Design of Superhard Ternary Compounds under High Pressure

Apr 6, 2010 - Ab initio evolutionary methodology for crystal structure prediction is performed to explore the high-pressure structures of two ternary ...
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J. Phys. Chem. C 2010, 114, 8609–8613

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Design of Superhard Ternary Compounds under High Pressure: SiC2N4 and Si2CN4 Hongbo Wang, Quan Li, Hui Wang, Hanyu Liu, Tian Cui, and Yanming Ma* National Laboratory of Superhard Materials, Jilin UniVersity, Changchun 130012, People’s Republic of China ReceiVed: February 2, 2010; ReVised Manuscript ReceiVed: March 22, 2010

Ab initio evolutionary methodology for crystal structure prediction is performed to explore the high-pressure structures of two ternary compounds, SiC2N4 and Si2CN4. For SiC2N4, we found intriguing high-pressure polymorphs with monoclinic C2/m and orthorhombic Cmmm symmetries containing tetrahedral CN4 and octahedral SiN6 units, respectively. For Si2CN4, two high-pressure monoclinic C2/m and P21/m structures both consisting of octahedral SiN6 units were discovered. Thermodynamic study demonstrated that it is energetically desirable to synthesize the Cmmm structured SiC2N4 and P21/m structured Si2CN4 at above 29 and 19 GPa, respectively. We have ruled out the earlier proposed high-pressure monoclinic structures for the two ternary compounds borrowed from known structural information. The newly predicted high-pressure phases of the two ternary compounds contain short, strong, and three-dimensional covalent bonding, which are responsible for the predicted superior mechanical properties, e.g., very large bulk and shear modulus. Hardness calculations suggest that Cmmm structured SiC2N4 and P21/m (C2/m) structured Si2CN4 possess superhardness of 58.7 and 51.7 GPa (51.6 GPa), respectively. The underlying mechanism for superhardness of the predicted structures has been discussed and explained. Our current finding has demonstrated again the major role played by high pressure in search for new superhard materials. I. Introduction Superhard materials are of great interest due to their wide range of industrial applications, from scratch-resistant coatings to polishing and cutting tools, etc. Over the past decades, extensive theoretical1-3 and experimental4-6 efforts have been devoted to finding new materials that are harder and thermally more stable than diamond. Especially, Cohen et al.1 designed β-C3N4 (P63/m) as a new low-compressibility material and estimated its bulk modulus and hardness to be exceeding that of diamond. This prediction gained support from subsequent first principles calculations for β-C3N4.7 However, growth of crystalline β-C3N4 with a large enough size has not been achieved so far. Instead, several hypothetical structures8-11 with C substituted for Si in polymorphs Si3N4 are proposed for potential superhard materials, since the incorporation of C into Si3N4 is expected to considerably enhance the hardness.11,12 Subsequently, two crystalline solids in the ternary Si-C-N systems, SiC2N4 and Si2CN4, have recently been synthesized at ambient pressure and high temperature, and their ambientpressure structures have been determined by X-ray powder diffraction to be cubic (space group, Pn3m) and orthorhombic (space group, Aba2), respectively.13 Linear SisNdCdNsSi fragments are revealed in the Pn3m structure of SiC2N4 and Aba2 structure of Si2CN4. Our hardness calculations of Pn3mtype SiC2N4 (16.9 GPa) and Aba2-type Si2CN4 (28.2 GPa) suggest that the ambient-pressure structures are not superhard materials. Pressure could effectively increase the density of materials, and thus significantly alter their electronic bonding states to modify the physical properties and/or induce the formation of new superhard states (e.g., the pressure-induced transition from graphite to diamond). Therefore, it is greatly desirable to explore the high-pressure structures of SiC2N4 and Si2CN4 to seek for * Author to whom any correspondence should be addressed. E-mail: [email protected].

