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Theoretical investigation on two novel high-pressure orthorhombic phases of superhard C3N2
Journal Pre-proof Theoretical investigation on two novel high-pressure orthorhombic phases of superhard C3N2 Junyi Du, Xiaofeng Li PII:
S0925-8388(19)33570-4
DOI:
https://doi.org/10.1016/j.jallcom.2019.152324
Reference:
JALCOM 152324
To appear in:
Journal of Alloys and Compounds
Received Date: 24 June 2019 Revised Date:
1 September 2019
Accepted Date: 17 September 2019
Please cite this article as: J. Du, X. Li, Theoretical investigation on two novel high-pressure orthorhombic phases of superhard C3N2, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/ j.jallcom.2019.152324. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Theoretical investigation on two novel high-pressure orthorhombic phases of superhard C3N2 Junyi Du1, Xiaofeng Li2, 1 2.
*
College of Mathematical Sciences, Luoyang Normal University, Luoyang 471934, China College of Physics and Electronic Information & Henan Key Laboratory of Electromagnetic Transformation and
Detection, Luoyang Normal University, Luoyang 471934, China
Abstract: Two novel high-pressure orthorhombic phases of C3N2 are probed via the PSO algorithm combined with first-principles calculations. Orthorhombic phases of C3N2 are energetically stable above 82 GPa in comparison to cubic C3N2. The phonon dispersion and elastic constant calculations have identified that Pmmn-C3N2 and Cmcm-C3N2 are dynamically and mechanically stable. The results showed they can be possibly synthesized at ambient condition. The calculated electronic properties indicated that Pmmn-C3N2 and Cmcm-C3N2 are semiconductors with a direct band gap of 1.3 eV for Pmmn-C3N2 and indirect band gap of 1.1 eV for Cmcm-C3N2. Strikingly, two new high-pressure phases Pmmn-C3N2 and Cmcm-C3N2 have high hardness 60.2 and 58.6 GPa, respectively. Their excellent mechanical properties are attributed to strong hybridizations of C-C and C-N atoms.
Keywords: First-principles; Phase diagram; Hardness; C3N2
Introduction Due to the extremely high hardness value of 107 GPa, diamond is regarded as the world's most promising superhard material [1]. However, diamond has its inherent shortcomings of brittleness, oxidization, and it easily reacts with iron [2]. These disadvantages restrict their practical applications to some degree. As a consequence, a lot of experimental and theoretical research has been devoted to the search of new superhard materials [3-13] which can be applied to the fundamental science and industries. As we know, it is commonly accepted that the strongly covalent-bonded solids formed by light elements B, C, N [14-18] are the potential superhard *
Corresponding author. Email: [email protected]
candidate materials, such as M-carbon, BC3, C3N4, c-BC2N, and c-B4C3. Especially more attention is focused on the compounds with C-N bond which benefits to the high hardness of materials because of the shorter C-C bond than that of C-C bond in diamond [19-21]. With the effort of Liu and Cohen [22, 23], the extraordinary hardness of hexagonal C3N4 has been reported. And it was regarded that such covalent solids including the carbon and nitrogen is the excellent superhard candidates. The results have motivated intense experimental interest to synthesize this kind of compounds [5-7]. Then, α-C3N4 and β-C3N4 phases have been suggested in theoretical work and then synthesized by experiment. Subsequently, some theoretical investigations [24, 25] proposed other important dense polymorphs of C3N4, such as α-C3N4, cubic C3N4 (c-C3N4), cubic phase with defect zinc-blende structure (dzb-C3N4), and pseudocubic phase (pc-C3N4). What is particularly exciting is that c-C3N4 even has a zero pressure bulk modulus (449-496 GPa) comparable to that (442 GPa) of diamond [26-30]. So far, many researchers have made great efforts to study new stoichiometric carbon nitrides theoretically [31-33] and experimentally [34–36]. Two compounds α-C3N2 and β-C3N2 with cubic symmetry are introduced and their hardness has been beyond 80 GPa [37]. A novel body-centered tetragonal CN2 [38] has been predicted, and the obtained tensile and shear strength are 46.6 GPa and 51.1 GPa, respectively. Previous theoretical investigations indicated that phases of these compounds are possible to be synthesized successfully in the future. However, C and N have the small and similar atom mass, and it is very difficult to determine the crystal structure and proportion of C and N experimentally. Therefore, the theoretical investigations about carbon nitrogen compounds play an important role in superhard materials composed of light element B, C, N etc. Therefore, the unusual high-pressure behaviors in C3N2 aroused our attention to investigate its unopened transformation phases in order to explore its novel characteristics. Therefore, in present work we investigate the high-pressure phases of C3N2 from 0 to 150 GPa by the effective particle swarm optimization algorithm [39, 40]. Two new orthorhombic phases of C3N2 under pressure is found to be more stable than the already proposed structures. The calculated Vickers hardness of Pmmn- and Cmcm-C3N2 reaches 60.2 GPa and 58.6 GPa, respectively. Their large bulk modulus of 408 and 406 GPa for Pmmn- and Cmcm-C3N2 also demonstrate that the predicted orthorhombic C3N2 is ultra-incompressible.
