First principles search for novel ultrahard high-density carbon allotropes: hexagonal C6, C9 and C12

Hexagonal carbon allotropes C6, C9 and C12 with qtz, sta and lon topologies, respectively, were predicted on the basis of crystal chemistry and first principles (DFT) calculations. The new allotropes are mechanically (elastic properties) and dynamically (phonons) stable phases and are characterized by ultra-high Vickers hardness, exceptionally high for qtz C6 and C12, close to the previously studied qtz C3. The electronic band structures of all new allotropes show semi-conducting to insulating behavior. lon C12 can be considered as novel superlonsdaleite.