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Hexagonal BCN with Remarkably High Hardness Lulu Liu, Ziyuan Zhao, Tong Yu, Shoutao Zhang, Jianyan Lin, and Guochun Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00252 • Publication Date (Web): 07 Mar 2018 Downloaded from http://pubs.acs.org on March 7, 2018

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The Journal of Physical Chemistry

Hexagonal BC2N with Remarkably High Hardness Lulu Liu, Ziyuan Zhao, Tong Yu, Shoutao Zhang, Jianyan Lin, 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: Pursuit of materials with desirable mechanical properties is an eternal theme. The reported BC2N exhibiting high hardness and superior stability is deemed as the potential alternative to diamond. However, its crystal structure has not been unambiguously determined thus far. Here, we identify a hitherto unknown R3m BC2N with the second-high hardness value of 71 GPa through first-principles swarm structure calculations. Intriguingly, the simulated X-ray diffraction patterns, K-edge spectra, and hardness value of R3m BC2N are in good agreement with the experimental measurement ones. Moreover, the R3m BC2N is more stable than the earlier proposed BC2N phases. These results indicate that our predicted BC2N is the most likely experimental candidate structure, awaiting experimental confirmation. R3m BC2N shows interesting structural features like honeycomb C sublattice and hexagonal B-N layer. Its unusual hardness can be attributed to the full sp3 bonding character and the higher number of C-C and B-N bonds compared to that of C-N and B-C. Electronic property analysis shows that R3m BC2N has a large band gap of 5.0 eV. Our work is also important to fully understand the ternary B-C-N compounds. values.31 Meanwhile, the lattice constants, elastic moduli, and sound velocities of low-density BC2N (LD-BC2N) structures are in excellent agreement with the experimental values.32 The x-ray diffraction (XRD) patterns of the tetragonal BC2N (z-BC2N) with P-42m symmetry well match the experimental observation. Moreover, another tetragonal BC2N (t-BC2N) with P-421m space group is also deemed as the synthesized c-BC2N.33 The lattice parameter of the (C2)/(BN)(111) superlattice matches experimental measurement.34 Above all, although the various BC2N phases are considered as the experimental candidate structures, uniform conclusion has not been reached. This is due to that most of the proposed structures are based on prototype replacement,31,32 superlattice,34 and bond-countering rule.33 With the rapid development of structural search technology, determining the global minimum structure for a given stoichiometry becomes possible.35–39 In this work, we adopt the effective particle swarm optimization algorithm40 to extensively search the ground state structure of BC2N in a wide pressure range from 0 to 100 GPa. A hexagonal BC2N with R3m symmetry is found to be more stable than the already proposed structures. The most striking structural character is the honeycomb C layer and B-N layer. The simulated XRD patterns and K-edge spectra perfectly match the experimental ones. The calculated Vickers hardness of R3m BC2N reaches 71 GPa, which is just below that of diamond. Its large bulk modulus of 392 GPa also demonstrates that the predicted BC2N is ultra-incompressible. 2. COMPUTATIONAL DETAILS For the crystal structure search, we employ the unbiased swarm intelligence structure prediction method as implemented in CALYPSO code.40,41 Its validity has been widely confirmed by a variety of systems, from element solids to binary and ternary compounds.42–46 Structural optimizations and electronic property calculations are performed using density functional theory within the Perdew-Burke-Ernzerhof (PBE)47 of generalized gradient approximation (GGA)48 as implemented in the VASP 5.3 code.49 The electron−ion interaction is described