Computational method
The search for low-energy crystalline structures of C3N2 at 0, 50, and 100 GPa is performed using the particle swarm optimization methodology as implemented in the CALYPSO code [39, 40] in simulation cells containing up to six formula units. This methodology is effectively capable of finding stable or metastable structures only depending on the given chemical composition, which has been identified by a lot of applications from element solid to binary and ternary compounds [41-45]. In the first generation, a population of crystal structures is randomly constructed. Starting from the second generation, 60% structures in the previous generation with the lower enthalpies are chosen to produce the structures of next generation by the PSO operators. The 40% structures in the new generation are randomly generated. For most of cases, the structure search for each chemical composition is converged
after 1000 ~ 1200 structures investigated.
The Vienna Ab initio Simulation Package (VASP) code [46] was adopted to perform structural relaxations and electronic properties calculations. The Perdew-Burke-Ernzerhof (PBE) [47] functional in the generalized gradient approximation was used. The well-established all electron projector-augmented wave method [48] was adopted with 2s22p4 and 2s22p5 as valence electrons for C and N atoms, respectively. A plane-wave basis set cutoff of 800eV and Monkhorst−Pack scheme with a dense k-point grid of spacing 2π × 0.03 Å−1 in Brillouin zone were found to give converged energy within 1 meV/atom. The optimization procedure was truncated when the residual forces for the relaxed atoms were less than 0.01 eV/ Å. In the band structure calculations, a much denser k-point grid of spacing 2π × 0.02 Å−1 are implemented for static run to get more accurate charge densities, which can ensure the high quality of band structure. The value -5 of smear is used. The 20 k-points are needed to calculate the eigenvalues along certain high symmetry lines in the BZ. In order to check the reasonability of parameters setting in calculating the band structure, we calculated the band structure of diamond by the same parameter (Fig.S1). The obtained band gap of diamond is 5.45 eV, which is close to that in reference [49]. Therefore, the band structures of C3N2 will be investigated according to the parameters mentioned above. To determine the dynamical stability, the phonon calculations were performed by using a supercell approach with the finite displacement method as done in the Phonopy code [50]. Electron localization function (ELF) was used to measure the degree of electron localization [51]. The elastic constants are calculated by a strain-energy approach, i.e., applying a small strain to the equilibrium lattice and fitting the dependence of the resulting change
in energy on the strain. The bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are derived from the Voigt–Reuss–Hill approximation [52]. The Vickers hardness was estimated using an empirical model [53], HV = 2(k 2G )0.585 − 3 , where k = G B .
Results and discussion By unbiased particle swarm optimization (PSO) algorithms for crystal structure predictions, we find that the cubic phases α-C3N2 and β-C3N2 are reproduced. Moreover, the enthalpy of cubic phase α-C3N2 is a bit lower than that of β-C3N2, which is in good agreement with recent work [37]. Though structure searching at 0, 50, and 100 GPa, two novel orthorhombic phases with Pmmn and Cmcm symmetry are uncovered, which are shown in Fig.1. For two orthorhombic phases of C3N2, they share common features: (a) The coordination number of C is 4, however, N is 3. (b) each buckled carbon nitride network consists of saddle-like hexagonal rings, which is connected by the bond formed by two N atoms. (c) For C atoms, there are two bonding ways: one is C atom bonded with its three nearest neighboring C atoms and one N atom, the other is C atoms connected with its two nearest C atoms and two N atoms. It is easily observed that C3N and C2N2 formed tetrahedron. For N atoms, N atom bonded with two C atoms and one N atom shows trigonal planar. Their configuration shape possibly attributed to the reasons as follows. Hybridization of one 2s orbit and three 2p orbits of C atom ensures four equivalent atomic orbits, i.e. sp3 hybridization orbits, whose shape is tetrahedron. For N atoms, the one 2s orbit and two 2p orbits of N atom formed three equivalent sp2 hybridization orbits, which exhibited trigonal plane structure. For Pmmn phase, the hexagonal ring contains five C atoms and one N atom. For Cmcm phase, there are two different types of hexagonal rings. One is composed of four C atoms and two N atoms (2C-N-2C-N) and the other includes six C atoms. Moreover, two kinds of hexagonal rings appear alternately. Compared with B atoms, C, N has more unpaired electrons and must form a network structure that pairs them. Meanwhile, square, pentagon, or hexagon faces is impossible stable due to Coulomb repulsion. These two constraints render the existence of saddle-like hexagonal rings in CN materials. In order to establish the bonding pattern in C3N2, the ELF of two predicted orthorhombic phases of C3N2 at 0 GPa are showed in Fig. 2. High ELF ( > 0.85) value indicates the formation of covalent bonds. The high electron localization indicated the strong covalent bond in the region between adjacent atoms. Moreover, C and N atoms are sp3-hybridized and
