Theoretical prediction of the structure and hardness of TiB4 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 TiB4 tetraborides are studied using the first-principles method. Similar to the TMB4 tetraboride, four tetraborides, orthorhombic (Immm), orthorhombic (Cmcm), tetragonal (P4/mbm) and hexagonal (P63/mmc) phases, are predicted based on the phonon dispersion and thermodynamic model. The stable TiB4 with orthorhombic (Immm and Cmcm) is first predicted. In particular, the theoretical hardness of Cmcm and Immm TiB4 is 53.3 GPa and 35.6 GPa, respectively. We predict that orthorhombic (Cmcm) TiB4 is a potential superhard material. Here, the calculated lattice parameters of the Cmcm TiB4 are a = 5.2230 A, b = 3.0627 A and c = 9.8026 A. The calculated lattice parameters of the Immm TiB4 are a = 5.0374 A, b = 5.6542 A and c = 3.0069 A. Naturally, the high hardness of Cmcm TiB4 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 TiB4, the hard discrepancy is that the bond strength of the B-B covalent bond in Immm TiB4 is weaker than the bond strength of the B-B covalent bond in Cmcm TiB4. In addition, the Debye temperature of the Cmcm TiB4 is higher than those of the other three TiB4 tetraborides. The high-temperature thermodynamic properties of TiB4 tetraboride are determined by the vibration in the B atom and B-B covalent bond. Therefore, our study indicates that a novel orthorhombic (Cmcm) TiB4 superhard material is found.