J. Phys. Chem. C 2010, 114, 9961–9964
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Semiconducting Superhard Ruthenium Monocarbide Zhisheng Zhao, Meng Wang, Lin Cui, Julong He, Dongli Yu, and Yongjun Tian* State Key Laboratory of Metastable Materials Science and Technology, Yanshan UniVersity, Qinhuangdao 066004, China ReceiVed: January 5, 2010; ReVised Manuscript ReceiVed: April 1, 2010
The ruthenium monocarbide (RuC) structure was investigated through a density functional theory based on the 10 structures of known transition-metal compounds. The calculations indicated that zinc blend structured RuC (ZB-RuC) is the most energetically stable at the ground state, and the calculated lattice parameters are more consistent with the experimental values than those recently reported of rock salt structured RuC (RSRuC). The structural stability of RuC was studied by calculating total energy, elastic constants, and phonon frequencies. Only ZB-RuC showed dynamical stability. It can be concluded that the most likely structure of the synthesized RuC is ZB-RuC rather than RS-RuC. From the calculated band structure and density of states (DOS), it was found that ZB-RuC is a semiconductor while other RuC structures are metallic. The estimated hardness indicates that ZB-RuC is a new superhard material with a Vickers hardness value of 42.8 GPa, compared with B4C. Even though it is a superhard material, the high B/G value (3.95) indicates that ZB-RuC is still a ductile material. 1. Introduction Superhard materials are of great importance to industrial applications, such as cutting tools, abrasives, oil exploitations, and coatings. Nowadays, the search for new superhard materials mainly focuses on two classes of materials. The first class contains the light-element compounds in the B-C-N-O system with strong covalent and short bonds, such as BCxN,1,2 BCx,3,4 and B6O.5 The second class consists of the light-element compounds of transition metals that have high valence electron density, such as IrN2, OsN2, PtN2, ReB2, OsB2, and PtC.6-11 The new transition-metal compounds, for example, ReB2,7 Re2C,12 and WB4,13 are expected to be superhard materials; unfortunately, their asymptotic hardness values are all lower than 40 GPa. According to a semiempirical hardness model,14 the metallic component in the transition-metal compounds will decrease their hardness significantly. Therefore, many efforts have been made to search for new semiconducting superhard transition metal compounds. Pyrite-type PtN2 and monoclinic IrN2 were found to be semiconducting materials,15,16 and their calculated hardness values from the hardness model14 are 60 and 58 GPa, respectively. It suggested that semiconducting superhard materials do exist in the light-element compounds of transition metals. Most transition-metal carbides (TiC, ZrC, HfC, VC, NbC, and TaC) have a rock salt structure with a few exceptions (MoC and WC) that have a tungsten carbide structure. A hexagonal ruthenium carbide, claimed to have been synthesized under ambient pressure and high temperature (2873 K) 40 years ago, was empirically determined to have a WC-type structure.17,18 Recently, a cubic phase of ruthenium carbide, synthesized by Sanjay Kumar et al. under high pressure and high temperature (∼10 GPa, ∼2000 K), was empirically proposed to have a rock salt structure.19 The experimental lattice parameter a of the cubic RuC was determined to be 4.614 Å,19 whereas the calculated value of rock salt structured RuC was only 4.299 Å.20 The * To whom correspondence should be addressed. E-mail: fhcl@ ysu.edu.cn.