sp2-hybridized, respectively. Their structure fits more reasonably with the assumption of hybrid orbitals. Pressure can change the thermodynamic stability and the reaction kinetics of a compound during its synthesis process. In order to investigate the thermodynamic stability of Pmmn and Cmcm phases, the formation enthalpy is calculated: ∆H (C3 N2 ) = H (C3 N2 ) − 3H (C) − 2H (N) , in which ∆H is the formation enthalpy, H is the enthalpy of diamond and cubic gauche (cg) nitrogen chosen as the reference phases. Fig. 3 shows the enthalpy curves for various structures and the decomposition with respect to our predicted P2/m structure. The chosen structural parameters of P2/m and P-4m2 phases are shown in Table S1. From Fig. 3, we can find that C3N2 is thermodynamically stable relative to the diamond and nitrogen, which are possible to synthesize experimentally under normal conditions. Moreover, with pressure up to 82 GPa, Pmmn phase is energetically more favorable relative to β-C3N2, and the enthalpy of Cmcm phase is only higher than 2.71 meV per atom than that of Pmmn phase. Therefore, Cmcm phase is a metastable phase for C3N2 under pressure. As following, we will discuss these two orthorhombic phases of C3N2. For Pmmn phase (10atoms/cell), the lattice constants at 100 GPa are a= 4.729 Ǻ, b=2.404 Ǻ, c= 4.636 Ǻ with carbon occupying 2a (0, 0, 0.214), 4f (0.253, 0, 0.405) positions and nitrogen occupying 2b (0, 0.5, 0.045), 2b (0, 0.5, 0.762) positions at 100 GPa. For Cmcm phase (20atoms/cell), the lattice parameters at 100GPa are a=4.737 Ǻ, b=9.267 Ǻ, c=2.401 Ǻ with carbon occupying 4c (0.5, 0.144, 0.75), 8g (0.749, 0.953, 0.25) and nitrogen occupying 4c (0.5, 0.229, 0.25), 4c (0, 0.871, 0.25). Moreover, at 100GPa the bond lengths of C-C bonds in Pmmn (Cmcm) phase of C3N2 are 1.459 Ǻ (1.455 Ǻ ) and 1.462 Ǻ (1.457 Ǻ) slightly shorter than the C– C bond-length in diamond (1.459 Å) at 100GPa, which possibly indicated the formation of sp3 hybridization similar to diamond. C-N bond lengths of them are 1.375 Ǻ and 1.406 Ǻ and N-N bond length is 1.292 Å. These bond lengths are all shorted than bond length in diamond, which indicated that Pmmn and Cmcm phases of C3N2 possibly have high hardness and bulk modulus. The mechanical properties (e.g., elastic constants, elastic moduli and elastic anisotropy, hardness, etc.) are important for potential technological and industrial applications of materials. Particularly, they provide information on the stability and stiffness of materials. The calculated elastic constants of and are showed in Table 1 as well as previous predicted α-C3N2, β-C3N2 for
comparison [37]. The elastic properties suggest two orthorhombic phases fulfilling the Born-Huang criterion [54]. These results reveal that the predicted orthorhombic phases are mechanically stable. Amazedly, Pmmn-C3N2, Cmcm-C3N2 show exceptionally high C33 values of 1318 GPa and 978 GPa, respectively, even more greater than that of cubic BN (820 GPa). It manifests an ultra-incompressibility of the short B−B bonds along [001] direction. For Pmmn (Cmcm) phase, the nearly equal C11 and C22 (C33) values indicated similar incompressibility along a and b axis (c axis), and the highest C33 (C22) showed c axis (b axis) orientation is most difficultly compressed. C44 is a key parameter indirectly governing the indentation hardness of a material. The predicted two stable orthorhombic structures possess a large C44 value beyond 330 GPa, reflecting that it has a strong strength of resisting the shear deformation. The bulk moduli of Pmmn-, Cmcm-C3N2 are 408 GPa and 406 GPa, respectively, similar to diamond (439 GPa). Another intriguing data is the higher shear modulus of Pmmn-C3N2 (392 GPa) and Cmcm-C3N2 (388 GPa) comparable to that of those of c-BN (376.19 GPa) and w-BN (375.24 GPa). Moreover, the high Young modulus and low Poisson ratio of them showed that Pmmn-C3N2 and Cmcm-C3N2 are potential superhard materials. According to above analysis, two orthorhombic phases not only exhibits a large bulk modulus and a high shear modulus, but also has a considerable Young modulus. Therefore, it is very necessary to obtain the hardness of the two phases. According to the empirical model [53], the calculated Pmmn-, Cmcm-C3N2 has a large hardness value of 60.2 GPa and 58.6 GPa respectively, which are lower than those of diamond (92.9 and 96.3 GPa) but comparable to c-BN (65.6 and 70.5 GPa). At the same time, phonon calculations can give a criterion for the crystal stability and indicate structural instability through soft modes mechanism. Therefore, the phonon dispersion curves of two orthorhombic phases were calculated and presented in Fig.4. There are no imaginary phonon frequencies in the pressure ranges at 80 GPa in the whole Brillouin zone. The results prove that these two structures are dynamically stable under pressure. It is noticed that the phonon modes can be clearly split into acoustic modes, low frequency optical modes from 0 to about 35 THz, and pseudomolecular vibrations modes from 35 to about 45 THz. The existence of “pseudomolecular” modes is related to the peculiar topology, and strongly distorted local coordination of N and C atoms in this phase. Moreover, no imaginary phonon frequencies are found at 0 GPa, which indicate that orthorhombic phases can be possibly synthesized at ambient
condition. These above unique bonding characteristics and mechanical properties motivate us to investigate their corresponding electronic properties. The electronic structure and total and partial density of states (DOS) for the C3N2 at 0 GPa are displayed in Fig. 5. The analysis of PDOS near the Fermi level shows that there is a large overlap between C 2s, 2p and N 2s, 2p, indicating that strong hybridizations occur between them, which is in consistence with the analysis of their structures. The electronic structure indicated their semi-conductor characteristic of the predicted orthorhombic phases of C3N2. We obtained the direct gap (1.3 eV) for Pmmn-C3N2 and indirect band gap (1.1 eV) for Cmcm-C3N2 at 0 GPa.
