Phase stability, mechanical properties and melting points of high-entropy quaternary metal carbides from first-principles

• Our first-principles calculations and thermodynamics formalism predict 15 quaternary high-entropy metal carbides (HEMCs) of group IVB and VB metals. • A three-dimensional phase diagram of the 15 HEMCs in terms of thermodynamic and structural parameters is obtained. • We find that all the 15 HEMCs exhibit the unusual property of both high hardness and high fracture toughness, as well as ultra-high melting points. • The methodology we have developed for this work may be generalized for predicting the single-phase stability of other potential high-entropy ceramics. With a combination of first-principles calculations and thermodynamics formalism of configurational mixing entropy, we have constructed three-dimensional phase diagram in terms of thermodynamic and structural parameters including the configurational mixing entropy and enthalpy, the temperature of the melting point, and the lattice constant difference of the constitute carbides for fifteen equiatomic quaternary high-entropy metal carbide (HEMC) ceramics of group IVB and VB refractory metals (RM = Ti, Zr, Hf, V, Nb, and Ta). We further predicted nine new HEMCs and provided an explanation for the existence of six experimentally realized quaternary HEMCs. In addition, our calculations of the melting points and mechanical properties show that the HEMCs have the unique properties of high hardness, high fracture toughness, and ultrahigh melting points. The computational procedure involved in this work may be used to design new high-entropy ceramics for specific applications.