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Tetragonal Structure BC as a Superhard Material Lulu Liu, Ziyuan Zhao, Shoutao Zhang, Tong Yu, and Guochun Yang J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 26 Apr 2017 Downloaded from http://pubs.acs.org on April 30, 2017

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The Journal of Physical Chemistry

Tetragonal Structure BC4 as a Superhard Material Lulu Liu, Ziyuan Zhao, Shoutao Zhang, Tong Yu and Guochun Yang* Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China

Abstract: Boron carbides have become one of excellent candidates of superhard materials. However, the reported BC4 does not belong to the superhard material. Recently, first-principles structure searching calculations have become a powerful tool to discover ground or metastable state structures with intriguing properties. Here, three more stable structures of BC4 than the reported one are uncovered by using swarm structural searches. They all satisfy dynamical and mechanical stability. All atoms in I41/amd and R-3m structures are in sp3 bonding states, whereas Cm structure is a mixture of sp2 and sp3 ones. Interestingly, I41/amd or R-3m BC4 is metallic, while Cm BC4 is a semiconductor. The most stable I41/amd-structured BC4 is an excellent superhard material from the standpoint of high bulk modulus (370 GPa), high shear modulus (353 GPa), large Young's modulus (804 GPa), low Poisson's ration (0.14), and acceptable Vickers hardness value (55.7 GPa). Our work is also important for fully understanding the structure and chemical bond of boron carbides.

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1. Introduction In some special application areas (e.g. cutting, polishing, and resistant to grinding), material with high hardness is one of necessary prerequisites.1 Diamond is the best known superhard material, however its inherent defects, such as brittleness, reaction with iron, and oxidization in air at high temperature, greatly limit its practical utility.2 As a consequence, the footsteps of finding excellent superhard materials never stop.3–7 Among the various potential superhard materials, boron carbides have drawn great attentions, and are deemed as good candidates of alternate diamond. This originates from boron doped diamond remarkably not only improving the ductility and stability of diamond but also enhancing oxidation resistance of diamond.8–11 Great efforts have been devoted to synthesizing various boron carbides. Initially, people tried to incorporate boron atoms into diamond lattice.9,12 However, the resulting B-C phases are usually unstable. Later, researchers found that use of graphite like B-C phases, as precursor materials, is proved to be an effective approach to synthesizing stable boron carbides at high pressure and high temperature conditions. Under this conditions, two dimensional graphitic sp2 bonding directly converts into three dimensional sp3 bonding. Using this approach, BC5 compound was synthesized at 24 GPa and 2200 K.13 Moreover, a cubic BC3 (c-BC3) phase was obtained by direct transformation of graphitic BC3 at 39 GPa and 2200 K.14 Based on the measured hardness values, BC5 and BC3 compounds are excellent superhard materials. Unfortunately, their crystal structures have not been determined under experimental conditions. Very recently, the crystal structures of c-BC3 was reliably determined by using unbiased structural search method.15 Other researchers also made certain contributions in solving the two structures.16–20 To further find potential superhard materials and enrich the understanding of structure and bonding, other B-C compounds with different chemical compositions, such as BC, BC2, and BC4, were also investigated.21–24 A tetragonal BC2 was proposed by first-principles calculations, and its theoretical Vickers hardness reaches 56 GPa.22 Notably, P42/mmc-structured BC4 exhibits low hardness (13 GPa) and shear modulus (15 GPa), which is far less than the criterion of superhard material. It is due that the C–C bond, linking the two adjacent boron-carbon cages along the c axis direction, leads to a weak ability to against shear elastic deformation.21 Subsequently, Zheng at al. further explored intrinsic mechanism of P42/mmc-structured BC4.23 Its calculated shear strength in (100)[001] direction is only 5 GPa. Intriguingly, BC4 with P42/mmc symmetry transforms into an 2


