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 Å, b = 3.0627 Å and c = 9.8026 Å. The calculated lattice parameters of the Immm TiB₄ are a = 5.0374 Å, b = 5.6542 Å and c = 3.0069 Å. 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.