First-principles study on the structure, hardness and electronic structure of TMB1.1 (TM = Rh, Ir and Ru) compounds

•The RhB1.1 phase is more stable than the IrB1.1 phase.•The calculated intrinsic hardness of RhB1.1 is about of 49.9 GPa.•The intrinsic hardness of RuB1.1 with tetragonal phase is about of 53.9 GPa.•The lower hardness of IrB1.1 is determined by the two sub-boundary B layers.

The structural information, hardness and electronic structure of TMB1.1 compounds are studied using first-principles approach. The calculated lattice parameters of RhB1.1 are in excellent agreement with experimental data, and the hexagonal structure of TMB1.1 compound is more stable than that of tetragonal structure. We found that the intrinsic hardness of RhB1.1 is 49.9 GPa, which is consistent with experimental result in contrast to the intrinsic hardness of IrB1.1 is only about of 29.8 GPa. The higher hardness of RhB1.1 is derived from the network Rh–B bonds with bonds synergistic effect. However, the lower hardness of IrB1.1 is originated from the two sub-boundary B layers. The staggered B layers separate three types of bonds: Ir–B bonds, B–B (I) covalent bonds and B–B (II) covalent bonds and weaken the bond strength.

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