Mechanical and electronic properties of B₁₂-based ternary crystals of orthorhombic phase

Using first-principles calculations, the structural, mechanical and electronic properties of the experimentally synthesized B(12)-based ternary crystals (AlMgB(14), AlNaB(14), AlLiB(14), Mg(2)B(14), MgSi(2)B(12), MgC(2)B(12), Li(2)Si(2)B(12) and Li(2)C(2)B(12)) have been investigated. The theoretical equilibrium lattice constants of these crystals agree with the experimental values. The Vickers hardness (H(v)) estimated from the theoretical Young's moduli ranges from 20 to 30 GPa, and the MgC(2)B(12) compound (H(v) = 31.4 GPa) is harder than α-boron. Based on the electron density of states and Mulliken population analysis, the origination of hardness and interaction between the interstitial atoms and the B(12) framework were discussed. Scaled bond order of the B-B bonds was used to interpret the hardness of these B(12)-based ternary compounds. The crystal hardness is primarily determined by the B(12) icosahedral skeleton, whereas the contributions of metal atoms manifest as the electron transfer from metal to B atoms. We also calculated the ideal tensile strength of AlMgB(14) and MgC(2)B(12) and found that the <001> and <010> directions are their cleavage directions under tensile strains, respectively.