From quartz (qtz) to diamond (dia) carbon topologies: Stepwise rationale from crystal chemistry and DFT investigations

From crystal chemistry and density functional theory DFT calculations, a stepwise rationale is proposed for the transformation from standalone distorted tetrahedron α-C₅ favored over standalone regular tetrahedron β-C₅ to high density – ultra hard orthorhombic α-C₆ and β-C₆ with qtz (quartz-based) topology characterized by 3D arrangements of distorted tetrahedra to lower density dia-C topology (diamond-like, with regular C4 tetrahedra). Progressive C insertions into orthorhombic α-C₅, α-C₆, and lastly into C₇ were operated leading to ultimate C₈ stoichiometry identified as diamond-like. C₇ was also used as template to devise C₃N₄ carbonitride with exceptional mechanical properties. The induced structural and physical changes are supported with elastic properties pointing to ultra-hardness, larger for qtz α,β-C₆ than dia C₈ and inferred dynamic stability for all stoichiometries from the phonons band structures. The thermodynamic quantities as the specific heat were compared with diamond experimental C_V. The electronic band structures reveal semi-conducting C₆, metallic C₇ characterized by diamond-defect structure, and insulating C₈. The results are meant to help further systemic understanding of tetrahedral carbon allotropes.