Ultra-hard rhombohedral carbon by crystal chemistry and ab initio investigations

Highlights: • New ultra-hard rhombohedral carbon form is reported from crystal chemistry construction. • The extended hexagonal three-dimensional network of h-C12 is formed of C4 tetrahedra like lonsdaleite. • The electronic band structure is characteristic of insulator with Egap=4eV similarly to diamond. • Larger value of bulk modulus versus lonsdaleite, and largest Vickers hardness (HV) versus diamond&lonsdaleite. A new ultra-hard rhombohedral carbon rh-C₄ (or hexagonal h-C₁₂) is reported as derived from 3R graphite through crystal chemistry construction and ground state energy within the density functional theory. A resulting cohesive extended hexagonal three-dimensional network of h-C₁₂ is identified as formed of C4 tetrahedra like in cubic and hexagonal diamond. The electronic band structure of rh-C₄ is characteristic of insulator with E_gap=4eV similarly to diamond. From the energy-volume equations of state and the set of elastic constants a larger value of bulk modulus versus lonsdaleite, and the largest Vickers hardness (H_V) versus both forms of diamond were revealed. The phonon band structure showing only real wave numbers further confirms the stability of the new carbon phase.