Orthorhombic ScB3 and hexagonal ScB6 with high hardness

Transition metal borides (TMBs) have received great interest since these intriguing borides could be considered potential applications for designing exotic materials with distinguished properties such as superhardness. The search for TMBs regarding high hardness value remains urgent. Given that Sc is the lightest transition metal element that often exhibits unique properties, in this paper, we undertake a comprehensive investigation of the Sc-B system at high pressures using the state-of-the-art structure search method within the framework of first-principles electronic structure. As a result, our structure searches identified several stable Sc-B phases (i.e., ScB, ${\mathrm{ScB}}_{3}, {\mathrm{ScB}}_{4}$, and ${\mathrm{ScB}}_{5}$) as well as a metastable ${\mathrm{ScB}}_{6}$. Strikingly, among these scandium borides, $Pnma {\mathrm{ScB}}_{3}$ contains a boron framework with open channels, while ${\mathrm{ScB}}_{6}$ possesses interlinking boron trimer units. Remarkably, our simulations suggest the hard features of $Pnma {\mathrm{ScB}}_{3}$ and $P{6}_{3}mc {\mathrm{ScB}}_{6}$ with high simulated Vickers hardness values of 38.3 and 39.8 GPa, respectively, which are mainly attributed to their peculiar strong covalent boron network. The excellent stability and high hardness of ${\mathrm{ScB}}_{3}$ and ${\mathrm{ScB}}_{6}$ render them promising candidates for superhard materials. Additionally, an orthorhombic boron allotrope $o\text{\ensuremath{-}}{\mathrm{B}}_{12}$ is predicted by removing Sc from $Pnma {\mathrm{ScB}}_{3}$, where this structure exhibits an estimated hardness value of 24.9 GPa and superconducting critical temperature ${T}_{\mathrm{c}}$ of 2.9 K at 1 atm. In this paper, we advance the existing knowledge of TMBs as well as provide implications for the search for TMBs with unique properties.