the potential superhard species. Earlier theoretical studies by Lowther et al.9,14 borrowed the crystal structure of β-Si3N4 as the high-pressure structural candidate, and very recently, Du et al.15 suggested that β-Si2CN4 (P21/m) transforms to the highpressure structure of γ-Si2CN4 (Fd-3m) at 26.4 GPa. These proposed high-pressure structures all possess a very high bulk modulus,9,10,14 having the potential to be superhard. However, it is known that the crystal structures are the key for the superior mechanical properties of materials. If other structures are stable instead, the predicted mechanical properties might be fundamentally revised. In this work, we have taken a new route to explore the high-pressure phases of SiC2N4 and Si2CN4 by using an ab initio evolutionary algorithm in crystal structural prediction unbiased by any known structural information. We uncovered several novel high-pressure phases, which are energetically much superior to earlier proposed structures, possessing very high hardness above 40 GPa, which is of great interest for future synthesis. II. Computational Methods and Details We use ab initio evolutionary simulations to search for the structure possessing the lowest free energy (i.e., the stable structure) at zero temperature and different pressures. The evolutionary simulations for SiC2N4 and Si2CN4 containing one to four formula units (f.u.) in the simulation cell were done at 30 and 100 GPa with the USPEX code.16-18 The details of this search algorithm and its several applications on exploring highpressure structures can be found in the literature.16-23 The most significant feature of this methodology is the capability of predicting the stable structure with only the knowledge of the chemical composition. The ab initio structure relaxations and electronic properties were performed using density functional theory24,25 within the Perdew-Burke-Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA)26 as implemented in the Vienna ab initio simulation package (VASP).27 The projector-augmented wave method28 was adopted,

10.1021/jp100990b  2010 American Chemical Society Published on Web 04/06/2010

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with 3s23p2, 2s22p2, and 2s22p3 treated as valence electrons for Si, C, and N atoms, respectively. The plane-wave kinetic energy cutoff of 520 eV and Monkhorst-Pack k-point meshes of 8 × 8 × 8 (C2/m SiC2N4), 8 × 8 × 12 (Cmmm SiC2N4), 12 × 12 × 6 (C2/m Si2CN4), and 4 × 12 × 8 (P21/m Si2CN4) were chosen to ensure that all of the structures are well-converged to be better than 1 meV per formula unit. The phonon frequencies were calculated using the direct supercell method, which uses the forces obtained by the Hellmann-Feynman theorem calculated from the optimized supercell. Elastic constants are calculated by the strain-stress method, and the polycrystalline bulk modulus, shear modulus, and Young’s modulus were thus derived from the Voigt-Reuss-Hill averaging scheme.29 According to the microscopic hardness model,30,31 the hardness of complex crystals should be calculated by a geometric average of all bonds as follows: µ

HV ) [

∏ (HVµ)n ]1/∑n µ

µ

where HµV ) 350(Nµe )2/3e-1.191fi /(dµ)2.5 is the hardness of the binary compound composed by µ-type bond, nµ is the number of bonds of type µ composing the actual complex crystal, Nµe is the number of valence electrons of type µ per cubic angstroms, and fµi is the ionicity of the binary compound composed by µ-type bond and is expressed as follows: µ

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Figure 1. (a) Crystal structure of C2/m SiC2N4. (b) Crystal structure of Cmmm SiC2N4. At zero pressure, the C2/m structure has the optimized lattice parameters of a ) 9.233 Å, b ) 2.615 Å, c ) 4.365 Å, and β ) 97.611°, with atomic positions of Si at 2b (0, 0.5, 0), C at 4i (0.8311, 0, 0.406), and N at 4i (0.0931, 0, 0.8352) and (0.3398, 0, 0.6067). For the Cmmm structure at zero pressure, the lattice parameters are a ) 4.983 Å, b ) 7.386 Å, and c ) 2.49 Å, with atomic positions of Si at 2a (0, 0, 0), C at 4j (0, 0.6484, 0.5), and two inequivalent N1 and N2 atoms at 4i (0, 0.7528, 0) and 4h (0.2822, 0, 0.5), respectively. The small, middle, and large spheres represent C, N, and Si atoms, respectively.

