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Prediction of a Three-Dimensional Conductive Superhard Material: Diamond-like BC2 Lifang Xu, Zhisheng Zhao, Li-Min Wang, Bo Xu, Julong He, Zhongyuan Liu, and Yongjun Tian* State Key Laboratory of Metastable Materials Science and Technology, Yanshan UniVersity, Qinhuangdao 066004, Hebei ProVince, China ReceiVed: July 25, 2010; ReVised Manuscript ReceiVed: NoVember 19, 2010
A tetragonal BC2 (t-BC2) phase originating from the cubic diamond structure was predicted by first-principles calculations. The t-BC2 structure has a tetragonal lattice (space group I41/amd, No. 141) and possesses the simple stacking sequence BC2BC2... along its c axis. The structural stability of the proposed t-BC2 was confirmed by calculations of the elastic constants and phonon frequencies. The electronic densities of states of t-BC2 show that all the B-C and C-C bonds in the crystal are metallic. Thus, t-BC2 possesses three-dimensional conductivity, which is different from the two-dimensional conductivity of the diamond-like t-BC3. The theoretical Vickers hardness of t-BC2 is 56.0 GPa, which is close to that of cubic boron nitride. The B/G ratio of t-BC2 is 1.09, which is larger than that of diamond (0.83), indicating that the t-BC2 phase is more ductile than diamond. Diamond and cubic boron nitride are two typical superhard materials. Due to their outstanding properties, such as extreme hardness, high thermal conductivity, and particular electronic property, they have found a wide variety of technological applications. However, both of the superhard materials are insulators. Theoretically predicted superhard materials, such as C3N41 and cubic BC2N2 with isoelectronic structure, are considered insulators or semiconductors as well. Recently, much interest has been focused on conductive superhard materials.3-8 Boron-doped diamond (BDD) is one of the conductive superhard materials, and boron doping provides the necessary electrical conductivity in this material. The BDD thin films are found to be particularly attractive for electrolysis and electroanalytical applications due to their unique properties.9 However, it has been well-known for a long time that only a few boron atoms can substitute for carbon atoms in the diamond lattice. Until recently, calculations and experimental results have suggested that large concentrations of boron (and/or nitrogen) can be included in diamond in a metastable form.3,4,10 An electron-deficient metallic tetragonal B2CN (t-B2CN) phase deduced from the diamond structure has been predicted theoretically.10 A dramatic increase in the amount of substitutional boron in diamond (∼16 atom %) has been achieved using the highpressure and high-temperature method from graphite-like BC5 (g-BC5) to diamond-like (d-BC5). The d-BC5 crystal possesses extreme Vickers hardness (71 GPa) and high thermal stability (up to 1900 K).4 Theoretically, a superhard diamond-like t-BC3 was proposed in our previous study. t-BC3 has an alternately metallic CBC block and insulating CCC block, allowing it to acquire the property of two-dimensional conductivity.3 It is expected that the d-BCx phases with higher boron content may exhibit superior electrical conductivity, high thermal, and chemical stability.4 Up to now, information about the atomic structure of d-BCx with more boron content has been unknown. On the other hand, it is not clear how large a perturbation of the electronic system of diamond will arise resulting from B * To whom correspondence should be addressed. E-mail: fhcl@ ysu.edu.cn.
substitution with more boron concentration. In this paper, our first-principles calculations focus on d-BC2 to find the possible configuration and predict its corresponding electronic and mechanical properties. Previous theoretical studies have shown that the B-B bond should not exist in the structures of B-C-N systems.11-13 The predicted most energetically stable t-BC3 phase has a sandwichlike layered structure with the BC3BC3... stacking sequence originating from the cubic diamond structure.3 According to the above theoretical results, d-BC2 should have a layer-by-layer structure without a B-B bond. Diamond and c-BN can be considered as 3C structures like 3C-SiC in Ramsdell notation.14 Therefore, the six-atom unit cell of the 3C structure is a good candidate for the construction of d-BC2 structures. Only two possible layered d-BC2 structures (d-BC2-1 and d-BC2-2) can be constructed as shown in Figure 1. On the other hand, we constructed a 24-atom diamond supercell from three diamond unit cells along the c axis, which consists of twelve layers with two atoms in a layer. On the basis of the supercell, the d-BC2 structure can be constructed by four layers of carbon atoms substituted by boron atoms. Then a series of hypothetical configurations of d-BC2 crystals were constructed by different stacking sequences with four layers of boron atoms and eight layers of carbon atoms; meanwhile, the adjacent boron layers were separated by different numbers of carbon layers to avoid B-B bond formation. The calculations were performed using the ab initio pseudopotential density functional method implemented in the CASTEP code.15 Exchange-correlation terms were treated by Perdew-Burke-Ernzerhof in generalized gradient approximation (GGA).16 The norm-conserving pseudopotentials were chosen to study the phonon modes. Ultrasoft pseudopotentials were expanded within a plane-wave basis set with a 310 eV cutoff energy in the processes of optimization and other calculations (such as density of states spectra, population analyses, and so on). The k-point sampling in the Brillouin zone was set at 10 × 10 × 4 according to the Monkhorst-Pack method.17 Structural optimization was performed until the energy change per atom was less than 5 × 10-6 eV, the forces on the
10.1021/jp106926g 2010 American Chemical Published on Web 12/08/2010
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Figure 2. Phonon dispersion curves of the t-BC2 structure.