1. INTRODUCTION Materials with extremely high hardness are indispensable in some fields such as cutting, polishing, and grinding.1–3 Diamond is the well-known superhard material because of the extremely high hardness value of 107 GPa,4 however its inherent shortcomings (e.g. brittleness, oxidization, and reaction with iron)5 restrict the practical applications to some degree. As a consequence, the pursuit of superhard materials with desirable properties is an eternal theme in condensed matter physics and materials science.6–13 B and N are the adjacent elements to C, sharing similar atomic radius. Their binary phases or elemental solids containing B or N dopant exhibit excellent mechanical performance and high stability. For instance, c-BN with acceptable hardness value shows better thermal stability and ductility in comparison with diamond.14 Boron-doped diamond makes much improvement in both oxidation resistance stability and ductility.15–18 The strong and directional covalent bonds among B, C, and N atoms produce tight and rigid networks with extreme resistance to shear.19 Naturally, dense ternary B-C-N phases are deemed as the excellent candidates of superhard materials.20 To search potential superhard materials, much effort has been made to synthesize the ternary B-C-N compounds. Up to now, at least four ternary B-C-N compounds (e.g. BCN,21 BC2N,22–26 BC4N,27,28 and BC6N29) have been synthesized at high-temperature and high-pressure conditions. Among them, BC2N has drawn much attention due to its high Vickers hardness (up to 76 GPa) as well as good stability and ductility.25,26 Unfortunately, the determination of its structure becomes rather difficult owing to the small grain size and similar atomic mass between B, C, and N. This inspires theoretical researchers to resolve this challenging problem. For instance, BC2N-m structures are obtained by replacing part of C atoms in diamond with B or N atoms, whose lattice constants and bulk moduli are in agreement with experimental ones.30 Tian et al. have proposed the body-centered cubic bc6-BC2N structure, formed by the maximum numbers of C-C and B-N bonds, whose bulk moduli are close to the experimental

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by means of the all-electron projector augmented wave (PAW)50 with 2s22p1, 2s22p2, and 2s22p3 valence electrons for B, C, and N atoms, respectively. A kinetic-energy cutoff of 750 eV and a Monkhorst-Pack scheme51 with a k-point grid of 2π × 0.03 Å–1 are adopted to ensure that total energy calculation is converged to less than 1 meV/atom. To verify the dynamical stability of the predicted structure, the phonon calculations are carried out by using the finite displacement approach52 as performed in the Phonopy code.53 The bulk modulus, shear modulus, and Young’s modulus are estimated within Voigt-Reuss-Hill approximation.54 The strain-stress method is used to calculate the elastic constants.55 The Vickers hardness is estimated by using microscopic hardness model.19,56–58 B, C, and N K-edge spectra are calculated by solving Bethe-Salpeter equation.59 Here, single particle core-hole effects are considered. The Raman and Infrared (IR) spectra vibrational frequencies are performed within the framework of the linear-response theory via the Quantum-ESPRESSO package.60 Norm-conserving pseudopotentials61 with 2s22p1, 2s22p2, and 2s22p3 as valence electrons are for B, C, and N and the local density approximation53 of exchange-correlation function. A 120 Ry plane wave cutoff energy and 15 × 15 × 4 k-meshes in the Brillouin-zone for the R3m and P-42m structures of BC2N are used. 3. RESULTS AND DISCUSSION Variable-cell structure searches for BC2N stoichiometry containing up to 4 formula units per simulation cell are performed at the selected pressures of 0, 25, 50, and 100 GPa. We identify a hitherto unknown hexagonal BC2N structure (space group R3m, 3 formula units per cell). Notably, the R3m BC2N phase is more stable than the earlier reported P4cc, Pmm2, P-421m, and P-42m phases in the whole considered pressure region (Figure 1a).33,62–64 All atoms in this structure form the typical sp3 hybridizations, showing strong and directional covalent bonding (Figure 2a). Its basic building blocks are the two kinds of honeycomb layers (Figure 2b). One contains only C atoms (Figure 2c), whereas the other has the alternate B and N atoms (Figure 2d). The two kinds of honeycomb layers are interconnected through C-N and C-B bonds. Moreover, the B or N atoms in the B-N layer project at the center of carbon hexagonal rings (Figure 2e). This structural character effectively avoids the formation of the B-B and N-N bonds. The presence of pure C honeycomb layer, containing strong C-C bonds, obviously indicates that our predicted BC2N is the high-density phase.32 This unique structure and bonding character are expected to R3m-BC2N phase having high hardness.34,65 To fully and accurately understand the electronic structures and chemical bonding of the predicted BC2N phase, we calculate its electron energy band and partial density of states (PDOS) by using the Heyd-Scuseria-Ernzerhof screened hybrid (HSE) 66 functional. The analysis of PDOS below the Fermi level shows that there is a large overlap between C 2p, B 2p, and N 2p, indicating that strong hybridizations occur between them, as shown in Figure 1b. This is in accordance with the structural analysis. R3m BC2N phase shows a wide indirect band gap of 5.0 eV (Figure 1c), which is slightly smaller than 5.47 eV of diamond.67