Conclusion In conclusion, we have uncovered two novel high-pressure orthorhombic phases Pmmn-C3N2 and Cmcm-C3N2, via the PSO algorithm combined with first-principles calculations. Orthorhombic phases of C3N2 are energetically stable above 82 GPa in comparison to cubic phases. The phonon dispersion and elastic constant calculations have identified that Pmmn-C3N2 and Cmcm-C3N2 are dynamically and mechanically stable. No imaginary phonon frequencies for Pmmn-C3N2 and Cmcm-C3N2 at 0 GPa are observed in the whole Brillouin zone, which showed their dynamic stability at ambient condition. The calculated electronic properties indicated that Pmmn-C3N2 and Cmcm-C3N2 are semiconductors with a direct band gap of 1.3 eV for Pmmn-C3N2 and indirect band gap of 1.1 eV for Cmcm-C3N2. Strikingly, two new high-pressure phases Pmmn-C3N2 and Cmcm-C3N2 have high hardness 60.2 and 58.6 GPa, respectively. Their excellent mechanical properties are attributed to strong hybridizations of C-C and C-N atoms. We believe that the current study will advance the understanding of chemistry and stimulate future experimental synthesis and determination of carbon nitrides.
Acknowledgement We acknowledge funding support from the National Natural Science Foundation of China under Grant No. 11774140, China Postdoctoral Science Foundation under Grant No. 2016M590033, Key Scientific Research Projects of Institutions of Higher Learning in Henan Province under Grant No. 19A140012, The Natural Science Foundation of Henan Province under Grant No.
162300410199, Program for Science and Technology Innovation Talents in University of Henan Province under Grant No. 17HASTIT015, and Open Project of the State Key Laboratory of Superhard Materials, Jilin University under Grant No. 201602.
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Figure Captions Fig.1 The crystal structure and atomic arrangement of (a) Pmmn phase (b) Cmcm phase of C3N2, green and purple balls represent C and N atoms, respectively. The inserted part is the formation way of hexagonal rings. Fig.2 Contours of the electronic localization function (ELF) of C3N2 at 0 GPa (a) Pmmn phase and (b) Cmcm phase, isosurface value is 0.85.The circle notes the N2 pairs, green and purple balls represent C and N atoms, respectively. Fig.3. Phase stability of various phases of C3N2 related to predicted P2/m under pressure, together with the diamond and nitrogen. Fig.4 The phonon spectrum of C3N2 under pressure: Pmmn phase (a) 0 GPa (b) 100 GPa; Cmcm phase (a) 0 GPa (b) 100 GPa. Fig.5 (a, c) Band structures and (b, d) partial density of states for Pmmn- and Cmcm-C3N2 at 0
GPa, respectively.
Table Captions Table1 The elastic constants Cij (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa) , and the hardness HV in unit of GPa, the Poisson’s ratio ν of Pmmn- and Cmcm-C3N2 at zero pressure, together with that of α-C3N2, β-C3N2 and Diamond. .
Table1 The elastic constants Cij (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa) , and the hardness HV in unit of GPa, the Poisson’s ratio ν of Pmmn- and Cmcm-C3N2 at zero pressure, together with that of α-C3N2, β-C3N2 and Diamond. Structure
C11
C33
C22
C44
C55
C66
C12
C23
C13
B
G
E
ν
HV
Pmmn-C3N2
966
1318
969
325
400
280
42
90
108
408
392
892
0.136
60.2
Cmcm-C3N2
956
978
1317
330
270
395
102
93
35
406
388
884
0.138
58.6
α-C3N2 [37]
867
327
137
380
365
829
0.136
68.2
β-C3N2[37]
834
329
98
343
368
813
0.105
68.5
Diamond
1058
569
129
439
524
1125
0.07
98
Fig.1
Fig.2
Fig.3
Fig.4
Fig.5
Highlights: (1) For the first time, novel superhard phases Pmmn and Cmcm of C3N2 are found, which are stable above 80 GPa. (2) The phonon spectrums of Pmmn and Cmmm phases of C3N2 have no imaginary frequencies at 0 GPa and 100 GPa, and they are dynamically stable. (3) Two phases of C3N2 at 0 GPa are semiconductors with high hardness with high hardness about 60 GPa comparable to c-BN.
