Crystal structure and physical properties of OsN: First-principle calculations

Solid State Communications 150 (2010) 759–762

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Crystal structure and physical properties of OsN: First-principle calculations Yinwei Li, Yanming Ma ∗ National Lab of Superhard Materials, Jilin University, Changchun 130012, People’s Republic of China

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Article history: Received 2 September 2009 Received in revised form 10 January 2010 Accepted 13 January 2010 by J.R. Chelikowsky Available online 18 January 2010 Keywords: A. Transition metal nitrides C. Structure prediction D. Ultra-incompressible

abstract Using ab initio evolutionary methodology for crystal structure prediction, we have found two orthorhombic structures of Pmn21 and Cmc21 for potential superhard OsN, energetically much superior to the previously proposed NaCl-type and WC-type structures. The Pmn21 structure which consisted of distorted OsN4 tetrahedra is stable up to 62 GPa, above which Cmc21 becomes energetically more favorable. The Cmc21 structure contains the Os–Os and Os–N–N chains and possesses the unique diatomic N–N bond. OsN within two orthorhombic phases is found to be an ultra-incompressible material due to the high bulk modulus (∼350 GPa), which originates from the strong and directional covalent bonds in two structures. Analysis of the calculated formation energy suggested that the two structures could be synthesized at moderate pressures of ∼20 GPa. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Synthesizing and designing superhard materials is of great scientific interest due to a variety of their industrial applications [1]. Many experimental and theoretical efforts in pursuing new superhard materials have motivated studies of transition metal nitrides, such as, TiN [2], NbN [3] and PtN2 [4,5]. Results indeed show that these nitrides are potential superhard materials. Recently, OsN2 and IrN2 were successfully synthesized under high pressure and high temperature [6]. The measured bulk modulus of 358(6) GPa [6] and the estimated hardness of 27 GPa [7] suggested that OsN2 is a hard material. The structural, mechanical, and electronic properties of these two nitrides have attracted extensive theoretical attention [7–15] and the simulation results have demonstrated that the two compounds possess very intriguing properties, such as the high bulk (362 ∼ 394 GPa [7,9,11]) and shear moduli (220 ∼ 249 GPa [7,11]) of OsN2 , which are attributed to a stacking of edge-shared OsN6 octahedra connected by strong N–N covalent bonds [7]. The excellent mechanical properties of OsN2 imply that OsN could also be a good candidate for superhard material. However, OsN has not been synthesized yet in an experiment and its crystal structure remains open. OsN was initially studied with the choice of NaCl-type structure, which possesses a very high bulk modulus of 372 GPa [16]. Later, Zhang et al. [15] and Zheng et al. [17] proposed that the hexagonal WC-type structure is energetically more stable than NaCl-type structure and has a

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similarly high bulk modulus of 343–405 GPa. The large bulk modulus indicated that OsN also promises to be superhard. However, NaCl-type and WC-type structures of OsN were proposed as educated guesses based on structures known for other materials. There is a possibility that hitherto unsuspected structures are stable instead. Crystal structure is an important prerequisite for understanding the properties of crystal solids. The lack of such information has hindered the development of this new fields. Therefore, it is desirable to search for the real structures of OsN. Here, we have predicted the crystal structures of OsN in a wide pressure range (0 ∼ 100 GPa) using a newly developed approach [18–20], merging ab initio total-energy calculations and a specifically devised evolutionary algorithm for crystal structure prediction. This method allows us to predict the most stable crystal structure and a number of low-energy metastable structures for a given compound at any P–T conditions knowing only the chemical composition [18–21]. Two orthorhombic Pmn21 and Cmc21 structures were predicted and found to be energetically much superior to those of the earlier proposed structures. The two structure types have never been reported in nitrides and can be used as structure prototypes. 2. Computational details Ab initio evolutionary simulations were done with the USPEX code [18–20]. The details of the search algorithm and its first several applications have been described elsewhere [21–25]. The underlying ab initio structure relaxations were performed using density functional-theory (DFT) within the generalized gradient approximation (GGA) [26], as implemented in the VASP code [27]. The all-electron projector augmented wave

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Y. Li, Y. Ma / Solid State Communications 150 (2010) 759–762

Table 1 Calculated lattice constants of a, b and c, volume per formula V of OsN within the NaCl-type, WC-type, Pmn21 , and Cmc21 structures. P (GPa)

a (Å)

b (Å)

NaCl-type

0

4.37 4.32a 4.335b

WC-type

0

2.76

Pmn21 Cmc21 a b

0 100

2.743 2.79 2.59

a

b

3

V (Å )

c (Å)

20.92 20.16a 20.37b 3.14

b

3.75 11.94

3.099 4.24 4.59

20.65 b

20.186b 22.18 17.73

Reference [16]. Reference [17].

