPT) [26] with the phonopy package [27]. To further study of thermodynamic stability, Born-Oppenheimer Molecular dynamics simulations were conducted by using NVT ensembles. A double numerical basis set including polarization (DNP) [28] and the PBE exchange correlation functional were used. The total simulation time was set to be 10.0 ps with a step of 2.0 fs at four different initial temperatures of 300 K, 1000 K, 1500 K and 2000 K.
structures were generated and then our search yields a highly stable ZrB4 monolayer sheet. In this sheet, the Zr atoms and the B atoms are all on the same plane and each Zr atom is surrounded by nine B atoms. Among them, there are six nearest-neighbored B and three secondary-neighbored B atoms. The lattice parameters are a = b = 4.628 Å, γ = 120.0°, and the ZrB4 monolayer sheet has a Pm(6) symmetry. Fig. 1(a) shows the configuration of the ZrB4 monolayer. It may be viewed as constructed by motifs of equilateral Zr-trigons. In this structure, there are two kinds of Zr-trigons, one with only a B atom at the center (ZrB-trigon), and the other with a B-trigon inside (ZrB3-trigon). These two Zr-trigons just make up the unit cell of this ZrB4 monolayer sheet. Every group of three unit cells joins together forming a Zr-hexagon, which are extended to a completely planar structure in a periodic arrangement. The distance between Zr atoms is 4.628 Å. For the B-trigons inside the Zr-trigons, the lengths of the BeB bonds are 1.650 Å, which is about the same as in the pure boron sheet (1.67 Å) [29]. Along with a slightly larger BeB bond (1.719 Å) connects the neighboring B atom lying at the center of the adjacent ZrB-trigon. There are two 2.345 Å bond lengths between Zr atom and the nearest-neighbored B, and one 2.672 Å distance between the Zr and the second-neighbored B atom in one primitive cell, resulting in an average of 2.454 Å ZreB bond length. To access the experimental feasibility of the newly predicted ZrB4
3. Results and discussions The ground state structures of ZrB4 were obtained through a comprehensive PSO search, which was followed by the full relaxation of random structures with VASP code. Overall, 1500 initial ZrB4 sheet
Fig. 2. Snapshots for the equilibrium structures of ZrB4 monolayer at the temperatures of (a) 300 K, (b) 1000 K, (c) 1500 K, and (d) 2000 K, at the end of 10 ps ab initio dynamic simulations. 44
Physica E: Low-dimensional Systems and Nanostructures 113 (2019) 43–46
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Fig. 4. The NBO analysis for ZrB4 monolayer. (a)–(c) The σ bonds for B-B and ZreB. The natural atomic hybrids are σ1 = 0.705(sp2.77)B+0.710 (sp2.96)B, σ2 = 0.760(sp2.09)B+0.650(sp0.59)B, and σ3 = 0.771(d)Zr+0.636(p)B, respectively. (d)–(h) The five d orbitals of Zr atom.
We further evaluate the thermodynamic stability of ZrB4 monolayer by performing the ab initio molecular dynamic simulation. We used relatively large 3 × 3 supercell and carried out the Born-Oppenheimer simulations with the NVT ensemble. Four different initial temperatures of 300 K, 1000 K, 1500 K, and 2000 K were used in the calculations. Snapshots of the geometries at the end of 10 ps simulations (Fig. 2) show that the ZrB4 monolayer can maintain its original topological structures at the temperature up to 1000 K, corresponding to an effective temperature of about 500 K, but it will collapse at extremely high temperatures of 1500 K and 2000 K. The results show that ZrB4 monolayer has a relatively high thermodynamic stability. To gain deep insight into the unique bonding nature and stabilizing mechanism in 2D ZrB4 monolayer sheet, the bonding characteristics were analyzed by calculating the deformation electron density, as shown in Fig. 3. It can be seen from Fig. 3(a) that there exist strong covalent bonds between B atoms. In one primitive cell, there are six BeB bonds, which just correspond to the twelve valence electrons of the four B atoms. They are 2c-2e BeB bonds. Furthermore, the Mülliken atomic charge analysis [31] also indicates few electron transfer. In general, a total of 0.190e transferred from a Zr atom to the six neighboring B atoms. As shown in Fig. 3(b), it is mainly the d-orbital characteristics on Zr atoms. For B atoms, there are obvious sp2-like hybridization, which is crucial for stabilizing the planar structure. The Natural bonding orbital (NBO) analysis [32] also confirm these bonding characteristics, as shown in Fig. 4. The analysis results indicate that the occupation number of the 2c2e BeB bonds are 1.601–1.804e. The ZreB bonds are mainly composed of Zr d orbital and B p orbital. In addition, the five d orbitals of Zr are given in Fig. 4(d–h). The Zr atom with relatively large atom radium, embedded into the networks of B atoms, and further reinforced the stability of this ZrB4 monolayer. Then, we investigated the electronic properties, including the band structure and corresponding projected density of states (PDOS) of the ZrB4 monolayer, as shown in Fig. 5. In the band structure, there are two band lines across the Fermi level. Thus, the ZrB4 monolayer is metallic. The high peaks of the PDOS around the Fermi level, which are predominantly composed of Zr-d states. It indicates high density of carriers
Fig. 5. Electronic structure of ZrB4 monolayer sheet. (a) Band structure and (b) PDOS. The Fermi energy is taken to be the zero energy.
