Emergent property of high hardness for C-rich ruthenium carbides: partial covalent Ru–Ru bonds

Hard materials are being investigated all the time by combining transition metals with light elements. Combining a structure search with first-principles functional calculations, we first discovered three stable stoichiometric C-rich ruthenium carbides in view of three synthesis routes, namely, the ambient phases of Ru2C3 and RuC, and two high pressure phases of RuC4. There is a phase transition of RuC4 from the Pm1 structure to the Rm structure above 98 GPa. The calculations of elastic constants and phonon dispersions show their mechanical and dynamical stability. The large elastic modulus, high Debye temperature and the estimated hardness values suggest that these hard ruthenium carbides have good mechanical properties. The analyses of electronic structure and chemical bonding indicate that chemical bonding, not carbon content, is the key factor for the hardness in these metallic C-rich ruthenium carbides. The partial covalent Ru–C bonds and strong covalent C–C bonds are responsible for the high hardness. Moreover, the emergence of partial covalent Ru–Ru bonds can enhance the hardness of RuC, while the ionic Ru–Ru bonds can weaken the hardness of Ru2C3.