Article pubs.acs.org/JPCC
Exploring High-Pressure Structures of N2CO Chunye Zhu,† Qian Li,† Yuanyuan Zhou,† Miao Zhang,† Shoutao Zhang,† and Quan Li*,‡,† †
State Key Lab of Superhard Materials and ‡College of Materials Science and Engineering, Jilin University, Changchun 130012, China
ABSTRACT: We have extensively investigated the crystal structures of N2CO under high pressure using the swarm structure searching technique in combination with density functional theory. Three single-bonded 3-dimensional structures with space groups of P43, P43212, and P21212 are discovered. We show that the P43 phase is the most stable structure compared with N2 and CO above 35.6 GPa. The distribution of the excess electrons on the N and O atoms does not form bonds but forms a stable lonepair state. The strong covalent bonds together with lone-pair states are the driving force for the high bulk shear modulus of N2CO. The P43 structure may be used as an advanced energetic material with an energy density of approximately 4.6 kJ g−1, which is a little higher than the modern explosive TNT (4.2 kJ g−1).
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INTRODUCTION
High pressure is a useful way to obtain new materials, with previously unknown structure or new chemical and physical properties.11,12 In 2004, Eremets et al. made a prominent contribution to successfully synthesize the cubic-gauche (cg) structure at high pressure (110 GPa) and high temperature (2000 K).13,14 N2 shows a large difference in energy between single-bond and triple-bond states. It is estimated to be one of the best HEDMs if the high pressure polymeric N2 can be synthesized and released at ambient conditions.15 Similarly, CO is isoelectronic and isostructural to N2, exhibiting similar crystal structures at low pressure.16 However, CO has different behaviors with respect to N2 at high pressures. It transforms into a polymerized and noncrystalline phase at low pressure 5 GPa and 300 K,17 while molecular N2 is stable over a wider range of pressure. The search of N2CO is meaningful due to its metastable nature and the importance for designing high-energy materials. In order to gain in-depth knowledge of crystal structure and the highpressure behavior in N2CO, we have performed an extensive search for stable high-pressure crystal structures of N2CO using an unbiased structure searching method18−21 in combination with ab initio calculations.
Metastable molecules are perceived as worthwhile synthetic goals, and their synthesis or evidence of their fleeting existence has been acclaimed.1 In many cases, some physical and chemical properties of the metastable materials are better than those in their stable state for the same chemical composition of materials. N2CO, an intriguing metastable material relevant to the strongest bonded diatomic molecules N2 and CO, has attracted special attention as a high energy density material (HEDM) and the component of planetary ices.2 It was first detected in the form of nitrosyl cyanide (NCNO) by Horsewood and Kirby in 1971.3 Experimentally, with the great development in synthetic chemistry, various isomers of the molecule gas N2CO have been observed.4−7 Maier et al. obtained ON−CN by irradiating cyanogen di-N-oxide in solid argon at 10 K with light of wavelength 254 nm.4 Zeng et al. found that the diazirinone (an isomer of N2CO) molecule could be trapped by thermal decomposition of OC(N3)2.7 Theoretically, the most stable isomer of the N2CO molecule was diazirinone on the potential energy surface.8 The enthalpy barrier for the dissociation of diazirinone to N2 and CO is 108 kJ mol−1, and the exothermicity is ∼400 kJ mol−1 for the reaction.9 The amounts of energy released per mass unit by dissociation of diazirinone and other theoretical isomers indicate these molecules as leading candidates for HEDM. Recently, Raza et al. studied HEDM for the stable structures containing carbon monoxide and nitrogen molecules.10 © 2014 American Chemical Society
Received: September 17, 2014 Revised: October 31, 2014 Published: November 4, 2014 27252
