Low-density superhard materials: Computational study of Li-inserted B-substituted closo-carboranes LiBC₁₁ and Li₂B₂C₁₀

Insertion of Li atoms into a B-substituted carbon cage produces two superhard compounds with relatively low density: LiBC₁₁ and Li₂B₂C₁₀. For each structure, phonon frequencies across the whole Brillouin zone are positive, indicating dynamic stability. Electronic structure calculations indicate that they are semiconductors under ambient conditions. Estimates of the Vickers hardness, based on a semi-empirical model, highlight the incompressible nature of these two compounds. We then performed calculations on the ideal strengths of these two structures to confirm the hardness and investigate origins of the mechanical properties. Strikingly, both LiBC₁₁ and Li₂B₂C₁₀ can be classed as superhard materials, with hardness values of 49 GPa and 41 GPa, respectively. The current results shed light on the properties of new superhard carbon cage structures more generally.