S0925-8388(19)33570-4
DOI:
https://doi.org/10.1016/j.jallcom.2019.152324
Reference:
JALCOM 152324
To appear in:
Journal of Alloys and Compounds
Received Date: 24 June 2019 Revised Date:
1 September 2019
Accepted Date: 17 September 2019
Please cite this article as: J. Du, X. Li, Theoretical investigation on two novel high-pressure orthorhombic phases of superhard C3N2, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/ j.jallcom.2019.152324. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Theoretical investigation on two novel high-pressure orthorhombic phases of superhard C3N2 Junyi Du1, Xiaofeng Li2, 1 2.
*
College of Mathematical Sciences, Luoyang Normal University, Luoyang 471934, China College of Physics and Electronic Information & Henan Key Laboratory of Electromagnetic Transformation and
Detection, Luoyang Normal University, Luoyang 471934, China
Abstract: Two novel high-pressure orthorhombic phases of C3N2 are probed via the PSO algorithm combined with first-principles calculations. Orthorhombic phases of C3N2 are energetically stable above 82 GPa in comparison to cubic C3N2. The phonon dispersion and elastic constant calculations have identified that Pmmn-C3N2 and Cmcm-C3N2 are dynamically and mechanically stable. The results showed they can be possibly synthesized at ambient condition. The calculated electronic properties indicated that Pmmn-C3N2 and Cmcm-C3N2 are semiconductors with a direct band gap of 1.3 eV for Pmmn-C3N2 and indirect band gap of 1.1 eV for Cmcm-C3N2. Strikingly, two new high-pressure phases Pmmn-C3N2 and Cmcm-C3N2 have high hardness 60.2 and 58.6 GPa, respectively. Their excellent mechanical properties are attributed to strong hybridizations of C-C and C-N atoms.
Keywords: First-principles; Phase diagram; Hardness; C3N2
Introduction Due to the extremely high hardness value of 107 GPa, diamond is regarded as the world's most promising superhard material [1]. However, diamond has its inherent shortcomings of brittleness, oxidization, and it easily reacts with iron [2]. These disadvantages restrict their practical applications to some degree. As a consequence, a lot of experimental and theoretical research has been devoted to the search of new superhard materials [3-13] which can be applied to the fundamental science and industries. As we know, it is commonly accepted that the strongly covalent-bonded solids formed by light elements B, C, N [14-18] are the potential superhard *
Corresponding author. Email: [email protected]
candidate materials, such as M-carbon, BC3, C3N4, c-BC2N, and c-B4C3. Especially more attention is focused on the compounds with C-N bond which benefits to the high hardness of materials because of the shorter C-C bond than that of C-C bond in diamond [19-21]. With the effort of Liu and Cohen [22, 23], the extraordinary hardness of hexagonal C3N4 has been reported. And it was regarded that such covalent solids including the carbon and nitrogen is the excellent superhard candidates. The results have motivated intense experimental interest to synthesize this kind of compounds [5-7]. Then, α-C3N4 and β-C3N4 phases have been suggested in theoretical work and then synthesized by experiment. Subsequently, some theoretical investigations [24, 25] proposed other important dense polymorphs of C3N4, such as α-C3N4, cubic C3N4 (c-C3N4), cubic phase with defect zinc-blende structure (dzb-C3N4), and pseudocubic phase (pc-C3N4). What is particularly exciting is that c-C3N4 even has a zero pressure bulk modulus (449-496 GPa) comparable to that (442 GPa) of diamond [26-30]. So far, many researchers have made great efforts to study new stoichiometric carbon nitrides theoretically [31-33] and experimentally [34–36]. Two compounds α-C3N2 and β-C3N2 with cubic symmetry are introduced and their hardness has been beyond 80 GPa [37]. A novel body-centered tetragonal CN2 [38] has been predicted, and the obtained tensile and shear strength are 46.6 GPa and 51.1 GPa, respectively. Previous theoretical investigations indicated that phases of these compounds are possible to be synthesized successfully in the future. However, C and N have the small and similar atom mass, and it is very difficult to determine the crystal structure and proportion of C and N experimentally. Therefore, the theoretical investigations about carbon nitrogen compounds play an important role in superhard materials composed of light element B, C, N etc. Therefore, the unusual high-pressure behaviors in C3N2 aroused our attention to investigate its unopened transformation phases in order to explore its novel characteristics. Therefore, in present work we investigate the high-pressure phases of C3N2 from 0 to 150 GPa by the effective particle swarm optimization algorithm [39, 40]. Two new orthorhombic phases of C3N2 under pressure is found to be more stable than the already proposed structures. The calculated Vickers hardness of Pmmn- and Cmcm-C3N2 reaches 60.2 GPa and 58.6 GPa, respectively. Their large bulk modulus of 408 and 406 GPa for Pmmn- and Cmcm-C3N2 also demonstrate that the predicted orthorhombic C3N2 is ultra-incompressible.