fiµ ) [1 - exp(-|Pc - Pµ |/Pµ)]0.735 where Pµ is the Mulliken overlap population of the µ-type bond and Pc is the overlap population of the bond in a pure covalent crystal of that specific structure or cluster. Mulliken overlap population is calculated using the pseudopotential plane wave technique through the CASTEP code.32 III. Results and Discussion 1. Crystal Structures. (i) SiC2N4. Our variable-cell simulations predicted a monoclinic C2/m structure stable at low pressure (4-12 GPa) and an orthorhombic Cmmm structure stable at high pressure (>29 GPa), as depicted in Figure 1a and b, respectively. The C2/m structure contains distorted tetrahedral CN4 and octahedral SiN6 units, which can be viewed as alternative packing of SiN6 and CN4 layers along the a direction. Within the Cmmm structure, each Si atom is octahedrally coordinated by six N atoms to form SiN6 octahedrons, which are surrounded by CN4 tetrahedrons. Figure 3a shows the enthalpy curves for our predicted structures (C2/m and Cmmm), ambient-pressure structure (Pn3m), and the decomposition into 1 /3Si3N4 + 2C + 4/3N2 with respect to the earlier proposed highpressure structure (P21/m).14 It is obvious that our predicted structures are energetically much more stable than the previous P21/m structure.14 In the decomposition calculation, the diamond structure for carbon, R-N2 (Pa-3) structure for nitrogen, and R-Si3N4 structure with P31c symmetry (γ-Si3N4, Fd-3m) for Si3N4 are used at low (high) pressure. It is found that the experimentally synthesized ambient-pressure Pn3m structure is metastable with respect to the decomposition. This resembles many other synthesized superhard materials (e.g., BC2N,33 BC3,34 and BC535). Notably, our predicted C2/m structure becomes more stable than the Pn3m structure above 4 GPa, though it remains metastable with respect to the decomposition up to 29 GPa. It is remarkable that the Cmmm structure becomes thermodynamically most stable above 29 GPa and the experimental synthesis

Figure 2. (a) Crystal structure of C2/m Si2CN4. (b) Crystal structure of P21/m Si2CN4. At zero pressure, the C2/m structure has the optimized lattice parameters a ) 15.793 Å, b ) 2.848 Å, c ) 4.8925 Å, and β ) 88.257°, with atomic positions of Si at 2a (0, 0, 0), 2d (0.0, 0.5, 0.5), and 4i (0.1793, 0, 0.66564), C atoms at 4i (0.65055, 0, 0.14819), and four inequivalent N atoms at 4i (0.31425, 0, 0.10321), (0.56305, 0.0, 0.17166), (0.06101, 0.0, 0.38218), and (0.69595, 0.0, 0.38218), respectively. For the P21/m structure at zero pressure, the lattice parameters are a ) 8.18 Å, b ) 2.86 Å, c ) 4.9 Å, and β ) 74.4735° with atomic positions of Si at 2e (0.50927, 0.25, 0.23039) and (0.13843, 0.25, 0.10154), C atoms at 2e (0.79774, 0.25, 0.44909), and four inequivalent N atoms at 2e (0.13181, 0.75, 0.33373), (0.10773, 0.75, 0.82868), (0.37688, 0.75, 0.48891), and (0.62596, 0.75, 0.02519) respectively.

