  Two novel three-dimensional (3D) crystal structures of carbon (C) and
germanium carbide (GeC2) were predicted using first-principles
density-functional theory (DFT) calculations. These newly discovered 3D carbon
allotrope and GeC2 are in the space group of Fmmm (space group number 69).
Their crystal structures have unique tetragonal/hexagonal rings formed by
either C or Ge/C atoms. Both structures were proven to be thermodynamically
stable through the phonon spectrum calculations. The C allotrope is a
semiconductor with a wide band gap of 3.65 eV predicted by the hybrid density
functional HSE06 method, while GeC2 is metallic. The new C allotrope has a low
mass density of 2.84 g/cm3. More importantly, it is proven to be energetically
stable with cohesive energy less than -7.5 eV/atom which is lower than many
other carbon allotropes implying the possibility to be fabricated in lab. Such
a carbon crystal structure with a low mass density and wide band gap once
synthesized would have wide applications in gas adsorption sensors and
photo-electronic devices.