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orthogonal structure with Cmmm symmetry under shear deformation. Its bulk modulus (343 GPa) and shear modulus (244 GPa) is much higher than those of P42/mmc-structured BC4. It is noted that most of boron carbides are metastable, and their stable structures strongly correlate with the synthetical conditions.13,14,25,26 This inspires us to study BC4 in a broad pressure range. In this work, we extensively explored the crystal structures of BC4 in the pressure range of 0-50 GPa using an unbiased swarm structure search. Three low-energy structures (I41/amd, R-3m, and Cm) were discovered. Among them, all atoms in I41/amd and R-3m structures form fully sp3 hybridizations exhibiting strong convelent bonding character, whereas Cm structure is a mixture of sp2 and sp3 hybridizations. I41/amd-structured BC4 is a promising superhard material in view of its high bulk modulus (370 GPa), high shear modulus (353 GPa), large Young's modulus (804 GPa), and low Poisson's ration (0.14). Our work broadens the understanding of the structural and mechanical properties of B-C compounds. 2. Computational details For the structure search, we employed the swarm intelligence based structure prediction method as implemented in CALYPSO code,25,27 which was unbiased by any prior known structures. Its validity has been widely confirmed by a diverse variety of materials.28–32 Structural optimizations and property

calculations

Perdew-Burke-Ernzerhof

were (PBE)

performed

using

density

function

generalized-gradient-approximation

theory

(GGA)

within

functional33

the as

implemented in the VASP5.3 code.34 The electron-ion interaction is described by pseudopotentials built within the scalar relativistic projector augmented wave approximation with 2s22p1 and 2s22p2 valence electrons for B and C atoms, respectively. A cutoff energy of 800 eV and appropriate Monkhorst-Pack k-meshes were selected, which yields a good convergence for the enthalpy. To verify the dynamical stability of the predicted structures, the phonon calculations were performed by using the finite displacement approach as performed in the Phonopy code.35 The bulk modulus, shear modulus, Young’s modulus were further estimated using Voigt-Reuss-Hill approximation.36 The strain-stress method was used to calculate the elastic constants.37 The Vickers hardness was estimated using an empirical model Hv = 2.0(k2G)0.585 − 3.0, where k = G/B. Here, G and B are shear modulus and bulk modulus, respectively.38

3



3. Results and discussion Boron carbides are usually synthesized under high pressure and high temperature conditions, such as BC513 and BC314. Thus, we performed variable-cell structure searches containing 1-4 formula units at the pressures of 0, 10, 25, and 50 GPa. The earlier reported P42/mm and Cmmm-structured BC4 were successfully reproduced in our structure searching.21,23 Besides the known candidate structures, we find a shortlist of candidate structures with space groups I41/amd, R-3m, and Cm. Subsequently, we calculated enthalpy versus pressure for the three new discovered BC4 structures relative to that of the P42/mmc phase (Figure 1a). Among the considered structures, I41/amd phase is the most stable in the whole considered pressure range, R-3m phase is the second stable, and Cm phase becomes more stable than P42/mmc above 5.4 GPa. The most stable BC4 crystalizes into a tetragonal structure (space group I41/amd, 4 formula units per units, Fugure 2a). The lattice parameters of I41/amd phase are a = 2.516 Å, c = 19.170 Å. It contains one equivalent B occupying 4b (0.5000, 0.5000, 0.0000) position and two inequivalent C’s sitting at 8e (0.5000, 0.0000, 0.0557) and at 8e (0.000, 0.5000, 0.1498) sites. The most striking structural character is all the atoms in sp3 bonding states. In general, the average bond length might play important role in determining hardness. The calculated average B-C and C-C bond lengths are 1.65 and 1.55 Å at 0 GPa, which are nearly close to C-C bond of 1.55 Å in diamond, suggesting that it may exhibit high hardness and large bulk modulus. The second stable phase with R-3m symmetry (6 formula units per units, Figure 2b) has the typical strong sp3 covalent bonds. Cm phase contains a mixture of sp2 and sp3 hybridizations (Figure 2c). To unveil electronic structures and understand chemical bonding of these BC4 phases, the electron energy bands and partial density of states (PDOS) were calculated. I41/amd-structured BC4 exhibits metallic feature (Figures 1b and 1c). Its metallicity mainly comes from the contribution of B-p and C-p. Below the Fermi energy level, there is substantial overlap between B-p and C-p orbitals, indicating strong B-C covalent bonding. Notably, there appears a sharp and narrow peak near the Fermi level, which associates with van Hove singularity, just as the observiation in H3S.39 R-3m-structured BC4 is also metallic with strong hybridizations between B and C atoms. For the Cm-structured BC4, the calculated energy band and PDOS reveal the semiconductor feature with indirect band gaps of 1.03 eV (Figure 3). 4


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Figure 1. (a) Calculated enthalpy versus pressure for various BC4 structures relative to that of the P42mmc phase. (b)-(d) Calculated electronic density of states, electronic band structure, and phonon dispersion curves of I41/amd-structured BC4 at 0 GPa.