of this phase is highly desirable. We have also considered another decomposition route into Si + 2C + 2N2, but the obtained enthalpy is much higher, ruling out the possibility of this dissociation. The dynamical stabilities of the C2/m and Cmmm structures have been examined by calculating the phonon dispersion curves as presented in Figure 4. The two structures are both dynamically stable within their stability field in view of the absence of any imaginary phonon frequency in the whole Brillouin zone (Figure 4). We have further examined the dynamical stability of these two structures at zero pressure to check whether the two phases can be quenchable to ambient pressure. It can be clearly seen that the C2/m structure is unstable with a soft phonon mode at the A point (Figure 4a), while the Cmmm structure is dynamically stable at zero pressure. The high-pressure synthesis and stabilization at ambient pressure of the Cmmm structure becomes feasible. We then mainly focus

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Figure 5. Calculated phonon dispersion curves for Si2CN4 with C2/m structure at 0 GPa (a) and 100 GPa (b) and P21/m structure at 0 GPa (c) and 100 GPa (d).

Figure 3. Enthalpies per formula unit of various structures as a function of pressure with respect to the earlier proposed P21/m structure for SiC2N4 (a) and Si2CN4 (b).

Figure 4. Calculated phonon dispersion curves for SiC2N4 with C2/m structure at 0 GPa (a) and 4 GPa (b) and Cmmm structure at 0 GPa (c) and 100 GPa (d).

on the exploration of the mechanical properties of the Cmmm structure in section II. (ii) Si2CN4. Analysis of our simulation results uncovered two energetically very competitive monoclinic structures: C2/m (Figure 2a) and P21/m (Figure 2b). P21/m has a slightly lower energy over C2/m in the whole pressure range studied (Figure 3b). In two structures, the Si atom has six nearest N neighbors to form SiN6 octahedrons, while the C atom is coordinated by three N atoms in the same plane. Enthalpy curves for the predicted structures (C2/m and P21/m), ambient-pressure structure (Aba2), earlier proposed high-pressure structure (Fd-3m),15 and the decomposition (2/3Si3N4 + C + 2/3N2) relative to the earlier proposed high-pressure structure (P21/m)9 are presented in Figure 3b. It is found that our predicted P21/m structure is more stable with respect to the synthesized experimental Aba2 structure above 6.6 GPa, though both of them are metastable at a wide pressure range of 0-19 GPa, above which our P21/m structure becomes thermodynamically most stable. Phonon dispersion curves for C2/m and P21/m structure have been calculated as shown in Figure 5. No imaginary phonon

frequency was found in the whole Brillouin zone, indicating that the two structures are dynamically stable even at zero pressure. It should be pointed out that for both ternary compounds Si atoms tend to form 6-fold-coordinated SiN6 octahedrons with N atoms under high pressure. This resembles the high-pressure behaviors of Si3N4. At ambient pressure, Si atoms form SiN4 tetrahedrons with N atoms in the ambient-pressure structure (P63/m), while SiN6 octahedrons are formed in the high-pressure phase (Fd-3m).36 2. Mechanical Properties. The total energies as a function of volume are fitted to the third-order Birch-Murnaghan equation of state to obtain the theoretical bulk modulus (B0) for the predicted Cmmm SiC2N4 (B0 ) 370 GPa), C2/m (B0 ) 288 GPa), and P21/m Si2CN4 (B0 ) 274 GPa), which are also confirmed by the Voigt-Reuss-Hill approximation as listed in Table 1. Obviously, they all have very high bulk modulus, and therefore could be possibly considered as candidates for the superhard materials. Hardness is related to a number of properties including linear compressibility and shear strength. A fundamental requirement for high hardness is that a stress in a given direction should not be transmitted along other directions, and therefore the shear modulus must also be high. We have, therefore, calculated the elastic modulus for these structures and also for c-BN and diamond for comparison (Table 1). We confirm an unusually high incompressibility as supported by the extremely large shear and Young’s modulus. It is noteworthy that the elastic properties of Cmmm SiC2N4 are comparable to those of c-BN. Moreover, the brittleness and ductility can be estimated by the Frantsevich rule,37 where the critical value of Poisson’s ratio is suggested to be less than 1/3 with a higher value corresponding to a better ductile nature. It is suggested that the two structures have much better ductile than those of c-BN and diamond. We then have explicitly calculated the intrinsic hardness for Cmmm SiC2N4 and C2/m and P21/m Si2CN4, and very large hardness values of 58.7, 51.7, and 51.6 GPa were derived, respectively, indicative of the superhard property. In order to obtain valuable insight into the predicted excellent mechanical properties, the partial density of states (DOS) of the Cmmm SiC2N4 and C2/m and P21/m Si2CN4 are presented in Figure 6. The results suggest that Cmmm SiC2N4 and P21/m Si2CN4 are semiconductors with band gaps of 1.8 and 0.25 eV, respectively. However, C2/m Si2CN4 is predicted to be weakly

