The crystal structures, phase stabilities, electronic structures and bonding features of iridium borides from first-principles calculations

We present results of an unbiased structure search for the lowest energy crystalline structures of various stoichiometric iridium borides, using first-principles calculations combined with particle swarm optimization algorithms. As a result, besides three stable phases of C2/m-Ir(3)B(2), Fmm2-Ir(4)B(3), and Cm-Ir(4)B(5), three promising metastable phases, namely, P2(1)/m-Ir(2)B, P2(1)/m-IrB, and Pnma-Ir(3)B(4), whose energies are within 20 meV per atom above the convex hull curve, are also identified at ambient pressure. The high bulk modulus of 301 GPa, highest shear modulus of 148 GPa, and smallest Poisson's ratio of 0.29 for C2/m-Ir(3)B(2) make it a promising low compressible material. C2/m-Ir(3)B(2) is predicted to possess the highest Vickers hardnesses, with a Vickers hardness of 13.1 GPa and 19.4 GPa based on Chen's model and Mazhnik-Oganov's model respectively, and a high fracture toughness of 5.17 MPa m(0.5). The anisotropic indexes and the three-dimensional surface constructions of Young's modulus indicate that Ir–B compounds are anisotropic with the sequence of the elastic anisotropy of Ir(2)B > IrB > Ir(4)B(5) > Ir(3)B(4) > Ir(4)B(3) > Ir(3)B(2). Remarkably, these iridium borides are all ductile. We further find that the four Ir–B phases of P2(1)/m-Ir(2)B, C2/m-Ir(3)B(2), P2(1)/m-IrB, and Fmm2-Ir(4)B(3) possess dominant Ir–B covalent bonding character, while strong B–B and Ir–B covalent bonds are present in Cm-Ir(4)B(5) and Pnma-Ir(3)B(4), which are responsible for their excellent mechanical properties.