TABLE 2: Chemical Bond Parameters and Hardness of t-BC2
Figure 1. Crystal structures of (a) d-BC2-1, (b) d-BC2-2, (c) d-BC2-3, and (d) the optimized structure of d-BC2-3. The boron and carbon atoms are represented as blue and black spheres, respectively.
atoms were less than 0.01 eV/ Å, and all the stress components were less than 0.02 GPa using the BFGS minimization method.18 Mulliken overlap populations were integrated by a distance cutoff of 3 Å. The phonon modes of the crystal structure were calculated with the linear response theory19 for the equilibrium structure obtained after the structural relaxation. The relaxed structural parameters, total energy Et, formation energy Ef, and other calculated properties of the three d-BC2 configurations shown in Figure 1 are summarized in Table 1. The calculated results show that the constructed d-BC2-3 structure shown in Figure 1c starting from the 24-atom supercell with the BC2BC2... stacking sequence along the c axis has the lowest total energy in the constructed configurations. The optimized structure of d-BC2-3 has a tetragonal lattice shown in Figure 1d, which is similar to that of t-BC3. We have named d-BC2 as t-BC2 hereafter. The t-BC2 structure also can be reproduced with a new route to explore the low-energy structures by using an ab initio evolutionary algorithm in crystal prediction. The details of this search algorithm and its several applications on exploring low-energy structures can be found in the literature.20-22 Both carbon and boron atoms are 4-foldcoordinated, and their bond lengths are 1.662 and 1.500 Å for the B-C and C-C bonds, respectively. The density of t-BC2 is 3.06 g/cm3, which is lower than that of sandwich-like t-BC3 (3.26 g/cm3).3 To check the mechanical stability of a structure, the elastic constants of the crystal should satisfy the generalized elastic stability criteria. For a stable tetragonal structure, its six independent elastic constants (C11, C33, C44, C66, C12, and C13) should satisfy the Born stability criteria: C11 > 0, C33 > 0, C44 > 0, C66 > 0, C11 - C12 > 0, C11 + C33 - 2C13 > 0, 2(C11 + C12) + C33 + 4C13 > 0.23 The calculated elastic constant values of t-BC2 are C11 ) C22 ) 820 GPa, C33 ) 585 GPa, C44 ) C55 )
bond type
ni
dx-y (Å)
Px-y
Nx-y e
f ix-y
Hx-y v
HV (GPa)
C-C B-C
8 16
1.500 1.662
0.84 0.63
0.787 0.506
0.186 0.276
86.9 44.9
56.0
337 GPa, C66 ) 389 GPa, and C13 ) C31 ) C12 ) C21 ) C23 ) C32 ) 164 GPa. Clearly, the calculated elastic constants of t-BC2 satisfy all the mechanical stability criteria, suggesting that the t-BC2 structure is mechanically stable. The bulk modulus of t-BC2 is 349 GPa, which indicates that t-BC2 is a lowcompressibility material. To examine the dynamical stability of t-BC2, the calculated phonon dispersion curves at high symmetry points are presented in Figure 2. No imaginary phonon frequency is observed in the Brillouin zone, indicating that t-BC2 is dynamically stable. To estimate the Vickers hardness of the t-BC2 crystal, a semiempirical microscopic hardness model can be used on the basis of the results of first-principles calculations.24 As shown in Table 2, there are only two types of bonds in the t-BC2 structure: B-C bonds and C-C bonds. The calculated overlap populations of the B-C bonds and C-C bonds are 0.63 and 0.84, respectively, indicating their strong covalent properties. The Mulliken charges are 0.39e for boron atoms and -0.19e for carbon atoms, meaning that there are partial ionic components in the covalent B-C and C-C bonds. In addition, metallic components were also found in B-C bonds and C-C bonds, as seen from the electronic density of states of t-BC2 shown in Figure 3. Thus, the