Computational method
The search for low-energy crystalline structures of C3N2 at 0, 50, and 100 GPa is performed using the particle swarm optimization methodology as implemented in the CALYPSO code [39, 40] in simulation cells containing up to six formula units. This methodology is effectively capable of finding stable or metastable structures only depending on the given chemical composition, which has been identified by a lot of applications from element solid to binary and ternary compounds [41-45]. In the first generation, a population of crystal structures is randomly constructed. Starting from the second generation, 60% structures in the previous generation with the lower enthalpies are chosen to produce the structures of next generation by the PSO operators. The 40% structures in the new generation are randomly generated. For most of cases, the structure search for each chemical composition is converged
after 1000 ~ 1200 structures investigated.
The Vienna Ab initio Simulation Package (VASP) code [46] was adopted to perform structural relaxations and electronic properties calculations. The Perdew-Burke-Ernzerhof (PBE) [47] functional in the generalized gradient approximation was used. The well-established all electron projector-augmented wave method [48] was adopted with 2s22p4 and 2s22p5 as valence electrons for C and N atoms, respectively. A plane-wave basis set cutoff of 800eV and Monkhorst−Pack scheme with a dense k-point grid of spacing 2π × 0.03 Å−1 in Brillouin zone were found to give converged energy within 1 meV/atom. The optimization procedure was truncated when the residual forces for the relaxed atoms were less than 0.01 eV/ Å. In the band structure calculations, a much denser k-point grid of spacing 2π × 0.02 Å−1 are implemented for static run to get more accurate charge densities, which can ensure the high quality of band structure. The value -5 of smear is used. The 20 k-points are needed to calculate the eigenvalues along certain high symmetry lines in the BZ. In order to check the reasonability of parameters setting in calculating the band structure, we calculated the band structure of diamond by the same parameter (Fig.S1). The obtained band gap of diamond is 5.45 eV, which is close to that in reference [49]. Therefore, the band structures of C3N2 will be investigated according to the parameters mentioned above. To determine the dynamical stability, the phonon calculations were performed by using a supercell approach with the finite displacement method as done in the Phonopy code [50]. Electron localization function (ELF) was used to measure the degree of electron localization [51]. The elastic constants are calculated by a strain-energy approach, i.e., applying a small strain to the equilibrium lattice and fitting the dependence of the resulting change
in energy on the strain. The bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are derived from the Voigt–Reuss–Hill approximation [52]. The Vickers hardness was estimated using an empirical model [53], HV = 2(k 2G )0.585 − 3 , where k = G B .
Results and discussion By unbiased particle swarm optimization (PSO) algorithms for crystal structure predictions, we find that the cubic phases α-C3N2 and β-C3N2 are reproduced. Moreover, the enthalpy of cubic phase α-C3N2 is a bit lower than that of β-C3N2, which is in good agreement with recent work [37]. Though structure searching at 0, 50, and 100 GPa, two novel orthorhombic phases with Pmmn and Cmcm symmetry are uncovered, which are shown in Fig.1. For two orthorhombic phases of C3N2, they share common features: (a) The coordination number of C is 4, however, N is 3. (b) each buckled carbon nitride network consists of saddle-like hexagonal rings, which is connected by the bond formed by two N atoms. (c) For C atoms, there are two bonding ways: one is C atom bonded with its three nearest neighboring C atoms and one N atom, the other is C atoms connected with its two nearest C atoms and two N atoms. It is easily observed that C3N and C2N2 formed tetrahedron. For N atoms, N atom bonded with two C atoms and one N atom shows trigonal planar. Their configuration shape possibly attributed to the reasons as follows. Hybridization of one 2s orbit and three 2p orbits of C atom ensures four equivalent atomic orbits, i.e. sp3 hybridization orbits, whose shape is tetrahedron. For N atoms, the one 2s orbit and two 2p orbits of N atom formed three equivalent sp2 hybridization orbits, which exhibited trigonal plane structure. For Pmmn phase, the hexagonal ring contains five C atoms and one N atom. For Cmcm phase, there are two different types of hexagonal rings. One is composed of four C atoms and two N atoms (2C-N-2C-N) and the other includes six C atoms. Moreover, two kinds of hexagonal rings appear alternately. Compared with B atoms, C, N has more unpaired electrons and must form a network structure that pairs them. Meanwhile, square, pentagon, or hexagon faces is impossible stable due to Coulomb repulsion. These two constraints render the existence of saddle-like hexagonal rings in CN materials. In order to establish the bonding pattern in C3N2, the ELF of two predicted orthorhombic phases of C3N2 at 0 GPa are showed in Fig. 2. High ELF ( > 0.85) value indicates the formation of covalent bonds. The high electron localization indicated the strong covalent bond in the region between adjacent atoms. Moreover, C and N atoms are sp3-hybridized and
