Structure and Properties of Novel Superhard C5N:A First-Principles Study
doi: 10.11858/gywlxb.20170606
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摘要: 通过使用在晶体结构预测方面成熟的粒子群优化算法，提出了6种化学计量比为5:1的氮化碳新相。采用基于密度泛函理论的第一性原理计算研究它们的结构、稳定性、机械性能和电子性质。计算结果表明，在提出的6种结构中，P62m-C5N是能量最稳定的。弹性常数和声子谱计算表明，这些结构在0 GPa时是机械稳定和动力学稳定的。电子计算显示，I41-C5N是金属性的，而其他5种结构是半导体。维氏硬度计算表明，除I41-C5N外，其余氮化碳都为超硬材料。通过形成焓计算，分析认为这6种结构能在目前实验所能达到的高压下合成(19~83 GPa)。Abstract: By using the developed particle swarm optimization algorithm on the crystal structural prediction, we proposed 6 novel carbon nitride phases with a 5:1 stoichiometry.Their structures, stability, mechanical and electronic properties were investigated by first-principle calculations with the density functional theory.Our calculations indicate that P62m-C5N is energetically favorable in the 6 structures.Both elastic constants and phonon-dispersion calculations show that these structures remain mechanically and dynamically stable at 0 GPa.Electronic calculations indicate that I41-C5N is metallic while the other 5 are semiconductive.The Vickers hardness shows that all the 6 structures are superhard materials except for I41-C5N.Formation enthalpy calculations suggest that these 6 structures can be synthesized at attainable high pressures (19-83 GPa).
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Key words:
- carbon nitride /
- first-principle calculations /
- superhard /
- high shear modulus
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Figure 1. Predicted structure graphs of C5N (The spheres in color black and blue represent C and N atoms, respectively.)
Figure 2. Formation enthalpy of the newly predicted C5N phases relative to graphite and nitrogenas a function of pressure
Table 1. Structure parameters of the newly predicted C5N
Phase Crystal system Space group Atoms positions Lattice parameters/
nmDensity/
(g·cm-3)Cell volume/
nm3P62m-C5N Hexagonal P62m C:6i (0.6686, 0, 0.6851)
C:4h (0.3333, 0.6667, 0.1846)
N:2e (0, 0, 0.2520)a=0.42610
c=0.449043.48366 0.0706056 I41-C5N Tetragonal I41 C:8b (1.3922, 0.3047, 0.2213)
C:8b (0.8888, 0.3025, 0.5651)
C:4a (0.5000, -0.5000, 0.6649)
N:4a (0.5000, -0.5000, 0.3717)a=0.56554
c=0.461993.32925 0.147761 Pbcn-C5N Orthorhombic Pbcn C:8d (0.8394, 1.1859, 0.6653)
C:8d (0.9443, 0.5105, 1.3780)
C:8d (0.7272, 1.4193, 1.3967)
C:8d (1.4165, 1.4451, 0.5433)
C:4c (0.5000, 1.3491, 0.7500)
C:4c (0.5000, 0.8125, 0.7500)
N:8d (1.3159, 0.7079, 1.4033)a=0.69219
b=0.75985
c=0.552513.38559 0.290603 P63cm-C5N Hexagonal P63cm C:12d (0.1549, 0.4103, 0.8667)
C:12d (0.4099, 0.1542, 0.6931)
C:6c (0.7822, 0, 0.6486)
C:4b (0.3333, 0.6667, 0.1247)
C:4b (0.3333, 0.6667, 0.9413)
C:2a (0, 0, 0.4143)
N:6c (0.7847, 0, 0.9101)
N:2a (0, 0, 0.1519)a=0.61546
c=0.943323.17945 0.309444 P212121-C5N Orthorhombic P212121 C:4a (-0.4660, 0.3648, 0.0251)
C:4a (-0.0356, 0.4140, 0.7846)
C:4a (0.4082, 0.7553, 0.4943)
C:4a (-0.3026, 0.2316, 0.4965)
C:4a (-0.3414, 0.7023, 0.9899)
C:4a (0.4321, 0.3975, 0.5198)
C:4a (-0.4450, 0.6928, 0.4812)
C:4a (0.1246, 0.4389, 0.5229)
C:4a (0.3131, 0.9248, 0.4703)
C:4a (-0.0722, 0.9907, 0.4778)
N:4a (-0.2536, 0.8681, 0.9885)
N:4a (-0.2860, 0.6001, 0.0557)a=0.80449
b=1.40889
c=0.256593.3830 0.290827 Pna21-C5N Orthorhombic Pna21 C:4a (0.6262, 0.2909, 0.7966)
C:4a (0.6669, 0.4999, 0.8488)
C:4a (0.4457, 0.1191, 0.1296)
C:4a (0.3513, 0.0085, 0.1102)
C:4a (0.4412, 0.8115, 0.8592)
C:4a (0.1030, 0.1609, 0.0666)
C:4a (0.9757, 0.2005, 0.3318)
C:4a (0.2617, 0.1527, 0.5419)
C:4a (0.7486, 0.6235, 0.4587)
C:4a (0.3119, 0.0399, 0.6076)
N:4a (0.3225, 0.4796, 0.8604)
N:4a (0.7712, 0.2000, 0.7768)a=0.40299
b=1.40205
c=0.516403.3720 0.291776 
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Table 2. Calculated independent elastic constants Cij of the newly predicted C5N
Phase C11/
GPaC22/
GPaC33/
GPaC44/
GPaC55/
GPaC66/
GPaC12/
GPaC13/
GPaC15/
GPaC23/
GPaC25/
GPaP62m-C5N 1194 930 252 113 18 I41-C5N 649 931 244 247 244 75 Pbcn-C5N 762 663 822 382 360 364 190 83 165 P63cm-C5N 873 490 192 170 35 P212121-C5N 902 847 893 299 341 347 120 93 40 902 847 Pna21-C5N 891 659 736 289 372 324 86 153 149 891 659
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Table 3. Calculated bulk modulus B, shear modulus G, Young's modulus E and Vickers hardness Hv ofthe newly predicted C5N (Also shown are G/B ratio and Poisson's ratio σ)
Phase B/GPa G/GPa E/GPa σ G/B Hv/GPa P62m-C5N 397 394 888 0.127 0.992 62.5 I41-C5N 335 238 577 0.213 0.711 30.0 Pbcn-C5N 347 338 765 0.133 0.973 55.0 P63cm-C5N 286 267 611 0.144 0.934 44.5 P212121-C5N 349 354 794 0.121 1.014 59.6 Pna21-C5N 338 321 731 0.139 0.949 51.6
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