Role of carbon vacancies in determining the structural, mechanical, and thermodynamic properties of (HfTaZrNb)C_1-x high entropy carbides: a first-principles study

High-entropy carbides (HECs), which exhibit a unique combination of properties that render them suitable for a variety of applications, have garnered significant interest. The role of vacancies in HECs, critical to their performance, remains insufficiently explored. This investigation delves into the stability, mechanical characteristics, electronic properties, and thermodynamic features of rock salt-structured (HfTaZrNb)C_1-x (x = 0.0, 0.125, 0.25, 0.375), employing density functional theory and the Debye–Grüneisen model. Our findings confirm the thermodynamic stability of (HfTaZrNb)C_1-x, as indicated by negative formation energies. Increasing vacancy content results in a decrease in lattice constants, modulus, hardness, and minimum thermal conductivity, alongside a reduction in elastic anisotropy and Debye temperature. Conversely, ductility is enhanced. Electronically, the research provides detailed insights into how vacancies influence bonding, elucidating the underlying reasons for variations in mechanical properties. This study deepens our understanding of vacancy impacts at the atomic level in HECs, providing vital data to inform future material design and application strategies.