chemical bonds in the t-BC2 crystal are composed of main covalent, partial ionic, and metallic components. The metallicity is induced by the electron-deficient boron atoms in the t-BC2 crystal. The major carriers are holes, and the valence electrons are mainly localized to form covalent bonds. For the hole conductors, the metallicity was excluded from the hardness calculation.25 On the basis of this view and our hardness formula,24 the hardness of the bonds in BC2 can be calculated as follows: Hv ) 350Ne2/3d-2.5e-1.191fi, where fi is the Phillips ionicity of the chemical bond, which can be calculated by fi ) [1 - exp(-|Pc - P|/P)]0.735}.26 Here we obtained the pure covalent population Pc ) 0.75 by calculating the overlap population of the C-C bonds in the supercell with 24 carbon atoms stacking on the basis of the cubic diamond model. The bond parameters of the t-BC2 crystal obtained from first-principles calculations are listed in Table 2. The calculated
TABLE 1: Equilibrium Lattice Parameters, Density (G), Total Energy (Et), Formation Energy (Ef), Bulk Modulus (B), and Shear Modulus (G) for Three d-BC2 Configurations d-BC2-1 d-BC2-2 d-BC2-3
symmetry
a (Å)
c (Å)
F (g/cm3)
Et (eV/atom)
Ef (eV/atom)
B (GPa)
G (GPa)
P3m1 P3jm1 I41/amd
2.582 2.600 2.520
6.598 6.520 11.919
3.04 3.03 3.06
-128.741 -128.788 -128.865
0.685 0.639 0.562
319 315 349
178 143 319
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Figure 3. Total and partial densities of states for (a) t-BC2 and (b) t-BC3. C1 is coordinated with the boron atom in the CBC block and the C2 atom in the CCC block in the t-BC3 structure.
hardness of t-BC2 is 56.0 GPa, indicating that it is a potential superhard material. Figure 3a plots the total density of states as well as the s and p partial density of states (PDOS) for each atom in the unit cell of t-BC2. To identify the difference in the electric conductivity between the t-BC2 and t-BC3 compounds, the electronic density of states of t-BC3 is presented in Figure 3b for comparison. For t-BC2, the top of its valence band is ∼3.5 eV above the Fermi level and there is a band gap between the valence band and conduction band, suggesting that t-BC2 has a metallic character. It is worth noting that the boron atoms in different layers have the same PDOS, and all the carbon atoms have the same PDOS as well. The empty bands above the Fermi level mainly come from 2p orbitals of boron and carbon atoms in the t-BC2 structure, indicating that the electron deficiency imported by the B atoms has been distributed to each atom in the system. In other words, the empty orbitals exist in every bond of t-BC2, and as such, all the B-C and C-C bonds within it are metallic. Therefore, the t-BC2 crystal possesses three-dimensional conductivity. The empty orbitals also existed in our previously predicted t-BC3 as shown in Figure 3b. However, the empty orbitals are only focused on the B-C bonds in the CBC block in the t-BC3 crystal: given that the B-C bonds exhibit metallicity and the C-C bonds are insulating, it is suggested that the t-BC3 crystal has the property of two-dimensional conductivity. The ratio of bulk modulus to shear modulus B/G is used to assess the brittle/ductile behavior of a crystal. Paugh27 proposed that a high (low) B/G value is often associated with ductility (brittleness), and the critical value that separates ductile and brittle materials is about 1.70. The calculated ratio B/G of t-BC2 is 1.09, which means it is brittle. The B/G ratio of diamond is 0.83, which means that the t-BC2 phase is more ductile than diamond. The formation energy Ef of t-BC2, calculated by Ef ) EBC2/4 - (2Egraphite/4 + Ea-B/12), is 0.562 eV/atom. The