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TABLE 1: Calculated Bulk Modulus B0, Shear Modulus G, Young’s Modulus E, Hardness Hv, and Poisson’s Ratio ν for SiC2N4 (Cmmm), and Si2CN4 (C2/m and P21/m) Derived from the Voigt-Reuss-Hill Averaging Scheme SiC2N4 (Cmmm) Si2CN4 (C2/m) Si2CN4 (P21/m) c-BN diamond a

B0 (GPa)

G (GPa)

E (GPa)

Hν (GPa)

ν

367.7 270.8 270.7 373.0 (373.0)a 434.6 (442.7)a

325.7 197.1 183.3 388.5 (393.3)a 523.2 (539.4)a

754.3 475.9 448.5 865.2 1120.0

58.7 51.6 51.7 65.3 (46-80)b 93.9 (96 ( 5)c

0.16 0.20 0.18 0.11 0.07

Reference 42. b Reference 6. c Reference 43.

IV. Conclusion

Figure 6. Partial density of states for Cmmm structured SiC2N4 (a), C2/m structured Si2CN4 (b), and P21/m structured Si2CN4 (c). The vertical dashed line indicates the Fermi energy.

metallic, which resembles BC5.38 It also can be clearly seen that the valence bands at ∼5 eV (Cmmm SiC2N4) and ∼1.5 eV (P21/m Si2CN4) below the Fermi surface originate mainly from the contributions of N p orbitals. The Si-N and C-N bonding in these structures is mainly governed by the strong hybridization of Si and C p with N p states, indicating a strong covalent bonding nature. Experience5,39 shows that superhard materials should have a three-dimensional netted structure with small bond volume and high strength of chemical bonds. Therefore, the one-dimensional SisNdCdNsSi chains and large bond volumes of SiC2N4 (18.67 Å3) and Si2CN4 (9.49 Å3) in the ambient-pressure structures are responsible for the low hardness. Instead, for the predicted high-pressure structures, three-dimensional stacking of CN4 tetrahedrons and SiN6 octahedrons, small bond volumes for Cmmm (3.27 Å3), C2/m (3.66 Å3) and P21/m structures (3.67 Å3) comparable to those of diamond (2.84 Å3), and c-BN (2.95 Å3), and the strong covalent bonds between Si/C and N are altogether responsible for the high hardness. Compared with the Cmmm SiC2N4, the hardness of C2/m and P21/m Si2CN4 is much lower. It is mainly dominated by three facts: (i) The bond volume of Cmmm SiC2N4 is evidently smaller. (ii) The C atom in the Cmmm SiC2N4 is coordinated by four N atoms to form CN4 netted tetrahedrons; however, C atoms in the C2/m and P21/m structures are only bonded to three N atoms in one plane. (iii) On the basis of Bader’s quantum theory of “atoms in molecules”,39-41 the calculated electron density on the critical point of the Si-N bond in Cmmm SiC2N4 (0.739 electrons/Å3) is larger than that of C2/m (0.612 electrons/ Å3) and P21/m Si2CN4 (0.655 electrons/Å3), indicating the stronger Si-N bonding in Cmmm SiC2N4. It is noted that the similar bonding feature, bond volume, and electron density on the critical point of the Si-N bond result in the close elastic property and hardness between C2/m and P21/m Si2CN4.