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projector augmented wave31 with 2s22p3, 2s22p2, and 2s22p4 electrons as valence electrons for N, C, and O atoms, respectively. The electronic wave functions were expanded in a plane-wave basis set with a cutoff energy of 900 eV for all cases. Monkhorst−Pack k-point32 meshes with a grid of 0.03 Å−1 for Brillouin zone sampling were chosen to achieve the total energy convergence of less than 1 meV/atom. The phonon dispersion curves were computed by the direct supercell calculation method as implemented in the Phonopy program.33 Single-crystal elastic constants were determined from the evaluation of stress tensor that generated small strain, and the bulk modulus and shear modulus were thus estimated by using the Voigt−Reuss−Hill approximation.34 The Mulliken overlap population is calculated using the pseudopotential plane wave technique through the CASTEP code.35 The theoretical Vickers hardness was estimated by using the Gao microscopic hardness model.36
COMPUTATIONAL METHOD
We performed structure predictions through a global minimization of free energy surfaces merging ab initio total-energy calculations implemented in CALYPSO (crystal structure analysis by particle swarm optimization) code.18−21 The method has successfully predicted the high-pressure structures of various systems, ranging from elements to binary and ternary compounds.22−28 The first-principles energetic calculations were carried out using density functional theory (DFT) with the Perdew−Burke−Ernzerhof exchange-correlation29 as implemented in the Vienna ab initio simulation package (VASP) code.30 The electron−ion interaction was described by means of
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RESULTS AND DISCUSSION We have performed structure predictions for N2CO with variable-cell simulation cell sizes of 1−4 formula units (f.u.) at 0, 50, and 100 GPa, respectively. We have found three highpressure structures with space groups P43 (4 f.u. per cell), P43212 (4 f.u. per cell), and P21212 (4 f.u. per cell), respectively. The P43 structure is consistent with the structure proposed by Raza et al.10 The enthalpy−pressure relations of the candidate structures are shown in Figure 1. The α-phase N2,37 cg-N13, and orthorhombic (I212121) and layered CO (Cmcm)38 were chosen as the reference structures. The P43 structure is stable above 35.6 GPa relative to N2 and CO, and the stability order for these three phases takes the sequence of P43 > P43212 > P21212. The crystal structures are shown in Figure 2. In these predicted structures, all the C atoms are tetrahedrally bonded with clear sp3 hybridization and connected to two N and two O atoms. N atoms are three
Figure 1. Enthalpies per formula unit of various structures as a function of pressure with respect to N2 and CO. Inset: The enthalpies of P21212 structures with respect to P2221 in more detail.
Figure 2. Structures of N2CO. (a) P43 structure. (b) P43212 structure. (c) P21212 structure. At ambient pressure, optimized lattice parameters of P43 structure take a = 5.202 Å, b = 5.202 Å, and c = 4.001 Å, with C at Wyckoff: 4a (0.8950, 0.5996, 0.8592), O at 4a (0.4478, 0.9193, 0.9497), and two N at 4a (0.9489, 0.8783, 0.8002) and 4a (0.5097, 0.3702, 0.0388) sites, respectively. The optimized lattice parameters of P43212 structure take a = 5.066 Å, b = 5.066 Å, and c = 4.253 Å, with C atoms occupying 4a (0.8932, 0.8932, 0.5), O atoms at 4a (0.0648, 0.9352, 1.25), and N atoms at 4b (0.8883, 0.4376, 1.3266). At 50 GPa, optimized lattice parameters of P21212 structure take a = 7.735 Å, b = 3.777 Å, and c = 3.282 Å, with C at Wyckoff: 4c (−0.1526, 0.2628, −0.4996), O at 4c (−0.7291, 0.9517, −0.3215), and two N at 4c (−0.0518, 0.1474, −0.8347) and 4c (0.0405, 0.6640, −0.1663) sites, respectively. 27253
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Figure 3. (a) Phonon dispersion relations of P43 at 0 and 50 GPa. (b) Phonon dispersion relations of P43212 at 0 and 50 GPa. (c) Phonon dispersion relations of P2221 at 0 and 50 GPa. (d) Phonon dispersion relations of P21212 at 25 and 50 GPa.
