Mechanical and Electronic Properties of XC₆ and XC₁₂

A series of carbon-based superconductors XC₆ with high T were reported recently. In this paper, based on the first-principles calculations, we studied the mechanical properties of these structures, and further explored the XC₁₂ phases, where the X atoms are from elemental hydrogen to calcium, except noble gas atoms. The mechanically- and dynamically-stable structures include HC₆, NC₆, and SC₆ in XC₆ phases, and BC₁₂, CC₁₂, PC₁₂, SC₁₂, ClC₁₂, and KC₁₂ in XC₁₂ phases. The doping leads to a weakening in mechanical properties and an increase in the elastic anisotropy. C₆ has the lowest elastic anisotropy, and the anisotropy increases with the atomic number of doping atoms for both XC₆ and XC₁₂. Furthermore, the acoustic velocities, Debye temperatures, and the electronic properties are also studied.