We have extensively explored the high-pressure crystal structures of SiC2N4 and Si2CN4 by ab initio evolutionary algorithm for crystal structure prediction. We discovered novel structures of monoclinic C2/m and orthorhombic Cmmm for SiC2N4 and monoclinic C2/m and P21/m structures for Si2CN4, ruling out the previously proposed high-pressure structures borrowed from the known structures. The calculated mechanical properties reveal that Cmmm SiC2N4 and C2/m and P21/m Si2CN4 are potential superhard materials, and the ductility is much improved in comparison with the diamond. The threedimensional netted structure with small bond volume and high strength of chemical bonds results in the superhard properties of these structures. We suggested that the Cmmm SiC2N4 and P21/m Si2CN4 can be synthesized above 29 and 19 GPa, respectively, and are feasible to be quenched. The current theoretical prediction will inevitably stimulate future experimental synthesis and has illustrated the major role played by high pressure in design of superhard materials. Acknowledgment. The authors gratefully acknowledge the National Natural Science Foundation of China (NSFC) under Grant No. 10874054, the NSFC awarded Research Fellowship for International Young Scientists under Grant No. 10910263, the China 973 Program under Grant No. 2005CB724400, the research fund for Excellent young scientist in Jilin University (No. 200905003), the 2007 Cheung Kong Scholars Program of China, and the National Foundation for Fostering Talents of basic Science (No. J0730311). References and Notes (1) Liu, A.; Cohen, M. L. Science 1989, 245, 841. (2) Mo, S. D.; Quyang, L. Z.; Ching, W. Y.; Tanaka, I.; Koyama, Y.; Riedel, R. Phys. ReV. Lett. 1999, 83, 5046. (3) Grumbach, M. P.; Sankey, O. F.; McMillan, P. F. Phys. ReV. B 1995, 52, 15807. (4) Teter, D. M.; Hemley, R. J. Science 1996, 271, 53. (5) Kaner, R. B.; Gilman, J. J.; Tolbert, S. H. Science 2005, 308, 1268. (6) Brazhkin, V. V.; Lyapin, A. G.; Hemley, R. J. Philos. Mag. A 2002, 82, 231. (7) Liu, A. Y.; Cohen, M. L. Phys. ReV. B 1990, 41, 10727. (8) Wang, C.-Z.; Wang, E.-G.; Dai, Q. Y. J. Appl. Phys. 1997, 83, 1975. (9) Lowther, J. E.; Amkreutz, M.; Frauenheim, T.; Kroke, E.; Riedel, R. Phys. ReV. B 2003, 68, 033201. (10) Zhang, X. Y.; Chen, Z. W.; Du, H. J.; Yang, C.; Ma, M. Z.; He, J. L.; Tian, Y. J.; Liu, R. P. J. Appl. Phys. 2008, 103, 083533. (11) Du, H. J.; Li, D. C.; He, J. L.; Yu, D. L.; Xu, B.; Liu, Z. Y.; Wang, H.-T.; Tian, Y. J. Diamond Relat. Mater. 2009, 18, 72. (12) Badzian, A. J. Am. Ceram. Soc. 2002, 85, 16. (13) Riedel, R.; Greiner, A.; Miche, G.; Dressler, W.; Fuess, H.; Bill, J.; Aldinger, F. Angew. Chem., Int. Ed. Engl. 1997, 36, 603. (14) Lowther, J. E. Phys. ReV. B 1999, 60, 11943. (15) Du, H.-J.; Guo, L.-C.; Li, D.-C.; Yu, D.-L.; He, J.-L. Chin. Phys. Lett. 2009, 26, 016403. (16) Oganov, A. R.; Glass, C. W. J. Chem. Phys. 2006, 124, 244704–1. (17) Oganov, A. R.; Glass, C. W.; Ono, S. Earth Planet. Sci. Lett. 2006, 241, 95.

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