Hard and superconducting cubic boron phase via swarm-intelligence structural prediction driven by a machine-learning potential

Boron is an intriguing element due to its electron deficiency and the ability form multicenter bonds in allotropes borides, exhibiting diversified structures, unique chemical bonds, interesting properties. Using swarm-intelligence structural prediction driven by a machine learning potential, we identified boron phase with 24-atom cubic unit cell, called $c\text{\ensuremath{-}}{\mathrm{B}}_{24}$, consisting of ${\mathrm{B}}_{6}$ octahedron addition well-known ${\mathrm{B}}_{2}$ pairs ${\mathrm{B}}_{12}$ icosahedra at ambient pressure. There appear unusual four-center-two-electron (4c-2e) icosahedron, originating from peculiar bonding pattern between pair which sharp contrast 3c-2e 2c-2e $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{B}}_{12}$. More interestingly, $c\text{\ensuremath{-}}{\mathrm{B}}_{24}$ metal superconducting critical temperature 13.8 K The predicted Vickers hardness (23.1 GPa) indicates that potential hard material. Notably, it also has good shear/tensile resistance (48.9/29.3 GPa). Our work not only enriches understanding properties boron, but sparks efforts on trying synthesize this particular compound, $c\text{\ensuremath{-}}{\mathrm{B}}_{24}$.