Superconductivity and high hardness in scandium-borides under pressure

Exploration of new superconducting or superhard transition-metal borides has attracted extensive interest in the past few decades. In this study, we conducted comprehensive theoretical investigations in the scandium-boron binary system by employing a structural search method based upon first-principles density functional theory. Among the six predicted superconducting scandium-borides, ScB₁₄ (Pm3̄) has the highest superconducting transition temperature T_c = 12.3 K and a Vickers hardness of 12.6 GPa at ambient pressure. The superconductor ScB₄ (C2/m) has T_c = 3.6 K and a high Vickers hardness of 25.5 GPa at ambient pressure. Further analysis indicates that the previously synthesized ScB₁₅ (P4₁) is of superhardness. Our discoveries not only enrich the phase diagram of scandium-borides, but also pave the way for future experimental validations and potential applications of superconducting scandium-borides in industry.