Surface energies in high-entropy carbides with variable carbon stoichiometry

The carbon vacancy in high-entropy carbides (HECs) has a significant impact on their physical and chemical properties, yet relevant studies have still been relatively few. In this study, we investigate the surface energies of HECs with variable carbon vacancies through first-principles calculations. The results show that the surface energy of the (1 0 0) surface of the stoichiometric HECs is significantly lower than that of (1 1 1) surface. With the decrease in carbon stoichiometry, the surface energies of both (1 0 0) and (1 1 1) surfaces increase gradually, which is mainly due to the weakening of covalent bonding and the decrease of metal Hirshfeld-I (HI) charges. However, the surface energy of (1 0 0) surface increases more quickly than that of (1 1 1) surface and will exceed that of (1 1 1) surface when the carbon stoichiometry decreases to a certain extent, which is primarily attributed to the greater decrease rate of metal HI charges of (1 0 0) surface.