positive formation energy indicates its metastable stability. The metastable character is also found in the recent study of the synthesized superhard d-BC5, which has a relatively narrow temperature range (∼200 K) of this phase formation.4 We hope that the presented superhard t-BC2 could be synthesized using the high-pressure and high-temperature method under appropriate temperature and pressure ranges. In summary, a superhard t-BC2 phase originating from the cubic diamond structure has been predicted by first-principles calculations. The structural stability of BC2 has been confirmed by the calculations of the elastic constants and phonon frequencies. The electronic density of states shows that the electron deficiency introduced by the B atom is distributed to each atom
in the system. Consequently, the t-BC2 phase possesses the property of three-dimensional conductivity. The calculated theoretical Vickers hardness of t-BC2 is 56.0 GPa, indicating that it is a potential conductive superhard material. Finally, the calculated B/G ratio of t-BC2 is larger than that of diamond, suggesting that t-BC2 is more ductile than diamond. Acknowledgment. This work was supported by the NSFC (Grant Nos. 50821001 and 50872118), FANEDD (Grant No. 2007B36), and NBRPC (Grant Nos. 2005CB724400 and 2010CB731605). References and Notes (1) Liu, A. Y.; Cohen, M. L. Science 1989, 245, 841. (2) Zhang, Y.; Sun, H.; Chen, C. F. Phys. ReV. Lett. 2004, 93, 195504. (3) Liu, Z. Y.; He, J. L.; Y, J.; Guo, X. J.; Sun, H.; Wang, H. T.; Wu, E.; Tian, Y. J. Phys. ReV. B 2006, 73, 172101. (4) Solozhenko, V. L.; Kurakevych, O. O.; Andrault, D.; Le Godec, Y.; Mezouar, M. Phys. ReV. Lett. 2009, 102, 015506. (5) Yang, J.; Sun, H.; He, J. L.; Tian, Y. J.; Chen, C. F. J. Phys.: Condens. Matter 2007, 19, 346223. (6) Dubrovinskaia, N.; Eska, G.; Sheshin, G. A.; Braun, H. J. Appl. Phys. 2006, 99, 033903. (7) Hirono, S.; Umemura, S.; Tomita, M.; Kaneko, R. Appl. Phys. Lett. 2002, 80, 425. (8) Wang, H. B.; Li, Q.; Wang, H.; Liu, H. Y.; Cui, T.; Ma, Y. M. J. Phys. Chem. C 2010, 114, 8609. (9) Swain, G. M.; Ramesham, R. Anal. Chem. 1993, 65, 345. (10) He, J. L.; Guo, L. C.; W, E.; Luo, X. G.; Tian, Y. J. J. Phys.: Condens. Matter 2004, 16, 8131. (11) Sun, H.; Jhi, S. H.; Roundy, D.; Cohen, M. L.; Louie, S. G. Phys. ReV. B 2001, 64, 094108. (12) Nozaki, H.; Itoh, S. J. Phys. Chem. Solids 1996, 57, 41. (13) Li, Q.; Wang, M.; Oganov, A. R.; Cui, T.; Ma, Y. M.; Zou, G. T. J. Appl. Phys. 2009, 105, 053514. (14) Ramsdell, L. S. Am. Mineral. 1947, 32, 64. (15) Segall, M. D.; Lindan, Philip, J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. J. Phys.: Condens. Matter 2002, 14, 2717. (16) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (17) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (18) Thomas, H. F.; Almlof, J. J. Phys. Chem. 1992, 96, 9768. (19) Gonze, X. Phys. ReV. B 1997, 55, 10337. (20) Oganov, A. R.; Glass, C. W.; Ono, S. Earth Planet. Sci. Lett. 2006, 241, 95. (21) Ma, Y. M.; Oganov, A. R.; Xie, Y. Phys. ReV. B 2008, 78, 014102. (22) Li, Q.; Ma, Y. M.; Oganov, A. R.; Wang, H.; Xu, Y.; Cui, T.; Mao, H. K.; Zou, G. T. Phys. ReV. Lett. 2009, 102, 175506. (23) Watt, J. P.; Peselnick, L. J. Appl. Phys. 1980, 51, 1525. (24) Guo, X. J.; Li, L.; Liu, Z. Y.; Yu, D. L; He, J. L.; Liu, R. P.; Xu, B.; Tian, Y. J.; Wang, H. T. J. Appl. Phys. 2008, 104, 023503. (25) Li, Q.; Wang, H.; Tian, Y. J.; Xia, Y.; Cui, T.; He, J. L.; Ma, Y. M; Zou, G. T. J. Appl. Phys. 2010, 108, 023507. (26) He, J. L.; Wu, E; Wang, H. T.; Liu, R. P.; Tian, Y. J. Phys. ReV. Lett. 2005, 94, 015504. (27) Pugh, S. F. Philos. Mag. 1954, 45, 823.
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