Electronic structure, mechanical and dynamical stability of hexagonal subcarbides M$_{2}$C (M = Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt): ab initio calculations

Ab initio calculations were used to study the properties of a series of hexagonal (Fe$_2$N-like) subcarbides M$_2$C, where M = Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt, and to calculate their equilibrium structural parameters, electronic properties, phase stability, elastic constants, compression modulus, shear modulus, Young's modulus, compressibility, Pugh's indicator, Poisson ratio, elastic anisotropy indices, and also hardness, Debye temperature, sound velocity, and low-temperature heat capacity. It is found based on these results that all the subcarbides are mechanically stable; however, their formation energies $E_{\operatorname{form}}$ are positive with respect to a mixture of $d$-metal and graphite. In addition, the calculation of the phonon spectra of these subcarbides shows the existence of negative modes, which indicates their dynamical instability. Thus, a successful synthesis of these subcarbides at normal conditions is highly improbable.