sp2-hybridized, respectively. Their structure fits more reasonably with the assumption of hybrid orbitals. Pressure can change the thermodynamic stability and the reaction kinetics of a compound during its synthesis process. In order to investigate the thermodynamic stability of Pmmn and Cmcm phases, the formation enthalpy is calculated: ∆H (C3 N2 ) = H (C3 N2 ) − 3H (C) − 2H (N) , in which ∆H is the formation enthalpy, H is the enthalpy of diamond and cubic gauche (cg) nitrogen chosen as the reference phases. Fig. 3 shows the enthalpy curves for various structures and the decomposition with respect to our predicted P2/m structure. The chosen structural parameters of P2/m and P-4m2 phases are shown in Table S1. From Fig. 3, we can find that C3N2 is thermodynamically stable relative to the diamond and nitrogen, which are possible to synthesize experimentally under normal conditions. Moreover, with pressure up to 82 GPa, Pmmn phase is energetically more favorable relative to β-C3N2, and the enthalpy of Cmcm phase is only higher than 2.71 meV per atom than that of Pmmn phase. Therefore, Cmcm phase is a metastable phase for C3N2 under pressure. As following, we will discuss these two orthorhombic phases of C3N2. For Pmmn phase (10atoms/cell), the lattice constants at 100 GPa are a= 4.729 Ǻ, b=2.404 Ǻ, c= 4.636 Ǻ with carbon occupying 2a (0, 0, 0.214), 4f (0.253, 0, 0.405) positions and nitrogen occupying 2b (0, 0.5, 0.045), 2b (0, 0.5, 0.762) positions at 100 GPa. For Cmcm phase (20atoms/cell), the lattice parameters at 100GPa are a=4.737 Ǻ, b=9.267 Ǻ, c=2.401 Ǻ with carbon occupying 4c (0.5, 0.144, 0.75), 8g (0.749, 0.953, 0.25) and nitrogen occupying 4c (0.5, 0.229, 0.25), 4c (0, 0.871, 0.25). Moreover, at 100GPa the bond lengths of C-C bonds in Pmmn (Cmcm) phase of C3N2 are 1.459 Ǻ (1.455 Ǻ ) and 1.462 Ǻ (1.457 Ǻ) slightly shorter than the C– C bond-length in diamond (1.459 Å) at 100GPa, which possibly indicated the formation of sp3 hybridization similar to diamond. C-N bond lengths of them are 1.375 Ǻ and 1.406 Ǻ and N-N bond length is 1.292 Å. These bond lengths are all shorted than bond length in diamond, which indicated that Pmmn and Cmcm phases of C3N2 possibly have high hardness and bulk modulus. The mechanical properties (e.g., elastic constants, elastic moduli and elastic anisotropy, hardness, etc.) are important for potential technological and industrial applications of materials. Particularly, they provide information on the stability and stiffness of materials. The calculated elastic constants of and are showed in Table 1 as well as previous predicted α-C3N2, β-C3N2 for
comparison [37]. The elastic properties suggest two orthorhombic phases fulfilling the Born-Huang criterion [54]. These results reveal that the predicted orthorhombic phases are mechanically stable. Amazedly, Pmmn-C3N2, Cmcm-C3N2 show exceptionally high C33 values of 1318 GPa and 978 GPa, respectively, even more greater than that of cubic BN (820 GPa). It manifests an ultra-incompressibility of the short B−B bonds along [001] direction. For Pmmn (Cmcm) phase, the nearly equal C11 and C22 (C33) values indicated similar incompressibility along a and b axis (c axis), and the highest C33 (C22) showed c axis (b axis) orientation is most difficultly compressed. C44 is a key parameter indirectly governing the indentation hardness of a material. The predicted two stable orthorhombic structures possess a large C44 value beyond 330 GPa, reflecting that it has a strong strength of resisting the shear deformation. The bulk moduli of Pmmn-, Cmcm-C3N2 are 408 GPa and 406 GPa, respectively, similar to diamond (439 GPa). Another intriguing data is the higher shear modulus of Pmmn-C3N2 (392 GPa) and Cmcm-C3N2 (388 GPa) comparable to that of those of c-BN (376.19 GPa) and w-BN (375.24 GPa). Moreover, the high Young modulus and low Poisson ratio of them showed that Pmmn-C3N2 and Cmcm-C3N2 are potential superhard materials. According to above analysis, two orthorhombic phases not only exhibits a large bulk modulus and a high shear modulus, but also has a considerable Young modulus. Therefore, it is very necessary to obtain the hardness of the two phases. According to the empirical model [53], the calculated Pmmn-, Cmcm-C3N2 has a large hardness value of 60.2 GPa and 58.6 GPa respectively, which are lower than those of diamond (92.9 and 96.3 GPa) but comparable to c-BN (65.6 and 70.5 GPa). At the same time, phonon calculations can give a criterion for the crystal stability and indicate structural instability through soft modes mechanism. Therefore, the phonon dispersion curves of two orthorhombic phases were calculated and presented in Fig.4. There are no imaginary phonon frequencies in the pressure ranges at 80 GPa in the whole Brillouin zone. The results prove that these two structures are dynamically stable under pressure. It is noticed that the phonon modes can be clearly split into acoustic modes, low frequency optical modes from 0 to about 35 THz, and pseudomolecular vibrations modes from 35 to about 45 THz. The existence of “pseudomolecular” modes is related to the peculiar topology, and strongly distorted local coordination of N and C atoms in this phase. Moreover, no imaginary phonon frequencies are found at 0 GPa, which indicate that orthorhombic phases can be possibly synthesized at ambient
condition. These above unique bonding characteristics and mechanical properties motivate us to investigate their corresponding electronic properties. The electronic structure and total and partial density of states (DOS) for the C3N2 at 0 GPa are displayed in Fig. 5. The analysis of PDOS near the Fermi level shows that there is a large overlap between C 2s, 2p and N 2s, 2p, indicating that strong hybridizations occur between them, which is in consistence with the analysis of their structures. The electronic structure indicated their semi-conductor characteristic of the predicted orthorhombic phases of C3N2. We obtained the direct gap (1.3 eV) for Pmmn-C3N2 and indirect band gap (1.1 eV) for Cmcm-C3N2 at 0 GPa.
