Four superhard tetragonal carbon allotropes: First-principles calculations

Based on density functional theory, four new three-dimensional sp(3) hybrid carbon allotropes have been designed in the P4(2)/mmc space group and named as P4(2)/mmc C-32-I, P4(2)/mmc C-32-II, P4(2)/mmc C-36, P42/mmc C-40 according to the number of carbon atoms in their conventional cell. They all have mechanical, dynamic, and thermal stability at 500 K and a low relative enthalpy. Larger bulk modulus and Young's modulus lead to good superhard characteristics of these four carbon allotropes. By means of Tian's model and Chen's model, their hardness are estimated to be between 40 and 70 GPa, especially the hardness of C-40 is as high as similar to 69 GPa, which has exceeded c-BN. Electronic band structure simulated by Heyd-Scuseria-Ernzerhof (HSE06) functional indicates that P4(2)/mmc C-32-I and P4(2)/mmc C-40 are indirect band gap semiconductors, while P4(2)/mmc C-32-II and P4(2)/mmc C-36 are direct band gap semiconductor. Furthermore, the XRD patterns of four carbon structures provide a theoretical basis for future experimental synthesis.

Automated summary

Based on density functional theory, four new three-dimensional sp(3) hybrid carbon allotropes have been designed with high mechanical and thermal stability, as well as superhard characteristics. Their hardness ranges from 40 to 70 GPa, with the hardness of C-40 reaching as high as 69 GPa, surpassing c-BN. The electronic band structure analysis shows that two of the allotropes are indirect band gap semiconductors, while the other two are direct band gap semiconductors. Additionally, the XRD patterns of these carbon structures provide a theoretical basis for future experimental synthesis.