The structural stabilities, mechanical properties and hardness of chromium tetraboride: Compared with low-B borides

Using the first-principles calculations, we provide a systemic understanding of the structural features and phase stability, mechanical and electronic properties, as well as the roles of boron (B) atom arrangement in the hardness for chromium borides. The structural and relative energy searches together with formation enthalpy confirm the most stable Cr2B with an orthorhombic Fddd symmetry, CrB with an orthorhombic Cmcm symmetry, CrB2 with a hexagonal P6(3)/mmc symmetry and chromium tetraboride (CrB4) with an orthorhombic Pnnm symmetry. The shear modulus, Young's modulus and C-44 increase with the boron content, while the Poisson's ratio and B/G ratio have an opposite tendency. Moreover, due to higher B content, strong three-dimensional (3D) covalent B networks and lower metallic contribution, CrB4 with Pnnm symmetry has the largest hardness value (46.8 GPa), exceeding the superhard limit, indicating its superhard nature.