For a given compound, its dynamical and mechanical stability are the two key parameters for practical application. Thus, we calculate the phonon spectra and the elastic constants of R3m-structured BC2N at 0 GPa. The absence of any imaginary phonon frequency, in the whole Brillouin zone, evidently demonstrates its dynamical stability (Figure 1d). For a hexagonal structure, there are five independent elastic constants. The calculated elastic constants are given in the following: C11 = 1024.76, C12 = 103.57, C13 = 61.17, C33 = 1022.42, C44 = 402.55. Based on Born stability criteria,68 the elastic constants for a hexagonal structure should satisfy the elastic stability criteria as follows: C44 > 0, C11 > |C12|, (C11 + 2C12) C33 > 2C213. These results reveal that the predicted BC2N is mechanically stable.

Figure 1. (a) Calculated enthalpy versus pressure for various BC2N phases relative to the P4cc phase. (b−d) Calculated electronic density of states, electronic band structure obtained from HSE functional, and phonon dispersion curves of R3m-structured BC2N at 0 GPa.

Figure 2. Crystal structure of BC2N. The red, black, and green spheres represent B, C, and N atoms, respectively. (a) The structure of R3m phase. The lattice parameters of R3m-structured BC2N at 0 GPa are a = b = 2.541 Å and c = 12.618 Å. Its B atoms sit at 3a (0.0000, 0.0000, 0.0515), C atoms occupy at 3a (0.0000, 0.0000, 0.5491) and 3a (0.0000, 0.0000, 0.9221), and N atoms occupy at 3a (0.0000, 0.0000,

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0.4280). (b) The basic building block of R3m-structured BC2N. (c) C honeycomb layer. (d) B-N honeycomb layer. (e) B or N atoms in the B-N layer are projected at the center of C layer.

XRD simulation to determine the experimental structure of BC2N is not an effective way. Electron energy-loss spectroscopy, also named as K-edge, is an effective way to probe the local chemical composition and chemical bonding information in light element materials.70–72 The simulated B, C, and N K-edge spectra of R3m and P-42m BC2N phases together with the available experimental spectra 25 are shown in Figures 3b-3d. As the observation in XRD, the K-edge spectra of R3m and P-42m BC2N are nearly the same and comparable to experimental ones. This is due to their similar bonding character of sp3 hybridization. It is well-known that Raman and infrared spectra are very sensitive to the specific chemical bonds. As a consequence, we calculate the Raman and infrared spectra of R3m and P-42m BC2N phases (Figure 4). As expected, there are obvious differences between them not only in band position but also in relative strength. Moreover, more peaks appears in P-42m BC2N than those of R3m BC2N, which results from low symmetry and more atoms in the unit cell of P-42m BC2N.73 Unfortunately, there are no experimental Raman and infrared spectra for comparison. These results indicate that it should be cautious for the determination of the experimental BC2N structure. Thus, using multi-technology methods are strongly suggested. Overall, we think that our predicted R3m BC2N is the most likely experimental candidate structure due to its not only high thermal stability but also the well matched experimental XRD patterns and EELS spectra.

Inspired by structural character and stability of R3m BC2N phase, we explore its potential as a superhard material. Determining the hardness of the considered structure is not an easy work because it needs accurate descriptions of both elastic and plastic deformation. Fortunately, based on the bond length, electronic density, and bond iconicity, a semi-empirical micro model, proposed by Gao et al, can successfully evaluate the intrinsic hardness of the covalent crystals.19,58,65,69 The expression of Gao’s model is given as following19,58:

H 350 / . . H ∏

(1)

/ ∑ H

1 "

#|%&#%' | %'

(

(2)

).*

(3)