Conclusion In conclusion, we have uncovered two novel high-pressure orthorhombic phases Pmmn-C3N2 and Cmcm-C3N2, via the PSO algorithm combined with first-principles calculations. Orthorhombic phases of C3N2 are energetically stable above 82 GPa in comparison to cubic phases. The phonon dispersion and elastic constant calculations have identified that Pmmn-C3N2 and Cmcm-C3N2 are dynamically and mechanically stable. No imaginary phonon frequencies for Pmmn-C3N2 and Cmcm-C3N2 at 0 GPa are observed in the whole Brillouin zone, which showed their dynamic stability at ambient condition. The calculated electronic properties indicated that Pmmn-C3N2 and Cmcm-C3N2 are semiconductors with a direct band gap of 1.3 eV for Pmmn-C3N2 and indirect band gap of 1.1 eV for Cmcm-C3N2. Strikingly, two new high-pressure phases Pmmn-C3N2 and Cmcm-C3N2 have high hardness 60.2 and 58.6 GPa, respectively. Their excellent mechanical properties are attributed to strong hybridizations of C-C and C-N atoms. We believe that the current study will advance the understanding of chemistry and stimulate future experimental synthesis and determination of carbon nitrides.
Acknowledgement We acknowledge funding support from the National Natural Science Foundation of China under Grant No. 11774140, China Postdoctoral Science Foundation under Grant No. 2016M590033, Key Scientific Research Projects of Institutions of Higher Learning in Henan Province under Grant No. 19A140012, The Natural Science Foundation of Henan Province under Grant No.
162300410199, Program for Science and Technology Innovation Talents in University of Henan Province under Grant No. 17HASTIT015, and Open Project of the State Key Laboratory of Superhard Materials, Jilin University under Grant No. 201602.
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Figure Captions Fig.1 The crystal structure and atomic arrangement of (a) Pmmn phase (b) Cmcm phase of C3N2, green and purple balls represent C and N atoms, respectively. The inserted part is the formation way of hexagonal rings. Fig.2 Contours of the electronic localization function (ELF) of C3N2 at 0 GPa (a) Pmmn phase and (b) Cmcm phase, isosurface value is 0.85.The circle notes the N2 pairs, green and purple balls represent C and N atoms, respectively. Fig.3. Phase stability of various phases of C3N2 related to predicted P2/m under pressure, together with the diamond and nitrogen. Fig.4 The phonon spectrum of C3N2 under pressure: Pmmn phase (a) 0 GPa (b) 100 GPa; Cmcm phase (a) 0 GPa (b) 100 GPa. Fig.5 (a, c) Band structures and (b, d) partial density of states for Pmmn- and Cmcm-C3N2 at 0
GPa, respectively.
Table Captions Table1 The elastic constants Cij (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa) , and the hardness HV in unit of GPa, the Poisson’s ratio ν of Pmmn- and Cmcm-C3N2 at zero pressure, together with that of α-C3N2, β-C3N2 and Diamond. .
Table1 The elastic constants Cij (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa) , and the hardness HV in unit of GPa, the Poisson’s ratio ν of Pmmn- and Cmcm-C3N2 at zero pressure, together with that of α-C3N2, β-C3N2 and Diamond. Structure
C11
C33
C22
C44
C55
C66
C12
C23
C13
B
G
E
ν
HV
Pmmn-C3N2
966
1318
969
325
400
280
42
90
108
408
392
892
0.136
60.2
Cmcm-C3N2
956
978
1317
330
270
395
102
93
35
406
388
884
0.138
58.6
α-C3N2 [37]
867
327
137
380
365
829
0.136
68.2
β-C3N2[37]
834
329
98
343
368
813
0.105
68.5
Diamond
1058
569
129
439
524
1125
0.07
98
Fig.1
Fig.2
Fig.3
Fig.4
Fig.5
Highlights: (1) For the first time, novel superhard phases Pmmn and Cmcm of C3N2 are found, which are stable above 80 GPa. (2) The phonon spectrums of Pmmn and Cmmm phases of C3N2 have no imaginary frequencies at 0 GPa and 100 GPa, and they are dynamically stable. (3) Two phases of C3N2 at 0 GPa are semiconductors with high hardness with high hardness about 60 GPa comparable to c-BN.