Samir F Matar*

Lebanese German University (LGU), Sahel-Alma, Jounieh, Lebanon

*Corresponding Author: Samir F Matar, Lebanese German University (LGU), Sahel-Alma, Jounieh, Lebanon.

Received: July 21, 2022; Published: July 28, 2022

Abstract

Within the carbon-silicon system, novel tetragonal C₈ and Si₈ allotropes and two silicon carbides Si₂C₆ and Si₄C₄ are devised. The propositions are based on density functional theory (DFT) calculations of template structures, optimized to ground state energies and subsequently derived physical properties. All four phases belong to primitive tetragonal space group P-4m2 N°115 characterized by large c/a tetragonality ratio. The structures consist of corner sharing C4 and Si4 tetrahedra highlighting covalent (in C₈) and polar covalent (in silicon carbides) chemical systems illustrated with charge density projections. C₈ is identified as ultra-hard with a Vickers hardness (H_V) amounting to 113 GPa, a result assigned to the large tetragonality ratio. Oppositely, Si₈ allotrope is found soft with H_V = 13 GPa alike cubic Si, and Si₄C₄ is identified with H_V =33 GPa alike experimental SiC. Larger C-content Si₂C₆ is identified as super-hard with H_V = 51 GPa. All new phases are mechanically (elastic constants with bulk and shear moduli) and dynamically (phonon band structures) stable. The electronic band structures are characteristic of insulating C₈ with, a large band gap of about 5 eV like diamond, and semi-conducting Si₂C₆, Si₄C₄, and Si₈ with band gaps of ~1 eV. The results are claimed as enriching further the Si-C system with novel materials aimed at diverse electronic and mechanic applications.

Keywords: DFT; Carbon; Silicon; Silicon Carbide; Super-hard; Elastic Constants; Phonons

References

1. M Baloga., et al. “Nano- versus macro-hardness of liquid phase sintered SiC”. Journal of the European Ceramic Society 25 (2005): 529-534.
2. Shuangshuang Zhang., et al. “CALYPSO software”. Chinese Physics B 28 (2019): 106104.
3. AR Oganov. “Crystal structure prediction: reflections on present status and challenges”. Faraday Discuss 211 (2018): 643.
4. P Hohenberg and W Kohn. “Inhomogeneous electron gas”. Physical Review B 136 (1964) 864-871.
5. W Kohn and LJ Sham. “Self-consistent equations including exchange and correlation effects”. Physical Review A 140 (1965): 1133-1138.
6. SF Matar and VL Solozhenko. “Crystal chemistry and first principles devising of C4 as the simplest dense carbon allotrope". Journal of Solid State Chemistry 314 (2022): 123424.
7. T Yang., et al. “Gas phase formation of c-SiC3 molecules in the circumstellar envelope of carbon stars”. PNAS (Proceedings of the National Academy of Sciences)29 (2019): 14471-14478.
8. SF Matar., et al. “First-principles investigations of tricarbon: From the isolated C3 molecule to a novel ultra-hard anisotropic solid”. Carbon Trends 6 (2022): 100132.
9. G Kresse., et al. “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set”. Physical Review B 54 (1996): 11169.
10. G Kresse and J Joubert. “From ultrasoft pseudopotentials to the projector augmented wave”. Physical Review B 59 (1999): 1758-1775.
11. PE Blöchl. “Projector augmented wave method”. Physical Review B 50 (1994): 17953-17979.
12. J Perdew., et al. “The Generalized Gradient Approximation made simple”. Physical Review Letter 77 (1996): 3865-3868.
13. WH Press., et al. “Numerical Recipes”. 2^nd Cambridge University Press: New York, USA, (1986).
14. PE Blöchl., et al. “Improved tetrahedron method for Brillouin-zone integrations”. Physical Review B 49 (1994): 16223-16233.
15. M Methfessel and AT Paxton. “High-precision sampling for Brillouin-zone integration in metals”. Physical Review B 40 (1989): 3616-3621.
16. HJ Monkhorst and JD Pack. “Special k-points for Brillouin Zone integration”. Physical Review B 13 (1976): 5188-5192.
17. A Togo and I Tanaka. “First principles phonon calculations in materials science”. Scripta Materialia 108 (2015): 1-5.
18. V Eyert. “Basic notions and applications of the augmented spherical wave method”. International Journal of Quantum Chemistry 77 (2000): 1007-1031.
19. SF Matar and VL Solozhenko. “Crystal chemistry rationale and ab initio investigation of ultra-hard dense rhombohedral carbon and boron nitride”. Diamond and Related Materials 120 (2021): 108607.
20. W Voigt. “Über die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper”. Annals Physics 274 (1889): 573-587.
21. DC Wallace. “Thermodynamics of crystals”. New York, USA: John Wiley and Sons (1972).
22. VV Brazhkin and VL Solozhenko. “Myths about new ultrahard phases: Why materials that are significantly superior to diamond in elastic moduli and hardness are impossible”. Journal of Applied Physics 125 (2019): 130901.
23. Silicon - Strength - Hardness - Elasticity - Crystal Structure (material-properties.org).
24. X-Q Chen., et al. “Modeling hardness of polycrystalline materials and bulk metallic glasses”. Intermetallics 19 (2011): 1275-1281.
25. RS Krishnan. “Raman spectrum of diamond”. Nature 155 (1945): 171.
26. Dengfeng Li., et al. “Stretch-Driven Increase in Ultrahigh Thermal Conductance of Hydrogenated Borophene and Dimensionality Crossover in Phonon Transmission”. Advanced Functional Materials 31 (2018): 1801685.

Citation

Citation: Samir F Matar. “First Principles Investigations in the Carbon-silicon System of Novel Tetragonal C₈ and Si₈ Allotropes, and Binary Si₂C₆ and Si₄C₄ Phases". Acta Scientific Applied Physics 2.8 (2022): 02-08.

Copyright

Copyright: © 2022 Samir F Matar. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.