From layered 2D carbon to 3D tetrahedral allotropes C12 and C18 with physical properties related to diamond: Crystal chemistry and DFT investigations

Mechanisms of changes from 2D to 3D (D = dimensionality) involving 2D C(sp²) trigonal paving to C(sp³) tetrahedral stacking are proposed through puckering of the 2D layers on one hand and interlayer insertion of extra C on the other hand. Such transformations, led to 3D hexagonal C₁₂ and C₁₈ allotropes respectively characterized by lon and bac topologies. Using density functional theory DFT calculations, the two allotropes were found cohesive and stable both mechanically (elastic properties) and dynamically (phonons). Comparisons of the physical properties with known uni C₆ were established letting identify ranges of large Vickers hardness: H_V (uni C₆) = 89 GPa, H_V (lon C₁₂) = 97 GPa, and H_V (bac C₁₈) = 70 GPa. Whilst C₆ was identified with acoustic phonons instability, C₁₂ and C₁₈ were found stable dynamically throughout the acoustic and optic frequency ranges. Furthering on the thermal properties the allotropes were characterized with a temperature dependence curve of the specific heat C_V close to experimental data of diamond with best fit for novel C₁₈. The electronic band structures reveal a small band gap of 1 eV for uni C₆ and larger direct band gap of 3 eV for the two other 3D allotropes. Such modulations of the electronic and physical properties should open scopes of carbon research.