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Formation and Stability of Cellular Carbon Foam Structures:An {\em Ab Initio} Study

We use ab initio density functional calculations to study the formation and structural as well as thermal stability of cellular foam-like carbon nanostructures. These systems with a mixed $sp^2/sp^3$ bonding character may be viewed as bundles of carbon nanotubes fused to a rigid contiguous 3D honeycomb structure that can be compressed more easily by reducing the symmetry of the honeycombs. The foam may accommodate the same type of defects as graphene, and its surface may be be stabilized by terminating caps. We postulate that the foam may form under non-equilibrium conditions near grain boundaries of a carbon-saturated metal surface.