Superhard $s{p}^3$ carbon allotropes with odd and even ring topologies

Four $s{p}^3$ carbon allotropes with six, eight, and 16 atoms per primitive cell have been derived using a combination of metadynamics simulations and topological scan. A chiral orthorhombic phase $o$C16 ($C{222}_1$) was found to be harder than monoclinic M-carbon and shows excellent stability in the high-pressure range. A second orthorhombic phase of $Cmmm$ symmetry, by $\sim$0.028 eV/atom energetically lower than W-carbon, can be formed from graphite at $\sim$9 GPa. In general, the mechanical response under pressure was found to depend on the structure topology, which reflects the way rings are formed from an initial graphene layer stacking.

Figure 1

Crystal structures of unique carbon phases. $o$C16-I and $m$C32 are characterized by a $5+7$ odd-odd ring pattern. $m$C12 represents a distinct $5+8$ odd-even ring topology, while $o$C16-II contains even rings only, $4+6+8$.

Figure 2

(a) Enthalpies (relative to graphite) of different carbon allotropes; (b) enthalpies of certain $s{p}^3$ carbon allotropes (relative to diamond) in the high-pressure range. The colors (lines) are the same as in (a).

Figure 3

Electronic band structures (top) and phonon dispersion curves (bottom) for (from left to right) $m$C12, $o$C16-I, $m$C32, and $o$C16-II carbon phases.

Figure 4

Comparison of M-carbon with $o$C16-I, $m$C12, and $o$C16-II with respect to their underlying puckered graphitic stacking. Layers are highlighted in turquoise (medium gray).

Figure 5

Simulated XRD pattern for $o$C16-I and $o$C16-II carbon phases ($\lambda =0.3329$ Å). The structural data are those of Table .