coordinated (two N−N bonds and one C−N bond), while O atoms are two coordinated and forming only C−O bonds in the lattices. P43 structure adopts a full 3D packing consisting of helical tunnels along the c-axis. P43212 and P21212 structures can be viewed as an infinite spiral N chain connecting to an infinite spiral C−O chain by C−N bonds along the c-axis and b-axis. These structures of N2CO are similar to previously predicted framework structures P21212139 of solid N and I21212138 of CO, which contain helical tubes. These helical tubes have strong interaction and thus stabilize the structures. The calculated bond lengths of N−N and C−N are 1.385−1.495 Å in these structures at ambient pressure, which are close to the previous covalent compounds CN240 (N−N, 1.447 Å; C−N, 1.468 Å). N2CO has the ability to form short and strong covalent bonds, which indicates it may possess high bond energy. To investigate the dynamic stability of predicted N2CO structures, we have calculated the phonon dispersion of N2CO (Figure 3). Obviously, the P43, P43212, and P21212 are dynamically stable in a wide range of pressures since there are no imaginary phonon frequencies. Remarkably, the new P2221 phase with 2 f.u. per cell was found by reoptimization of the P21212 phase at low pressure (0−20 GPa), as shown in Figure 1. This phase transition is apparently a second-order or quasisecond-order phase transition, where lattice dynamics generally plays an important role in understanding the mechanism of this phase transition.41,42 In order to understand the relationship between the two structures, we have studied the lattice dynamics properties of the P2221 structure. The calculated phonon dispersions of P2221 at different pressures are shown in Figure 3c. With increasing pressure, the transverse-acoustic (TA) mode decreases and softens. At 50 GPa, there are two imaginary mode regions in the phonon of the TA mode at the Y (0.0 0.5 0.0) point and X−S direction, revealing that a reversible phase transition from P2221 to our predicted P21212 structure occurs under high
Figure 4. Calculated squared phonon frequency υ2 of the TA phonon mode at the Y point as a function of pressure. Inset (a): The eigenvector for the TA phonon mode at the Y point for the P2221 structure extending two times along the Y axis. The arrows show the directions of atomic displacement. Inset (b): The structure of the P21212 phase.
pressure. The squared phonon frequencies of the TA at the Y point show a relationship with pressure as shown in Figure 4. An almost linear relation between υ2 and P is obtained, indicating the TA phonon softening that occurred near the high-pressure phase boundary (Y point) provides the driving force for the transition from the P2221 to P21212 phase at about 24.9 GPa, which is in agreement with the transition pressure (∼25 GPa) as shown in Figure 1. The schematic representation of the eigenvectors for the soft TA mode at the Y point of the P2221 structure is shown in the inset (a) of Figure 4. The arrows represent the directions of the atomic vibrations. To study the mechanical properties of N2CO, the elastic constants were calculated. Notice that the P21212 structure 27254
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Table 1. Calculated Elastic Constants Cij (GPa), Bulk Modulus B (GPa), Shear Modulus G (GPa), and Hardness (GPa) phase
C11
C22
C33
C44
C55
C66
C12
C13
C23
B
G
Hυ
P43-N2CO P43212-N2CO P2221-N2CO tI16-B2CO diamond
654 580 872 600 1058
654 580 461
803 799 639 646
327 379 315 304 569
327 379 348
262 196 237 283
96 78 112 182 129
181 216 162 144
181 216 241
336 331 333 310 439
293 287 277 265 524
71 70 54 50 93
Figure 5. Contours of the ELF of N2CO with isosurface = 0.8. (a) P43 structure, (b) P43212 structure, and (c) P21212 structure.
spontaneously transforms into the P2221 structure at ambient pressure; therefore, the P2221 structure was adopted as a candidate structure of elastic constants calculation. The elastic stability is a necessary condition for a stable crystal. We calculated the ambient-pressure elastic constants Cij of the P43, P43212, and P2221 structures by the strain−stress method listed in Table 1. For comparison, tI16-B2CO43 and diamond are also added in Table 1. For a stable orthorhombic structure, Cij has to satisfy the elastic stability criteria44
bonds, which is a necessary condition for superhard materials. We thus calculated the Vickers hardness of N2CO employing the microscopic hardness model.36 Notice that the lone-pair states are almost no contribution to the hardness of N2CO, thus we calculate the hardness without considering the lone-pair states and the calculation values of 71, 70, and 54 GPa for P43, P43212, and P2221 (Table 1) at equilibrium. The hardness of P2221 is lower than the other two structures due to its lower Mulliken overlap population. Electronic band structure and partial density of states (DOS) of the P43 structure are shown in Figure 6. The calculated results reveal the nonmetallic features of this structure with an indirect band gap of 3.4 eV at ambient pressure. The electronic states near the Fermi level are mainly