(PAW) method [28,29] was adopted with the plane-wave kinetic energy cutoff of 520 eV. The PBE–GGA method has been demonstrated to be excellent in providing accurate and reliable predictions of structural and energetic properties of nitrides systems [30]. The use of Monkhorst–Pack k points meshes of 12 × 9 × 8 for Pmn21 , 8 × 8 × 4 for Cmc21 , 8 × 8 × 7 for WC-type and 8 × 8 × 8 for NaCl-type structures were shown to give excellent convergence of the total energies. The structure optimizations were then performed at selected pressures up to 140 GPa. During the structure optimization, the total energy was minimized by varying cell parameters and atomic positions under the restriction of the given symmetry. In the geometrical optimization, all forces on atoms were converged to less than 0.001 eV/Å, and the total stress tensor was reduced to the order of 0.01 GPa. The phonon dispersion curves were computed by the direct supercell calculation method [31] implemented in the PHONON program [32]. This method uses the forces obtained by the Hellmann–Feynman theorem calculated from the optimized supercell through the VASP code [27]. Convergence check gave the use of a 3 × 2 × 2 supercell for the Pmn21 structure and a supercell of 3 × 1 × 2 for the Cmc21 phase.

Fig. 1. (Color online) Crystal structures of OsN within the Pmn21 (a) and Cmc21 (b) structures. The Os and N atoms are represented as big and small spheres, respectively. The atomic coordinates for the Pmn21 structure at ambient pressure in 2a sites are Os (0, 0.86, 0.89) and N (0, 0.35, 0.70). For Cmc21 at 100 GPa, the atomic positions in 4a sites are Os1 (0, 0.47, 0.82), Os2 (0, 0.15, 0.93), N1 (0, 0.86, 0) and N2 (0, 0.77, 0.82).

a

b

3. Results and discussion Since most nitrides materials are synthesized under pressure [4,6], it is essential to include external pressure in the crystal structure prediction. Evolutionary variable-cell simulations are performed at 0, 50 and 100 GPa, in all cases with 2, 4, 6, 8, 12, and 16 atoms in the unit cell. We predicted two orthorhombic structures of Pmn21 and Cmc21 as the most energetically favorable structures. The Pmn21 structure (Fig. 1(a)) contains two OsN formula units in a unit cell, in which both Os and N atoms occupy the Wyckoff 2a(0, y, z ) sites. Table 1 lists the optimized structure parameters at ambient pressure. Each metal Os has four neighboring N atoms, forming distorted OsN4 tetrahedrons connected by corners. In the OsN4 tetrahedron, the Os–N bond distances are calculated to be 1.989, 2.038(×2) and 2.085 Å at ambient pressure. For the Cmc21 structure (Fig. 1(b) and Table 1 for structural parameters at 100 GPa), the unit cell contains eight formula units and both Os and N atoms sit at 4a(0, y, z ) positions. At 100 GPa, it is found that regular Os–Os chains run along the c-axis with the bond distance of 2.439 Å. The distance between two Os–Os chains along the aaxis is found to be 2.585 Å, which is slightly larger than the Os–Os bond distance inside the chains. In addition, the Cmc21 structure possesses the intriguing diatomic N–N unit with a bond distance of 1.358 Å. The two N–N units are well separated by a metal Os atom and form an Os–N–N chain along the c-axis. In this chain, the Os–N distances are 1.957 and 2.034 Å. The N–N bond distance is 1.419 Å at ambient pressure, which is close to the value ∼1.4 Å observed in OsN2 [6] and suggests that the N2 groups are not triply bonded molecules, but singly bonded N42− pairs.

Fig. 2. (Color online) (a) The calculated enthalpies (per f.u.) of the Cmc21 , WCtype and NaCl-type structures of OsN relative to the Pmn21 phase as a function of pressure. (b) Formation enthalpies of the Pmn21 and Cmc21 structures with respect to pure elements (Os + α − N2 /2).