Here, we build a supercell with 324 atoms to reliably obtain these parameters in above formula. The resultant bond length , bond numbers , , valence electron density , Phillips ionicity , and Vickers hardness - of R3m BC2N are listed in Table 1. It is noted that , is the number of bonds in unit cell. Superscript µ denotes the four different kinds of covalent bonds (i.e. C-C, C-N, C-B, and B-N). Moreover, the pure covalent population ./ is obtained by replacing all B and N atoms with C atoms in the supercell.63 Finally, the calculated Vickers hardness of R3m BC2N reaches 71 GPa, which is the second high among the known superhard materials. This unusually high hardness value can be understood by the fact that the sum of C-C and B-N bonds is much larger than that of C-N and B-C ones (Table 1). On the other hand, its hardness value is close to experimental value of 76 GPa26. This inspires us to explore whether our predicted R3m BC2N phase is the experimental structure. Table 1. Calculated bond parameters and Vickers hardness of R3m BC2N.

.,

./

3

0.753

0.63

0.82

0.37

64.60

9

0.641

0.84

0.82

0.06

80.99

1.565

9

0.623

0.7

0.75

0.14

70.53

1.633

3

0.480

0.87

0.75

0.22

48.35

Bond

C-N

1.528

C-C

1.550

B-N B-C

,

-

Figure 3. Calculated XRD patterns and K-edge spectra of R3m and P-42m BC2N compared with the measured XRD patterns of the experimentally synthesized BC2N. (a) XRD patterns with wavelength of 0.4246 Å at 0 GPa. (b) Boron K-edge spectra. (c) Carbon K-edge spectra. (d) Nitrogen K-edge spectra.

For compounds containing different elements with the similar atomic mass, it is difficult to distinguish the different phases based on the XRD patterns. On the other hand, the XRD patterns of P-42m BC2N have been considered to be the experimental structure due to the well-matched experiment XRD patterns.64 To get the reliable conclusion, all the five considered BC2N phases are used to simulate the XRD patterns for the two reported experiments.25,26 Unexpectedly, the simulated XRD patterns of the four considered phases (e.g. P-421m, R3m, P4cc, and P-42m) are in good agreement with the experimental ones (Figure S1 and Figure 3a).25 Thus, using

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extensive structure search of BC2N to explore its ground state structure. The identified BC2N with R3m symmetry shows good dynamical and thermal stability. The honeycomb C atom layer and B-N layer are interconnected to form rigid framework with full sp3 hybridizations. The calculated Vickers hardness is 71 GPa, which is just below the well-known diamond. The large number of C-C and B-N bonds is responsible for the unusual hardness. BC2N shows remarkably wide indirect band gap of 5.0 eV. The various BC2N phases show similar XRD patterns and K-edge spectra, whereas they exhibit different Raman and infrared spectra. Our work indicates determining the structure of this kind of compounds needs the use of multiple technical methods.

Figure 4. (a) Raman spectra of R3m and P-42m BC2N. (b) IR spectra of R3m and P-42m BC2N. Stress-strain relations can be used to probe the local bond deformation and breaking mechanism when a load is applied.55 The calculated tensile stress of R3m-structured BC2N along four directions is shown in Figure 5a. The weakest tensile direction is along the [001] direction with a peak stress of 59.6 GPa. After the critical tensile stain (ε = 0.10), the stress suddenly decreases, accompanying the broke of C-N and B-N bonds (Figure 5c). This phenomenon has also been observed in covalent solids with sp3 hybridization (i.e. diamond and c-BN).34,35 Since tensile stress along the [001] direction has the lowest peak value, (001) plane is the easy cleavage plane. Thus, the shear stress is calculated in three directions of [100], [010], and [110] in the (001) plane. Interestingly, the three shear directions show the same peak stress value of 71.2 GPa. At critical point ε = 0.24, there is no obvious bonding broken, whereas a big lattice deformation is observed (Figure 5d and Figure S2). This behavior can be understood by the fact that honeycomb C and B-N layers is parallel to (001) plane, leading to small anisotropy.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Computational details, simulated XRD patterns and structure of R3m phase at ε = 0.24 under shear stress.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] ORCID Guochun Yang: 0000-0003-3083-472X Notes

The authors declare no competing financial interest. ACKNOWLEDGMENTS This work is supported by the Natural Science Foundation of China under Nos. 21573037, 11704062, and 11504007; the Natural Science Foundation of Jilin Province (No. 20150101042JC); and The Postdoctoral Science Foundation of China (under Grant No. 2013M541283).

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