Structure, Stability, and Mechanical Properties of Boron-Rich Mo-B Phases: A Computational Study

Molybdenum borides were studied theoretically using first-principles calculations, parameterized lattice model, and global optimization techniques to determine stable crystal structures. Our calculations reveal the structures of known Mo-B phases, attaining close agreement with experiment. Following our developed lattice model, we describe in detail the crystal structure of boron-rich MoB phases with 3 ≤ x ≤ 9 as the hexagonal P6₃/mmc-MoB₃ structure with Mo atoms partially replaced by triangular boron units. The most energetically stable arrangement of these B₃ units corresponds to their uniform distribution in the bulk, which leads to the formation of a disordered nonstoichiometric phase, with ordering arising at compositions close to x = 5 because of a strong repulsive interaction between neighboring B₃ units. The most energetically favorable structures of MoB correspond to the compositions 4 ≲ x ≤ 5, with MoB₅ being the boron-richest stable phase. The estimated hardness of MoB₅ is 37-39 GPa, suggesting that the boron-rich phases are potentially superhard.