Figure 2. Crystal structures of BC4. The pink and purple spheres represent B and C atoms, respectively. (a) I41/amd phase, (b) Cm phase, and (c) R-3m phase. The lattice parameters of R-3m phase are a = 2.555 Å, c = 32.232 Å. Its B atom sits at 6c (0, 0, 0.5762), and C atoms ocuppy at 6c (0.000, 0.000, 0.0247), 6c (0.000, 0.000, 0.627), 6c (0.000, 0.000, 0.8883), 6c (0.000, 0.000, 0.842). The lattice parameters of Cm phase are a = 4.517 Å, b = 2.614 Å, c = 10.058 Å, the B atoms sit at 2a (0.9508, 0.5000, 0.9824) and 2a (0.0561, 0.000, 0.1251). The C atoms occupy at 2a (0.9160, 0.5000, 0.3237), 2a (0.8874, 0.5000, 0.1657), 2a (0.7559, 0.000, 0.5796), 2a (0.0878, 0, 0.5282), 2a (0.0842, 0.000, 0.3748), 2a (0.7600, 0.000, 0.7358), 2a (0.1194, 0.000, 0.9426), 2a (0.0946, 0.000, 0.7869). 5



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Figure 3. (a) Electronic band structure of R-3m-structured BC4 at 0 GPa. (b) Projected density of states of R-3m-structured BC4 at 0 GPa. (c) Electronic band structure of Cm-structured BC4 at 0 GPa. (d) Projected density of states of Cm-structured BC4 at 0 GPa. Table. 1. Calculated bulk modulus (B), shear modulus (G), Young’s modulus (E), Poisson’s ratio (ν), and hardness (Hv) of the three predicted BC4 and diamond. Unit except Poisson’s ratio is in GPa. Phase

B

G

E

B/G

ν

Hv

Cm

344

303

702

1.13

0.16

45.6

R-3m

367

319

743

1.15

0.16

46.6

I41/amd

370

353

804

1.05

0.14

55.7

Diamond

434

564

1181

0.77

0.05

10740

The phonon spectra and the elastic constants of three predicted BC4 structures were calculated to verify the dynamical and mechanical stability, the results show that these phases are dynamically stable without showing any imaginary phonon frequency in the whole Brillouin zone (Figures 1d and S1). For the tetrahedral BC4, six independent elastic constants are obtained (Table S1). Based on Born stability criteria,41 the elastic constants for a tetrahedral structure should satisfy the generalized 6


