Computational Analysis of Stable Hard Structures in the Ti-B System

The lowest energy crystalline structures of various stoichiometric titanium boride (Ti-B) intermetallic compounds are sought based on density functional theory combined with the particle-swarm optimization (PSO) technique. Besides three established experimental structures, i.e., FeB-type TiB, AlB₂-type, and Ta₃B₄-type Ti₃B₄, we predict additional six metastable phases at these stoichiometric ratios, namely, α- and β-phases for TiB, TiB₂, and Ti₃B₄, respectively. Moreover, we predict the most stable crystalline structures of four new titanium boride compounds with different stoichiometric ratios: Ti₂B-PS_A, Ti₂B₃-PS_B, TiB₃-PS_C, and TiB₄-PS_D. Notably, Ti₂B-PS_A is shown to have lower formation energy (thus higher stability) than the previously proposed Al₂Cu-type Ti₂B. The computed convex-hull and phonon dispersion relations confirm that all the newly predicted Ti-B intermetallic crystals are thermodynamically and dynamically stable. Remarkably, the predicted α-TiB₂ and β-TiB₂ show semi-metal-like electronic properties and possess high Vickers hardnesses (39.4 and 39.6 GPa), very close to the lower limit of superhard materials (40 GPa). Analyses of band structure, density of states, electronic localization function, and various elastic moduli provide further understanding of the electronic and mechanical properties of the intermetallic titanium borides. We hope the newly predicted hard intermetallic titanium borides coupled with desirable electronic properties and high elastic modulus will motivate future experimental synthesis for applications such as high-temperature structural materials.