Families of Superhard Crystalline Carbon Allotropes Constructed via Cold Compression of Graphite and Nanotubes

We report a general scheme to systematically construct two classes of structural families of superhard $s{p}^3$ carbon allotropes of cold-compressed graphite through the topological analysis of odd $5+7$ or even $4+8$ membered carbon rings stemmed from the stacking of zigzag and armchair chains. Our results show that the previously proposed $M$, bct-${\mathrm{C}}_4$, $W$ and $Z$ allotropes belong to our currently proposed families and that depending on the topological arrangement of the native carbon rings numerous other members are found that can help us understand the structural phase transformation of cold-compressed graphite and carbon nanotubes (CNTs). In particular, we predict the existence of two simple allotropes, $R$ and $P$ carbon, which match well the experimental x-ray diffraction patterns of cold-compressed graphite and CNTs, respectively, display a transparent wide-gap insulator ground state and possess a large Vickers hardness comparable to diamond.

Figure 1

(a),(b),(c) and (d) illustrate the crystallographic structures of the proposed $S$ carbon, $R$ carbon, $S\mathrm{\text{−}}{S}_1{Z}_2$, and $S\mathrm{\text{−}}{S}_1{A}_2$ phases. Left column: three-dimensional crystalline structures and right column: the two-dimensional (2D) projections of the $2\times 2\times 1$ supercell along their $b$ or $c$ axis. For $S$ carbon, the $3\times 1\times 2$ supercell is used. The gray background highlights the armchair chains and white background denotes the zigzag chains.

Figure 2

(a),(b) and (c) illustrate the crystallographic structures of the bct-${\mathrm{C}}_4$ carbon, $Z$ carbon, $P$ carbon (this work). Left column: three-dimensional unit cells and right column: the 2D projections of the $2\times 2\times 1$ supercell of bct-${\mathrm{C}}_4$ and of the $1\times 2\times 1$ supercells of $Z$ carbon along their $c$ axis, and the 2D projections of the $1\times 1\times 2$ supercells of $P$ carbon along its b-axis. (d),(e) and (f) show the 2D projections in the $1\times 2\times 1$ supercells along the $c$ axis for three typical lattice structures of the $B\mathrm{\text{−}}{B}_1{A}_4$ series.

Figure 3

Calculated enthalpy difference per atom with respect to graphite for a series of carbon allotropes as a function of pressure. The stable pressures of these proposed allotropes compared to graphite are labeled.

Figure 4

(a) Simulated XRD patterns (with wavelength of 0.3329 Å) for selected phases at 18.4 GPa compared with experimental results from Ref. 5 for cold-compressed graphite. (b) Simulated XRD patterns of the five allotropes in $B$ family at ambient pressure, in comparison with the date measured from the quenchable phase recovered from cold-compressed CNTs [16]. The red arrows highlight five main experimental peaks.