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elastic stability criteria as follows: C11 > 0, C33 > 0, C44 > 0, C66 > 0, C11 − C12 > 0, C11 + C33 − 2C13 > 0, 2C11 + C12 + C33 + 4C13 > 0. This clearly indicates that the tetrahedral BC4 is mechanically stable. The other predicted structures also satisfy the mechanical stability criteria (Detailed information can be found in the supporting information). To study the mechanical properties and estimate the hardness of the preditcted BC4 structures, we calculated their bulk modulus (B), shear modulus (G), Young's modulus (E), and Poission’s ration (ν) (Table. 1). B is a measure of the object's resistance to stress.41 In general, the higher B is, the larger incompressible is. Among the three crystals, the I41/amd phase has the largest bulk modulus, which reaches 95% of that in diamond. The calculated G of I41/amd phase is 353 GPa, which is 62.6% and 87.2% of those in diamond and c-BN, respectively.42–44 Cm-structured BC4 has the lowest B and G, which is mainly attributed to the mixture of sp2 and sp3 bonding. The ration value of B/G can be used to describe the ductility or brittleness of materials.41 The calculated B/G for the I41/amd, R-3m, and Cm phases are 1.13, 1.15 and 1.05, which is far below the criteria value (1.75). Poisson’s ratio (ν) is another parameter of measuring mechanical properties. Material with the low Poisson’s ratio would show a very big lateral expansion when compressed.45 I41/amd phase has the low Poisson’s ratio reflecting its superhard nature. Finally, the calculated Vickers hardness of I41/amd-structured BC4 is 55.7 GPa, which is larger than hardness standard (40 GPa) and is comparable to that of c-BN (∼65 GPa).43 Based on above results, I41/amd-structured BC4 would be a good candidate of superhard material. Here, we conducted stress-strain relations calculations37,46 to unveil the local bond deformation and breaking mechanisms when applied a load. Figure 4a shows the calculated tensile stress of I41/amd-structured BC4 along four directions. The weakest tensile direction is along [100] direction with peak stress of 90 GPa. Notably, this peak stress is close to that observed in diamond (92.9 GPa) and much larger than c-BN (65 GPa).43 After the critical tensile stain (ε = 0.18), the stress suddenly decreases, which has been observed in covalent solids with sp3 hybridization (i.e. diamond and c-BN).23,43,44 Subseqently, we performed atomistic structural deformation modes to provide the microscopic mechanism of its ideal strength and the fracture behavior under the tensile loading conditions. The bond length as a function of the [100] tensile direction strain was shown in Figure 4c. At equilibrium (ε = 0), the bond-lengths of C1-C2, C5-C6, B1-C1, and B3-C8 are 1.51, 1.54, 1.67 and 1.66 Å, respectively. When tensile strain is at 0.18, their bond-lengths are 1.44 (C1-C2), 3.90 (C5-C6), 7



4.41 (B1-C1), and 3.88 Å (B3-C8). The B1-C1 and B3-C8 are aligned in the [100] direction, causing direct bond stretch and breaking, as shown the dashed line in Figure 5. Meanwhile, a large jump of ∠B1C1B2 is observed from 101.6° to 56° at the bond breaking point (Figure 4e). Based on the weakest tensile direction [100], the shear stress was calculated in three directions of [01-1], [010], and [00-1] in (100) plane (Figure 4b). Among them, the weakest shear direction is observed in the (100)[00-1] with peak stress of 34.2 GPa. Further analysis indicates that B1-C1 bond length becomes larger and larger with increasing the shear strain, whereas B2-C5 or C5-C6 bond length changes rather small. At critical point ε = 0.08, the distance of B1-C1 is 2.05 Å (Figure 4d). The biggest change of ∠B1C1B2 also occurs (Figure 4f and Figure 5).

Figure 4. (a) The calculated stress-strain relations of I41/amd pahse in various tension deformation directions. (b) The calculated stress-strain curves on various shear-sliding planes. (c) Bond length under tensile strain. (d) Bond length under shear strain. (e) Bond angle under tensile strain. (f) Bond angle under shear strain.

8


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Figure 5. Left panel: structure of I41/amd pahse at ε = 0. Right panel (top): structure of I41/amd pahse at ε = 0.18 under tensile stress. Right panel (bottom): structure of I41/amd pahse at ε = 0.08 under shear stress. 4. Conclusion Unbiased structure searching and density functional total energy calculations discovered three lower energy BC4 phases. I41/amd and R-3m structures adopt sp3 hybridizations with metallic feature, while Cm structure forms the mixture of sp2 and sp3 hybridizations with an indirect band gap of 1.03 eV. These three structures are dynamically and mechanically stable. The calculated elastic constants and bulk modulus indicate that I41/amd-structured BC4 is ultra-incompressible as expected from their short and strong covalent bonding. The calculated Vickers hardness of the I41/amd phase reaches 55.7 GPa. Our work provides a theoretical basis for further experimental research of BC4. Associated content Supporting information Computational details, phonon spectra of three predicted BC4 compounds at 50 GPa, and elastic constants of various BC4 compounds at 0 GPa. Author information ORCID Shoutao Zhang: 0000-0002-0971-8831 Guochun Yang: 0000-0003-3083-472X Corresponding Author 9



*E-mail: [email protected] Notes The authors declare no competing financial interest. Acknowledgements This work is supported by the Natural Science Foundation of China under Nos. 21573037 and 11504007; The Natural Science Foundation of Jilin Province (No. 20150101042JC); The Postdoctoral Science Foundation of China (under Grant No. 2013M541283). References (1)

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