difference is so significant that the RuC structure suggested by Sanjay Kumar et al. is doubtful. From the density of states (DOS),20 the rock salt structured RuC shows the metallic conductivity which will result in its low hardness. However, it was found that the structure of the synthesized RuC is not rock salt but zinc blende structure by our calculations. Because the microstructures of materials are crucial for their macroscopic properties, it is very important to determine the actual structure of RuC synthesized in experiment. The calculated results show that the zinc blende structured RuC is a potential semiconducting superhard material. 2. Computation Methods In this paper, 10 possible RuC structures based on the structures of known transition-metal compounds were investigated using first-principles calculations. Ten potential crystal structures for RuC were determined: tungsten carbide structure (WC-RuC), wurtzite structure (WZ-RuC), hexagonal nickeline structure (NiAs-RuC), rock salt structure (RS-RuC), zinc blende structure (ZB-RuC), cesium chloride structure (CsCl-RuC), cubic iron monosilicide structure (SG P213; FeSi-RuC), orthorhombic chromium monoboride structure (SG Cmcm; CrB-RuC), orthorhombic titanium monoboride structure (SG Pnma; TiBRuC), and orthorhombic manganese monophosphide structure (SG Pnma; MnP-RuC). Calculations were performed using CASTEP code.21 The Vanderbilt ultrasoft pseudopotential22 was used with the cutoff energy of 350 eV for the plane wave basis set. The exchange correlation terms were treated by the Perdew-Berke-Ernzerhof (PBE) form of generalized gradient approximation (GGA).23 The k-point samplings in the Brillouin zone were performed using the Monkhorst-Pack scheme.24 Conventional unit cells were used for the considered structures during the full optimizations process, electronic properties, and the calculations of elastic constants, while primitive cells were used during the dynamical calculations. The structural optimization was performed until the energy change of per atom was less than 5 × 10-6 eV, the forces on atoms were less than 0.01 eV/Å, and all the stress
10.1021/jp1000896 2010 American Chemical Society Published on Web 05/11/2010
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TABLE 1: Calculated Equilibrium Lattice Parameters (a, b, and c) at the Ground State, Total Energies (eV/f.u.), Zero-Pressure Elastic Stiffness Constants (GPa), Bulk Modulus B (GPa), and Shear Modulus G (GPa) of RuC Polymorphs phase ZB-RuC Cubic RuC RS-RuC RS-RuC RS-RuC CsCl-RuC WC-RuC WC-RuC NiAs-RuC WZ-RuC a
a(Å) expt.a theor.b theor.b expt.c
4.545 4.614 4.302 4.299 4.327 2.660 2.921 2.908 2.912 3.245
b(Å)
2.921 2.908 2.912 3.245
c(Å)
2.672 2.822 5.399 5.215
Etotal
C11
-2756.52 -2755.60
C33
C44
C12
345.31
66.32
-2755.08 -2756.14
507.82 504.5 487.7 805.53 387.36
-2756.08 -2756.20
414.87 328.65
C13
B
G
B/G
216.00
259.11
65.65
3.95
229.49 233.8 226.7 110.09 353.56
209.98
322.27 324.0 313.7 341.91 338.60
38.45 59.4 65.2 96.66 63.13
8.38
763.48
9.68 8.8 21.6 24.75 93.05
3.54 5.36
795.79 376.79
160.65 27.24
308.68 221.88
178.13 184.77
324.03 246.31
115.78 46.11
2.80 5.34
Reference 19. b Reference 20. c Reference 17.
components were less than 0.02 GPa. Mulliken overlap populations were integrated by a distance cutoff of 3 Å. The phonon frequencies were calculated with the linear response theory25,26 for semiconducting ZB-RuC, and with the finite displacement method added in the recent version of CASTEP code for those that showed metallic properties. Here the finite displacement calculations are carried out in the supercell, circumventing the sphere described by the cutoff radius, which directly give all the nonzero elements of the force constant matrix. The selecting methods above are consistent with our calculating methods before.14,32 In addition, the calculated results showed in Table 1 are also satisfying, compared with those obtained by Fan et al.20 These indicate the computational scheme used in this work is credible. 3. Results and Discussion 3.1. Determination of Crystal Structure. 3.1.1. Total Energies and Lattice Parameters. After full geometry optimizations at the ground state, only six RuC structures can keep their initial symmetries, as shown in Figure 1. The MnP-RuC changes to inverse NiAs,31 structured RuC and FeSi-RuC changes to ZB-RuC, and TiB-RuC and CrB-RuC are distorted. The calculated total energies, elastic stiffness constants, and equilibrium lattice parameters of the six remaining RuC structures are listed in Table 1. According to the calculated total energies, the relative stability order of the six RuC structures is ZBRuC > WZ-RuC > WC-RuC > NiAs-RuC > RS-RuC > CsClRuC. Among them, four RuC polymorphs are more stable than the RS-RuC. We found that the calculated a (4.545 Å) of the most stable ZB-RuC is very close to the experimental a (4.614 Å)19 with deviations less than 2%, whereas the calculated a (4.302 Å) in RS-RuC is significantly smaller than the reported a value of the RuC. Thus, the most likely structure of RuC synthesized by Sanjay Kumar et al. may be the ZB-RuC structure. 3.1.2. Mechanical Stability and Dynamical Stability. To verify the mechanical stability of the six polymorphs, their elastic stiffness constants were calculated (see Table 1). The strain energy for a mechanically stable crystal must be positive, that is to say, the following restrictions should be satisfied:27 for a cubic crystal, C11 > 0, C44 > 0, C11 > |C12|, (C11 + 2C12) > 0; for a hexagonal crystal, C44 > 0, C11 > |C12|, (C11 + 2C12) C33 > 2 (C13).2 From Table 1, it can be seen that the listed six polymorphs are mechanically stable at the ground state. Among them, C44 of RS-RuC has the lowest value, indicating its relative weak stability. In order to further check the dynamical stability of the six RuC polymorphs, their phonon dispersion curves were calculated. The phonon dispersion curves for ZB-RuC and RSRuC at the ground state are presented in Figure 2. Only the
Figure 1. Crystal structures of six RuC polymorphs: (a) ZB-RuC, (b) RS-RuC, (c) CsCl-RuC, (d) WC-RuC, (e) WZ-RuC, and (f) NiAs-RuC. The Ru and C atoms are represented as green and red spheres, respectively.
