Design of superhard high-entropy diborides via high-throughput DFT and thermodynamics calculations

We performed extensive high-throughput density functional theory (DFT) and thermodynamics calculations that led to the prediction of single-phase stability, mechanical properties, and melting points of a series of superhard high-entropy diborides (HEBs). We constructed a three-dimensional phase diagram using a unique combination of the mixing entropy, mixing enthalpy, melting point, and lattice size difference for the set of 56 equiatomic quinary diborides consisting of transition metals (TM = Ti, Zr, Hf, V, Nb, Ta, Mo, and W). The phase diagram allowed us to predict that all 56 quinary diborides are high-entropy materials, with fourteen already experimentally realized. Our calculations show that, for each of the quinary diborides, the driving force of the formation (the entropy term in the Gibbs free energy of mixing) suppresses the resistance of the formation (the enthalpy term) when the temperature is high (but still well below the melting point), suggesting that it is feasible to synthesize 42 new HEBs. Furthermore, all 56 quinary diborides exhibit high hardness, high fracture toughness, and ultrahigh melting points. In particular, we predict a new superhard high-entropy material, TiZrHfVTaB10, with a hardness of approximately 41 GPa.