Our computational approach is based on constant-pressure static quantum–mechanical calculations at T = 0 K, so the Gibbs free energy is reduced to enthalpy [33]. Fig. 2(a) shows the enthalpy curves for different structures relative to that of Pmn21 . One observes clearly that the two predicted structures are much more favorable than the NaCl-type and WC-type structures in the whole pressure range. In particular, at ambient pressure, the enthalpy of the Pmn21 structure is 1.75 eV and 2.22 eV lower than those of the WC-type and NaCl-type structures, respectively. Note that the calculated lower enthalpy of the WC-type structure compared to that of the NaCl-type structure in this work is in a good agreement with earlier theoretical studies [15,17]. It is important to note that, with increasing pressure up to 62 GPa, the Cmc21 structure becomes most stable. The structural stability of the Pmn21 and Cmc21 polymorphs has been checked by the phonon calculations. As shown in Fig. 3, no imaginary phonon frequency was detected in the whole Brillouin zone at both ambient and high pressures, indicating the dynamical stability of the Pmn21 and Cmc21 structures. Formation enthalpies of the Pmn21 and Cmc21 phases with pressure were calculated with the formula of 1H = H (OsN)

Y. Li, Y. Ma / Solid State Communications 150 (2010) 759–762

a

b

Fig. 3. (Color online) Calculated phonon dispersion curves for the Pmn21 phase (a) at 0 and 50 GPa and the Cmc21 phase (b) at 0 and 100 GPa. The solid black and dashed red lines are the results at zero and high pressures, respectively. Table 2 The calculated elastic constants Cij (GPa), the zero-pressure bulk modulus B0 (GPa) and shear modulus G (GPa) for the Pmn21 and the Cmc21 structures. Phase

P

Pmn21

0 594 712 536 50 902 1035 762 0 636 619 753 100 1267 1198 1475

Cmc21

761

C11

C22

C33

C44

C55

C66

C12

C13

C23

156 186 197 310

239 331 129 161

245 322 152 320

172 304 222 568

198 348 144 406

314 351 193 540 228 353 177 606

B0

G

−H (solid Os) −H (solid molecular N2 in the α - phase [34]) as plotted in Fig. 2(b). It is found that the formation enthalpies for both compounds are positive at zero pressure, as expected, since external pressure is a necessary condition in the synthesis of transition metal nitrides [4,6]. Indeed, upon application of pressure, the two phases become stable compared with the constituent elements at pressures above 20 GPa for Pmn21 and 27 GPa for Cmc21 . Therefore, present calculations give direct evidence that the two compounds can be synthesized in the experiment. The mechanical properties (elastic constants, anisotropy, brittleness) of two predict orthorhombic phases are important for the potential technological and industrial applications. The elastic constants for two orthorhombic phases were calculated by the strain–stress method and listed in Table 2. For the orthorhombic crystals, the mechanical stability requires the elastic constants satisfying the following conditions: Cii > 0 (i = 1 ∼ 6),

(C11 + C22 − 2C12 ) > 0, (C11 + C33 − 2C13 ) > 0, (C22 + C33 − 2C33 ) > 0, [C11 + C22 + C33 + 2(C12 + C13 + C23 )] > 0. It is clear that the Pmn21 and Cmc21 structures are mechanically stable at both ambient and high pressures. The shear anisotropic factors of the Pmn21 (Cmc21 ) OsN obtained from the present results are A1 = 4C44 /(C11 + C33 − 2C13 ) = 0.85(0.72), A2 = 4C55 /(C22 + C33 − 2C23 ) = 1.54(0.56), and A3 = 4C66 /(C11 − C22 − 2C12 ) = 1.01(0.75) for the (100), (010) and (001) shear planes, respectively, indicating the high degree of anisotropy of the Pmn21 and Cmc21 phases. The calculated bulk modulus of OsN (351 and 353 GPa for Pmn21 and Cmc21 phases, respectively) is close to the observed value (358 GPa) of OsN2 , indicating that the two orthorhombic OsN phases are also low compressible materials. Furthermore, the brittle behavior of OsN was also predicted by the values of G/B (0.6 and 0.5 for Pmn21 and Cmc21 phases, respectively). In order to understand the elastic properties, the total and partial densities of states (DOS) of the two orthorhombic phases

Fig. 4. (Color online) Calculated total and partial density of states for OsN within the Pmn21 (a) and Cmc21 (b) structures at ambient pressure. Vertical dashed line is the Fermi energy.

