Novel Ultrahard Carbon Allotropes from Crystal Chemistry and First Principles: Rhombohedral ene-C21 and yne-C24

Rhombohedral ene-C21 and yne-C24, characterized by the presence of C=C and C≡C bonds, respectively, inserted into the 9R diamond polytype C18, are proposed as novel ultrahard carbon allotropes from crystal chemistry and first principles. Like 9R C18, they belong to the cfe topology characteristic of layered SiC polytypes. With ultrahard properties approaching those of diamond and lonsdaleite, ene-C21 and yne-C24 are dynamically stable with phonon signatures identifying C=C and C≡C high frequency vibrations similar to molecular allene and acetylene. The electronic band structures correspond to insulating C18, metallic ene-C21 and semiconducting yne-C24.