Theoretical prediction of the structure and hardness of TiB 4 tetraborides from first-principles calculations.

To search for a novel transition metal boride superhard material, the structural configuration, hardness and bonding state of the boron rich TiB 4 tetraborides are studied using the first-principles method. Similar to the TMB 4 tetraboride, four tetraborides, orthorhombic ( Immm ), orthorhombic ( Cmcm ), tetragonal ( P 4/ mbm ) and hexagonal ( P 63/ mmc ) phases, are predicted based on the phonon dispersion and thermodynamic model. The stable TiB 4 with orthorhombic ( Immm and Cmcm ) is first predicted. In particular, the theoretical hardness of Cmcm and Immm TiB 4 is 53.3 GPa and 35.6 GPa, respectively. We predict that orthorhombic ( Cmcm ) TiB 4 is a potential superhard material. Here, the calculated lattice parameters of the Cmcm TiB 4 are a = 5.2230 Å, b = 3.0627 Å and c = 9.8026 Å. The calculated lattice parameters of the Immm TiB 4 are a = 5.0374 Å, b = 5.6542 Å and c = 3.0069 Å. Naturally, the high hardness of Cmcm TiB 4 is related to the octagon B-B cage structure, which is composed of three different B-B covalent bonds. Although the B-B cage structure is formed in Immm TiB 4 , the hard discrepancy is that the bond strength of the B-B covalent bond in Immm TiB 4 is weaker than the bond strength of the B-B covalent bond in Cmcm TiB 4 . In addition, the Debye temperature of the Cmcm TiB 4 is higher than those of the other three TiB 4 tetraborides. The high-temperature thermodynamic properties of TiB 4 tetraboride are determined by the vibration in the B atom and B-B covalent bond. Therefore, our study indicates that a novel orthorhombic ( Cmcm ) TiB 4 superhard material is found.