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

Molybdenum borides were studied theoretically using first-principles calculations, empirical total energy 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 $MoB_x$ phases with 3<x<9 as the hexagonal $P6_3/mmc$-$MoB_3$ structure with Mo atoms partially replaced by triangular boron units. The most energetically stable arrangement of these $B_3$ units corresponds to their uniform distribution in the bulk of the crystal structure, which leads to the formation of a disordered nonstoichiometric phase, with ordering arising at compositions close to x=5 due to a strong repulsive interaction between neighboring $B_3$ units. The most energetically favorable structures of $MoB_x$ correspond to the compositions 4<x<5, with $MoB_5$ being the boron-richest stable phase. The estimated hardness of $MoB_5$ is 37-39 GPa, suggesting that the boron-rich phases are potentially superhard.