Local orders, lattice distortions, and electronic structure dominated mechanical properties of (ZrHfTaM1M2)C (M = Nb, Ti, V)

High-entropy carbides (HECs) are regarded as potential candidate structural materials with attractive mechanical properties due to their ultra-high hardness. It is essential to reveal the atomic and electronic basis for strengthening mechanism in order to develop the advanced HECs. In the present work, ((Zr0.2Hf0.2Ta0.2M0.2M0.22)-M-1)C (M = Nb, Ti, V) are selected as case studies. The effects of transition metals (M) on the lattice parameters, bulk modulus, enthalpy of formation, electron work function (EWF), and bonding morphology/strength of HECs are comprehensively studied by first-principles calculations. It is found that the lattice parameters, equilibrium volumes, and bulk modulus of HECs are improved with the increase of M atomic volumes. The atomic-size differences among various groups of elements not only result in the lattice mismatch/distortion but also contribute to the formation of weak spots. In the view of bonding charge density, the electron redistributions caused by the coupling effect of the lattice distortion and valance electron differences can be revealed obviously, which identify the different bonding strength. Moreover, in terms of EWF, the proposed power-law-scaled hardness of HECs is validated and matches well with those reported theoretical and experimental results, providing a strategy to design advanced HECs with excellent mechanical properties.