ZB-RuC structure was found to have no imaginary phonon frequency in the whole Brillouin zone. However, RS-RuC and the other four RuC structures all have imaginary phonon frequencies, indicating that they are dynamically unstable. Therefore, the structure of the synthesized RuC should be of a zinc blende structure by our calculations of lattice parameters, total energies, elastic constants, and phonon frequencies. 3.2. Conductivity, Hardness, and Ductile Property. The band structure and density of states (DOS) of ZB-RuC are shown in Figure 3. ZB-RuC has an indirect band gap of 0.6 eV, indicating the rare property of semiconductivity among the transition-metal light-element compounds. Due to the underestimation of the density functional method, the exact band gap
Semiconducting Superhard Ru Monocarbide
J. Phys. Chem. C, Vol. 114, No. 21, 2010 9963
Ne ) (nRuZRu + nCZC)/V
(2)
where nRu and nC are the numbers of Ru and C atoms in one unit cell of ZB-RuC, respectively, ZRu (or ZC) is the valence electron number of Ru atom (or C atom), and V is the volume of ZB-RuC unit cell. Phillips ionicity fi of Ru-C bonds can be calculated by a generalized ionicity scale fh28 Figure 2. Phonon dispersion curves for the optimized (a) ZB-RuC and (b) RS-RuC at the ground state.
fi ) (fh)0.735 ) [1 - exp(-|PC - P|/P)]0.735
(3)
where fh is the population ionicity scale of a bond, P is the overlap population of a bond, and Pc is the overlap population of bonds in a specified pure covalent crystal. For zinc blende structures, Pc )0.75.28 Here fm can be calculated by
fm )
kTDF 0.026DF nm ) ) ne ne ne
(4)
Figure 3. (a) Band structure and (b) DOS of ZB-RuC.
of ZB-RuC should be wider. Strong p-d orbit hybridized states are observed between Ru and C atoms, indicating high bond strength. The hardness of the ZB-RuC is calculated according to our semiempirical hardness model, which considers the role of d valence electrons.14,28 It is worth noting how many electrons from the Ru d valence electrons take part in the bonding of ZB-RuC. According Hund’s rules, electrons are comparably stable when they locate in full, half-filled, and empty d shells. Therefore, for transition metals, which have fewer than five d valence electrons, all the d electrons can participate in bonding. However, when there are more than five d valence electrons, it is difficult to identify the number of bonding d electrons. It must be determined by the coordination numbers of metal atoms in compounds. With higher coordination numbers, metal atoms have to lose all of their d electrons to participate in bonding. However, with lower coordination numbers, they have to meet the requirement of the half-filled d shells first, and then the surplus electrons will take part in the bonding. Thus, a ZRu (the valence electron numbers of Ru participating in bonding) of 3 is used in the semiempirical hardness model calculations for the 4-fold-coordinated Ru in ZB-RuC. Here the calculated formulate of Vickers hardness is as follows14
HV(GPa) )
-2.5 -1.191fi-32.2fm0.55 1051N2/3 e e d
(1)
where Ne is the electron density, fi is the Phillips ionicity of Ru-C bond, d is the Ru-C bond length, and fm is a factor of metallicity. The electron density Ne can be calculated by
where nm and ne are the number of electrons that can be excited at the ambient temperature and the total number of the valence electrons in unit cell, respectively, and DF is the total density of states of unit cell at the Fermi level. For semiconducting ZB-RuC, fm ) 0. The calculated bond parameters and Vickers hardness of the semiconducting ZB-RuC and other known transition metal monocarbides were listed in Table 2. It can be seen that the theoretical hardness values are consistent with the experimental values. For the transition metal monocarbides, they usually have the rock salt structure or hexagonal structure with the metallic component, however, only RuC is found to be a zinc blende structured semiconductor. Due to the effect of metallicity, the hardness values of these monocarbides except RuC do not exceed 40 GPa. Up to now, RuC is the hardest transition metal monocarbide. The hardness of the ZB-RuC is 42.8 GPa, which can rival to that of B4C.29 Most materials with high hardness are brittle material, for example, diamond, cBN, and WC, etc. However, ductile materials with high hardness are rare. A high (low) B/G value is often associated with ductility (brittleness), and the critical value that separates ductile and brittle materials is about 1.75.30 The ratio B/G of ZB-RuC is 3.95, indicating ZB-RuC is ductile. 