contributed by N-2p and a few O-2p states. The partial DOS profiles for C-2p, N-2p, and O-2p are very similar from −15 to −10 eV, reflecting the significant hybridization between these orbitals and a strong covalent interaction between the C−N bonds and C−O bonds. Despite that DFT calculations usually underestimate the energy band gap, its high-pressure behavior can still be compared and discussed in the calculations. We then investigated the effect of the pressure on the energy band gap as shown in Figure 7a. Our results show that the sizes of band gaps of the P43, P43212, and P2221 have positive pressure dependence. For insight into the phenomena, we have examined the pressure-induced charge redistribution. The charges of the localized lone pair for the P43 phase decrease with increased pressure, and the bonding electrons between the N−N bonds are strengthened as shown in Figure 7b and c. The strengthened bonding interaction makes the band gap broaden. The influence of pressure on the band gap is insensitive in the P21212 structure. Generally speaking, the strong covalent bonds possess high bond energy which will release once breaking these bonds. N2CO can be considered as a potentially interesting high-energy density material since it is unstable at ambient condition and tends to dissociate into CO and N2 with releasing a great deal of heat. The enthalpy difference for the dissociation of the P43 to N2
Cii > 0 (i = 1 − 6); C11 + C22 + C33 + 2(C12 + C13 + C23) > 0; (C11 + C22 − 2C12) > 0; C11 + C33 − 2C13 > 0; (C22 + C33 − 2C23) > 0
The calculation results clearly suggest that P43, P43212, and P2221 are mechanically stable. From the calculated elastic constants, we further estimate the polycrystalline bulk modulus B and shear modulus G using the Voigt−Reuss−Hill approximation.34 The bulk moduli are calculated to be 331, 333, and 336 GPa for the P43, P43212, and P2221 structures, respectively. The shear moduli are 293, 287, and 277 GPa for the P43, P43212, and P2221 structures, respectively. The calculated moduli of these three phases of N2CO are much smaller than those of diamond; however, the calculated mechanical properties are respecting better than those of the theoretically predicted material B2CO, indicating it should be grouped into an incompressible material. To understand the bonding of high-pressure N2CO phases, we have examined the electron localization function (ELF). These three structures have common characteristics of the ELF, such as the high electron localization, which can be seen between C−N, C−O, and N−N bonds as shown in Figure 5, indicating strong covalent bonding. The O atoms are 2-fold coordinated and form a pair of lone-pair electrons. The N atoms are 3-fold coordinated and form a stable localized lone-pair nonbonding state. Covalent compounds formed by light elements, e.g., B, C, N, and O, have the ability to form short and strong 3-dimensional covalent 27255
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Figure 6. Band structure (left) and electronic density of states (right) of P43 at ambient pressure. The zero of energy is at the Fermi level.
Figure 7. (a) Energy band gap of N2CO vs pressure. (b) The ELF of the P43 structure at 0 GPa. (c) The ELF of the P43 structure at 40 GPa. Isosurface of ELF = 0.86.
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and CO is estimated to be 2.7 eV at ambient pressure, corresponding to an energy density of approximately 4.6 kJ g−1, which is higher than the modern explosive TNT (4.2 kJ g−1).45
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
CONCLUSIONS
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In conclusion, we have explored the high-pressure structures of N2CO under high pressure and investigated their electronic, dynamic, and mechanical properties via first-principle simulations. We predicted three single-bonded N2CO structures with space group of P43, P43212, and P21212. Under decompression, the optimization of P21212 structure at ambient pressure spontaneously generates a new 2 f.u. per cell structure with space group of P2221. Phonon calculations have confirmed P43, P43212, and P2221 are dynamically stable at ambient pressure. The calculated elastic modulus indicates the ultra-incompressible nature. Increasing pressure promotes a peculiar charge transfer from localized lone-pair states to covalent bonds, which strengthens the bonding interaction and broadens the band gap in the P43 phase. At ambient pressure, the calculated energy density for the P43 phase is approximately 4.6 kJ g−1, suggesting N2CO may be a good candidate as a high energy density material. Our results are encouraging for further experimental and theoretical research.
ACKNOWLEDGMENTS We thank the China 973 Program (2011CB808200), Natural Science Foundation of China under Nos. 11274136, 51202084, 11474125, 11025418, and 91022029, the 2012 Changjiang Scholars Program of China, the fund of CAEP-SCNS (R20140302), and Changjiang Scholar and Innovative Research Team in University (IRT1132). Part of the calculations was performed in the High Performance Computing Center of Jilin University.
