Hallow diamonds: stability and elastic properties

We conjecture about the possibility of periodic sp3-bonded carbon lattices formed by regular arrays of fullerenic cavities (hollow diamonds (HDs)) as a generalization of clathrates. We describe three infinite series of HDs having Nn(n + 1)(2n +1)/3 atoms per unit cell, for any natural number n and N = 17 (face center cubic), 20 (hexagonal) or 23 (simple cubic lattices). Each of the series tends to diamond for n → ∞. Using the semi-empirical many-body Tersoff potential for the carbon-carbon interaction, we have calculated with a simulated annealing procedure the ground-state structure, the total energy and the elastic constants of the smallest HDs (fcc-C34, hex-C40 and sc-S46), comparing the results to diamond.