4. Conclusion In summary, the structure and stability of ten polymorphs of ruthenium monocarbide were studied using first-principles calculations. Among the considered polymorphs, six RuC structures were determined to be mechanically stable; however, of those six, only ZB-RuC was dynamically stable at the ground state. Seen from the calculated band structure and DOS, ZBRuC is semiconductive while the other five structures are
TABLE 2: Calculated Bond Parameters and Vickers Hardness of Transition Metal Monocarbides crystal
a (Å)
V (Å3/ unit cell)
d (Å)
Ne
P
Pc
fi
fm (×10-3)
Hv,theor. (GPa)
Hv,expt. (GPa)
ZB-RuC PtC TiC ZrC HfC VC NbC TaC
4.545 4.508 4.318 4.694 4.692 4.170 4.514 4.353
93.90 91.62 80.51 103.43 103.29 72.51 91.98 82.48
1.968 2.254 2.159 2.347 2.346 2.085 2.257 2.177
0.298 0.611 0.392 0.310 0.347 0.496 0.391 0.436
0.45 0.37 0.41 0.39 0.43 0.41 0.35 0.38
0.75 0.43 0.43 0.43 0.43 0.43 0.43 0.43
0.589 0.248 0.107 0.181 0 0.107 0.311 0.200
0 2.136 1.113 1.162 1.089 3.510 2.333 1.639
42.8 24.7 34.0 21.0 26.8 23.0 16.1 26.0
32,a 28-35b 25,c 25.9b 26.1b 27.2,b 29c 17.6,c 19.6b 24.5d
a
Reference 33. b Reference 34. c Reference 35. d Reference 36.
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metallic, which may have peculiar optical properties like the III-V and II-VI semiconducting compounds. The calculated Vickers hardness value of ZB-RuC is 42.8 GPa, comparable to that of B4C. The calculated ratio B/G of ZB-RuC is 3.95, indicating that it is ductile. By comparing the computed total energies, lattice parameters, mechanical stabilities, and phonon stabilities, it is determined that the cubic phase of ruthenium carbide synthesized experimentally should be zinc blende structured RuC, which is a new semiconducting superhard material. It takes a new perspective to search for superhard materials among the semiconducting transition-metal lightelement compounds. Acknowledgment. This work was supported by NSFC (Grant Nos. 50532020, 50872118, and 50821001), FANEDD (Grant No. 2007B36), PCSIRT (Grant No. IRT0650), and by NBRPC (Grant No. 2005CB724400). References and Notes (1) Solozhenko, V. L.; Andrault, D.; Fiquet, G.; Mezouar, M.; Rubie, D. C. Appl. Phys. Lett. 2001, 78, 1385. (2) Zhao, Y.; He, D. W.; Daemen, L. L.; Shen, T. D.; Schwarz, R. B.; Zhu, Y.; Bish, D. L.; Huang, J.; Zhang, J.; Shen, G.; Qian, J.; Zerda, T. W. J. Mater. Res. 2002, 17, 3139. (3) Solozhenko, V. L.; Kurakevych, O. O.; Andrault, D.; Godec, Y. L.; Mezouar, M. Phys. ReV. Lett. 2009, 102, 015506. (4) Solozhenko, V. L.; Dubrovinskaia, N. A.; Dubrovinsky, L. S. Appl. Phys. Lett. 2004, 85, 1508. (5) He, D. W.; Zhao, Y. S.; Daemen, L.; Qian, J.; Shen, T. D.; Zerda, T. W. Appl. Phys. Lett. 2002, 81, 643. (6) Chung, H. Y.; Weinberger, M. B.; Levine, J. B.; Kavner, A.; Yang, J. M.; Tolbert, S. H.; Kaner, R. B. Science 2007, 316, 436. (7) Qin, J. Q.; He, D. W.; Wang, J. H.; Fang, L. M.; Lei, L.; Li, Y. J.; Hu, J.; Kou, Z. L.; Bi, Y. AdV. Mater. 2008, 20, 1. (8) Cumberland, R. W.; Weinberger, M. B.; Gilman, J. J.; Clark, S. M.; Tolbert, S. H.; Kaner, R. B. J. Am. Chem. Soc. 2005, 127, 7264. (9) Young, A. F.; Sanloup, C.; Gregoryanz, E.; Scandolo, S.; Hemley, R. J.; Mao, H. K. Phys. ReV. Lett. 2006, 96, 155501. (10) Crowhurst, J. C.; Goncharov, A. F.; Sadigh, B.; Evans, C. L.; Morrall, P. G.; Ferreira, J. L.; Nelson, A. J. Science 2006, 311, 1275.
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