Phase stability and mechanical properties of ruthenium borides from first principles calculations

The phase stability and mechanical properties of ruthenium borides Ru7B3, RuB, Ru2B3, RuB2, RuB3 and RuB4 have been investigated systemically by first-principles calculations within density functional theory. The results show that ReB2–RuB2 (ReB2–RuB2 represents RuB2 in ReB2-type structure, the same hereinafter), TcP3–RuB3 and MoB4–RuB4 are more thermodynamically and mechanically stable than other structures at ambient conditions. The large bulk modulus, large shear modulus, large Young’s modulus, small Poisson’s ratio and large Debye temperature show that they should be ultra-incompressible hard material. Further analyses on density of states unravel the covalent bonding (B–B and Ru–B) as the force of the good mechanical properties. Combing enthalpy–pressure relationship with convex hull, it is interesting to note that the synthesized Ru7B3–Ru7B3, Ru2B3–Ru2B3 and hypothetical WB–RuB, ReB2–RuB2 should be the ground state phases at zero pressure, while around 60 GPa the predicted MoB4–RuB4 becomes a stable phase; Ru7B3–Ru7B3, WB–RuB, ReB2–RuB2 and MoB4–RuB4 are the most stable phases at about 100 GPa. High pressure is advantageous to synthesis of ruthenium borides.