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REFERENCES
(1) Hoffmann, R.; Hopf, H. Learning from Molecules in Distress. Angew. Chem., Int. Ed. 2008, 47, 4474−4481. (2) Kim, Y.; Zhang, F.; Kaiser, R. Laboratory Simulation of Kuiper Belt Object Volatile Ices under Ionizing Radiation: CO-N2 Ices as a Case Study. Phys. Chem. Chem. Phys. 2011, 13, 15766−15773. (3) Horsewood, P.; Kirby, G. Nitrosyl Cyanide: A Possible Intermediate in the Formation of N-Cyano-1, 2-Oxazines from Conjugated Dienes. J. Chem. Soc. D: Chem. Commun. 1971, 1139−1140. 27256
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(4) Maier, G.; Reisenauer, H. P.; Eckwert, J.; Naumann, M.; De Marco, M. Isomers of the Elemental Composition CN2O. Angew. Chem., Int. Ed. Engl. 1997, 36, 1707−1709. (5) de Petris, G.; Cacace, F.; Cipollini, R.; Cartoni, A.; Rosi, M.; Troiani, A. Experimental Detection of Theoretically Predicted N2CO. Angew. Chem. 2005, 117, 466−469. (6) Moss, R. A.; Chu, G.; Sauers, R. R. Unprecedented Chemistry of an Aryloxychlorodiazirine: Generation of a Dihalodiazirine and Diazirinone. J. Am. Chem. Soc. 2005, 127, 2408−2409. (7) Zeng, X.; Beckers, H.; Willner, H.; Stanton, J. F. Elusive Diazirinone, N2CO. Angew. Chem., Int. Ed. Engl. 2011, 50, 1720−1723. (8) Zhu, R.; Lin, M. Ab Initio Study on the Oxidation of NCN by O (3p): Prediction of the Total Rate Constant and Product Branching Ratios. J. Phys. Chem. A 2007, 111, 6766−6771. (9) Korkin, A. A.; von Ragué Schleyer, P.; Boyd, R. J. Theoretical Study of Metastable N2CO Isomers. New Candidates for High Energy Materials? Chem. Phys. Lett. 1994, 227, 312−320. (10) Raza, Z.; Pickard, C. J.; Pinilla, C.; Saitta, A. M. High Energy Density Mixed Polymeric Phase from Carbon Monoxide and Nitrogen. Phys. Rev. Lett. 2013, 111, 235501. (11) Schettino, V.; Bini, R. Molecules under Extreme Conditions: Chemical Reactions at High Pressure. Phys. Chem. Chem. Phys. 2003, 5, 1951−1965. (12) McMillan, P. F. New Materials from High-Pressure Experiments. Nat. Mater. 2002, 1, 19−25. (13) Eremets, M. I.; Gavriliuk, A. G.; Trojan, I. A.; Dzivenko, D. A.; Boehler, R. Single-Bonded Cubic Form of Nitrogen. Nat. Mater. 2004, 3, 558−563. (14) Eremets, M.; Gavriliuk, A.; Trojan, I. Single-Crystalline Polymeric Nitrogen. Appl. Phys. Lett. 2007, 90, 171904−171904−171903. (15) McMahan, A.; LeSar, R. Pressure Dissociation of Solid Nitrogen under 1 Mbar. Phys. Rev. Lett. 1985, 54, 1929. (16) Mills, R.; Olinger, B.; Cromer, D. Structures and Phase Diagrams of N and CO to 13 GPa by X-Ray Diffraction. J. Chem. Phys. 1986, 84, 2837. (17) Lipp, M. J.; Evans, W. J.; Baer, B. J.; Yoo, C.-S. High-EnergyDensity Extended CO Solid. Nat. Mater. 2005, 4, 211−215. (18) Wang, Y.; Lv, J.; Zhu, L.; Ma, Y. Crystal Structure Prediction Via Particle-Swarm Optimization. Phys. Rev. B 2010, 82, 094116. (19) Wang, Y.; Lv, J.; Zhu, L.; Ma, Y. Calypso: A Method for Crystal Structure Prediction. Comput. Phys. Commun. 