monolayer, the stability was first evaluated by calculating its cohesive energy (Eb). Here, Eb=(EZr +4EB-EZrB4)/5, where EZr, EB, and EZrB4 are the total energies of a single Zr atom, a single B atom, and one unit cell of the ZrB4 monolayer, respectively. The computed cohesive energy of ZrB4 monolayer sheet is 6.152 eV/atom, which is higher than those of FeB6 (5.79–5.56 eV/atom) [10], FeB2 (4.87 eV/atom) [13], and Be2C (4.86 eV/atom) [30]. The large cohesive energy suggests that the ZrB4 monolayer is a strongly bonded network and a stable phase of ZreB system. Then, the dynamical stability of ZrB4 monolayer was evaluated by computing the phonon dispersion along the high-symmetry lines in first Brillouin zone, as shown in Fig. 1(b). The absence of imaginary frequencies suggests the kinetic stability of the ZrB4 monolayer. The highest frequency reaches up to 37.280 THz, indicating the robust ZreB and BeB interactions in this novel ZrB4 monolayer. 45
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at Fermi level and accordingly, outstanding electric conductivity of the ZrB4 monolayer. Considering the relativistic effect of Zr atom, the band structures with spin orbit coupling (SOC) was calculated and discussed in Section I of the Supplementary Information. Finally, the magnetic moment and the elastic constants were evaluated as shown in the Supplementary Information (Sections II and III).
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4. Conclusions In summary, we performed comprehensive DFT computations to check the possibility to obtain graphene-like materials containing planar hypercoordinate transition metal atoms. The calculations identified a 2D ZrB4 monolayer. It has a planar structure by extending the Zr-hexagon, which is formed by jointing three ZrB4 unit cells. This ZrB4 monolayer has sound thermodynamic, kinetic and thermal stabilities. It can retain its original topological planar structure at an effective temperature of about 500 K. The newly predicted ZrB4 monolayer is a metallic material with high conductivity, due to the high density of electronic states around the Fermi Level. These results has provided some promising strategy to stabilize the 2D boron networks and to design boron related 2D materials, which could greatly enrich the diversity of graphene-like materials. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 11274089 and 11304076), the Natural Science Foundation of Hebei Province for Distinguished Young Scholars (Grant No. A2018205174), and the Program for High-level Talents of Hebei Province (Grant No. A201500118). We also acknowledge partially financial support from the 973 Project in China under Grant No. 2011CB606401. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.physe.2019.04.011. References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Superconductivity at 39 K in magnesium diboride, Nature 410 (2001) 63–64. [2] H.Y. Chung, M. Weinberger, J.B. Levine, A. Kavner, J.M. Yang, S.H. Tolbert, R.B. Kaner, Response to comment on “Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure”, Science 316 (2007) 436–439. [3] A. Sussardi, T. Tanaka, A.U. Khan, L. Schlapbach, T. Mori, Enhanced thermoelectric properties of samarium boride, J. Materiomics 1 (2015) 196–204. [4] T. Mori, K.A. Gschneidner, J.C. Bunzli Jr., V. Pecharsky, Handbook on the Physics and Chemistry of Rare Earths, vol. 38, Elsevier, Amsterdam, 2008, pp. 105–173. [5] J.K. Burdett, E. Canadell, G.J. Miller, Electronic structure of transition-metal borides with the AlB2 structure, J. Am. Chem. Soc. 108 (1986) 6561–6568. [6] N.N. Greenwood, R.V. Parish, P. Thornton, Metal borides, Q. Rev. Chem. Soc. 20 (1966) 441–464.
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