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 sp(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-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.