Prediction of potential hard sodium carbaboride compounds assuming sp³-bonded covalent clathrates

Boron-carbon clathrates have attracted great attention due to their unique sp³-bonded structure and excellent electronic properties. Here, by performing first-principles calculations, we predicted six stoichiometric Na-B-C clathrates (NaBC₁₁, Na₂B₂C₁₀, NaB₂C₁₀, Na₂B₄C₈, NaB₄C₈, and Na₂B₆C₆) based on Na-doped boron-carbon clathrates. As a result, NaBC₁₁, Na₂B₂C₁₀, and NaB₂C₁₀ were found to become energetically favorable. Under ambient conditions, the electronic structure calculations show that NaBC₁₁ and Na₂B₂C₁₀ are indirect band gap semiconductors, and NaB₂C₁₀, Na₂B₄C₈, and NaB₄C₈ exhibit metallic features. Na₂B₂C₁₀ and Na₂B₄C₈ are found to be synthesized at 22.7 and 14.2 GPa, respectively. Interestingly, the formation enthalpies of NaB₂C₁₀ and NaB₄C₈ (x = 0, 1, and 2) clathrates decrease in turn with the increased number of Na atoms in the same synthetic paths. Moreover, the ideal indentation strengths of NaBC₁₁, Na₂B₂C₁₀, and NaB₂C₁₀ approach 40 GPa, indicating that they are hard materials with superior hardness. These findings offer valuable insights for advancing the synthesis of boron-carbon clathrates.