2012, 183, 2063−2070. (20) Wang, Y.; Miao, M.; Lv, J.; Zhu, L.; Yin, K.; Liu, H.; Ma, Y. An Effective Structure Prediction Method for Layered Materials Based on 2d Particle Swarm Optimization Algorithm. J. Chem. Phys. 2012, 137, 224108. (21) Lv, J.; Wang, Y.; Zhu, L.; Ma, Y. Particle-Swarm Structure Prediction on Clusters. J. Chem. Phys. 2012, 137, 084104. (22) Peng, F.; Miao, M.; Wang, H.; Li, Q.; Ma, Y. Predicted Lithium− Boron Compounds under High Pressure. J. Am. Chem. Soc. 2012, 134, 18599−18605. (23) Wang, X.; Wang, Y.; Miao, M.; Zhong, X.; Lv, J.; Cui, T.; Li, J.; Chen, L.; Pickard, C. J.; Ma, Y. Cagelike Diamondoid Nitrogen at High Pressures. Phys. Rev. Lett. 2012, 109, 175502. (24) Zhao, Z.; Tian, F.; Dong, X.; Li, Q.; Wang, Q.; Wang, H.; Zhong, X.; Xu, B.; Yu, D.; He, J. Tetragonal Allotrope of Group 14 Elements. J. Am. Chem. Soc. 2012, 134, 12362−12365. (25) Wang, H.; John, S. T.; Tanaka, K.; Iitaka, T.; Ma, Y. Superconductive Sodalite-Like Clathrate Calcium Hydride at High Pressures. Proc. Nati. Acad. Sci. 2012, 109, 6463−6466. (26) Zhu, L.; Wang, Z.; Wang, Y.; Zou, G.; Mao, H.-k.; Ma, Y. Spiral Chain O4 Form of Dense Oxygen. Proc. Natl. Acad. Sci. 2012, 109, 751− 753. (27) Li, Q.; Zhou, D.; Zheng, W.; Ma, Y.; Chen, C. Global Structural Optimization of Tungsten Borides. Phys. Rev. Lett. 2013, 110, 136403. (28) Lu, C.; Miao, M.; Ma, Y. Structural Evolution of Carbon Dioxide under High Pressure. J. Am. Chem. Soc. 2013, 135, 14167−14171. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865.
(30) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169. (31) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758. (32) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (33) Togo, A.; Oba, F.; Tanaka, I. First-Principles Calculations of the Ferroelastic Transition between Rutile-Type and CaCl2-Type SiO2 at High Pressures. Phys. Rev. B 2008, 78, 134106. (34) Hill, R. The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. A 1952, 65, 349. (35) Segall, M.; Lindan, P. J.; Probert, M.; Pickard, C.; Hasnip, P.; Clark, S.; Payne, M. First-Principles Simulation: Ideas, Illustrations and the Castep Code. J. Phys.: Condens. Matter 2002, 14, 2717. (36) Gao, F.; He, J.; Wu, E.; Liu, S.; Yu, D.; Li, D.; Zhang, S.; Tian, Y. Hardness of Covalent Crystals. Phys. Rev. Lett. 2003, 91, 015502. (37) Bolz, L.; Boyd, M.; Mauer, F.; Peiser, H. A Reexamination of the Crystal Structures of and Nitrogen. Acta Crystallogr. 1959, 12, 247−248. (38) Sun, J.; Klug, D. D.; Pickard, C. J.; Needs, R. J. Controlling the Bonding and Band Gaps of Solid Carbon Monoxide with Pressure. Phys. Rev. Lett. 2011, 106, 145502. (39) Ma, Y.; Oganov, A. R.; Li, Z.; Xie, Y.; Kotakoski, J. Novel High Pressure Structures of Polymeric Nitrogen. Phys. Rev. Lett. 2009, 102, 065501. (40) Li, Q.; Liu, H.; Zhou, D.; Zheng, W.; Wu, Z.; Ma, Y. A Novel Low Compressible and Superhard Carbon Nitride: Body-Centered Tetragonal CN2. Phys. Chem. Chem. Phys. 2012, 14, 13081−13087. (41) Ozoliņs,̌ V.; Zunger, A. Theory of Systematic Absence of NaClType (β-Sn−Type) High Pressure Phases in Covalent (Ionic) Semiconductors. Phys. Rev. Lett. 1999, 82, 767. (42) Baroni, S.; de Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Phonons and Related Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001, 73, 515. (43) Li, Y.; Li, Q.; Ma, Y. B2CO: A Potential Superhard Material in the BCO System. Europhys. Lett. 2011, 95, 66006. (44) Watt, J. P. Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals with Orthorhombic Symmetry. J. Appl. Phys. 1979, 50, 6290−6295. (45) Babrauskas, V. Ignition Handbook; Fire Science Publ.: Issaquah, Washington, 2003.
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