Structural stability and mechanical properties of TiB₆: A CALYPSO-guided exploration for superhard applications

Titanium–boron (Ti–B) compounds exhibit great promise as superhard materials due to titanium’s low atomic mass and abundant valence electrons. In this work, we systematically investigated the crystal structures of TiB₆ under pressures ranging from 0–100 GPa using the CALYPSO algorithm combined with first-principles calculations. Phonon dispersion analysis and elastic-constant evaluations confirm the dynamic and mechanical stability of five predicted TiB₆ structures. Notably, the α-Amm2-TiB₆ structure was predicted to have a remarkable Vickers hardness of 56 GPa, as estimated by Chen’s empirical model. All five structures are thermodynamically stable under ambient conditions, suggesting viable synthetic pathways. Their outstanding bulk moduli and ultrahigh hardness further classify them as potential incompressible and superhard materials. These theoretical insights lay a robust foundation for future experimental synthesis efforts.