Triply periodic minimal surfaces decorated with curved graphite

Abstract Hypothetical negatively curved structures derived from graphite are described, in which all carbon atoms rest on triply periodic minimal surfaces (TPMS). The D minimal surface was calculated using the Weierstrass representation. By applying the Bonnet transformation to the D surface, the gyroid and P surfaces were constructed. Curvatures, densities, lattice parameters and energies have been calculated for all structures. The absolute value of the maximum Gaussian curvature is smaller than that for C 60 fullerene. A new periodic graphite net with the same topology as the I-WP minimal surface, using 5-, 6- and 8-membered rings is found possible. The stability of 11 negatively curved graphitic structures has been determined using Tersoff's three-body potential. All the structures described are more stable than C 60 ,mainly because the 120° bond angles in ordinary graphite are almost preserved in the 7- and 8-membered carbon rings. The way is now open to explore the decoration of minimal surfaces with further arrangements of atoms of different elements.