were calculated at zero pressure, as shown in Fig. 4. Both phases show metallic behavior by evidence of the finite electronic DOS at the Fermi level. This is quite similar to OsN2 , where the metallicity has been experimentally observed due to the lack of Raman activity [6]. From the partial DOS, it reveals that the peaks from −17.5 to −15.0 eV in the Pmn21 phase and from −14.5 to −13.0 eV in the Cmc21 phase are mainly attributed to N 2s states with a small contribution from Os 6s and 5d and N 2p. The states above −8.5eV in the Pmn21 phase and −10 eV in the Cmc21 phase mainly originate from Os 5d and N 2p orbitals with slight contributions of Os 6s. It is found that Os 5d orbital has a strong hybridization with N 2p orbital, indicating the existence of covalent bonding in these two compounds. Also, it is noticed that there is a larger overlap between Os 5d and N 2p orbitals in the Pmn21 compound (Fig. 4(a)), implying a stronger covalent bonding. This is understandable from its tetrahedrally bonded structure. In addition, N 2s and 2p orbital are more spread in the Cmc21 phase due to the formation of the single N–N bond. The charge density distributions of both phases in (100) planes were presented in Fig. 5(a) and (b) to further understand the bonding properties. We find obvious directional Os–N bonding, consistent with its covalent nature. Interestingly, we also detect the N–N and Os–Os bonds in the Cmc21 structure, in apparent contrast to the Pmn21 structure. Strong covalent bonding suggests that both Pmn21 and Cmc21 compounds could be potential superhard materials. 4. Conclusion In summary, we have proposed two orthorhombic Pmn21 and Cmc21 structures in OsN using ab initio evolutionary simulation. These two structures are energetically much superior to the previously proposed NaCl-type and WC-type structures. Analysis of the calculated phonon dispersion curves indicated that the two predicted orthorhombic phases are dynamically stable. The electronic DOS and charge density calculations suggest that the two materials are partially covalently bonded metallic compounds. In view of the strongly covalent bonding and low compressibility of the two structures, we suggest that OsN could be a potential superhard material. More importantly, we have demonstrated that OsN could be experimentally synthesized at readily attainable pressures. This finding will inevitably stimulate extensive experimental work on synthesizing this potentially technologically useful material with unusual bonds involving noble metal osmium.

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Fig. 5. (Color online) The total charge density contours of the Pmn21 (a) and Cmc21 (b) structures, respectively, in the (100) plane at ambient pressure.

Acknowledgments We are thankful for financial support from the China 973 Program under Grant No. 2005CB724400, the National Natural Science Foundation of China under Grant No. 10874054, the NSAF of China under Grant No. 10676011, and the 2007 Cheung Kong Scholars Programme of China. References [1] R.B. Kaner, J.J. Gilman, S.H. Tolbert, Science 308 (2005) 1268. [2] Handbook of Chemistry and Physics, 77th ed., vol. 12, CRC, Boca Raton, FL, 1996, 205. [3] X.J. Chen, V.V. Struzhkin, Z. Wu, M. Somayazulu, J. Qian, S. Kung, A.N. Christensen, Y. Zhao, R.E. Cohen, H. Mao, Proc. Natl. Acad. Sci. USA 102 (2005) 3198. [4] E. Gregoryanz, C. Sanloup, M. Somayazulu, J. Badro, G. Fiquet, H. Mao, R.J. Hemley, Nature Mater. 3 (2004) 294. [5] H. Gou, L. Hou, J. Zhang, H. Li, G. Sun, F. Gao, Appl. Phys. Lett. 88 (2006) 221904. [6] A.F. Young, C. Sanloup, E. Gregoryanz, S. Scandolo, R.J. Hemley, H.K. Mao, Phys. Rev. Lett. 96 (2006) 155501. [7] Z.W. Chen, X.J. Guo, Z.Y. Liu, M.Z. Ma, Q. Jing, G. Li, X.Y. Zhang, L.X. Li, Q. Wang, Y.J. Tian, Phys. Rev. B 75 (2007) 054103. [8] C.Z. Fan, S.Y. Zeng, L.X. Li, Z.J. Zhan, R.P. Liu, W.K. Wang, P. Zhang, Y.G. Yao, Phys. Rev. B 74 (2006) 125118. [9] R. Yu, Q. Zhan, L.C. De Jonghe, Angew. Chem. Int. Edit 46 (2007) 1136. [10] J.A. Montoya, A.D. Hernandez, C. Sanloup, E. Gregoryanz, S. Scandolo, Appl. Phys. Lett. 90 (2007) 011909.

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