A metallic carbon allotrope with superhardness: a first-principles prediction

Abstract

Carbon has abundant allotropes with superhardness, but few of them are metallic. From first-principles calculations, we propose a stable metallic carbon allotrope (Hex-C₂₄) phase with superhardness. The Hex-C₂₄ can be thought of as a superlattice of carbon nanotubes and graphene nanoribbons composed of sp²- and sp³-hybridized carbon atoms. A possible synthetic route towards Hex-C₂₄ from graphyne multilayers is evaluated by calculating the transition states between the two phases. Our calculations show that at a uniaxial pressure of around 25 GPa, the energy barrier of this endothermic transition is estimated to be 0.04 eV per atom, while at a pressure of 34 GPa, the transition is barrierless for specific initial configurations. The cohesive energy, elastic constants, and phonon frequencies unambiguously confirm the structural stability. The hardness of the Hex-C₂₄ is estimated to exceed 44.54 GPa, which is 1/2 that of diamond. The Hex-C₂₄ phase is metallic with several bands across the Fermi level. Both mechanical and metallic properties of Hex-C₂₄ are anisotropic.