First principles study the stability and mechanical properties of MC (M = Ti, V, Zr, Nb, Hf and Ta) compounds

•The stability and elastic constants of carbides are studied by first principles.•The rules of modulus of MC compounds are discussed by their group.•The hardness of carbides is estimated in this paper at the first time.

The first principles calculations based on density functional theory (DFT) were adopted to investigate the stability, elastic constants, chemical bonding, Debye temperature and hardness of MC (M = Ti, V, Zr, Nb, Hf and Ta) compounds. The cohesive energy and formation enthalpy of these carbides indicate that they are thermodynamically stable structures. The population analysis was used to discuss the chemical bonding of these carbides. The elastic constants and moduli of these compounds were calculated. The results show that the bulk moduli of the carbides of transition metals from the fourth group (TiC, ZrC, HfC) are lower than the fifth group (VC, NbC, TaC). However, the Young’s moduli of the carbides from fourth group are higher than the fifth group. The hardness of compounds was estimated using a semi empirical hardness theory.