4.3 Properties

We also computed the mechanical and optical properties (see Supplementary Materials). Similar to previous theoretical investigations 25; 87; 88; 236; 237; 238; 239; 240, all of these candidate allotropes exhibit high hardnesses 33 and bulk moduli, which are comparable with those of diamond. Fig. 5.3 shows the calculated total and partial electronic densities of states in both systems. The DFT band gaps of M-carbon, X-carbon, bct-C$_4$, and Y-carbon are 3.6, 3.8, 2.7 and 2.9 eV, and we should bear in mind that DFT always underestimate the band gaps - so the real gaps are larger, and all of these $sp^3$-allotropes should be transparent colorless insulators.

Figure 8.11: Enthalpies of various carbon structures relative to graphite-2H.