Optimizing hardness and toughness in high-entropy refractory ceramics via tuning the valence electron concentration

Bottom-up design of high entropy ceramics is a promising approach for realizing materials with unique combinations of outstanding properties. A downside of this approach is that the vast compositional space complicates the identification of candidate systems with desired properties. For example, refractory ceramics are materials of crucial importance for applications at elevated temperature and pressure. However, their characteristic brittleness considerably narrows potential uses. Here, we offer a simple yet fundamental criterion -- valence electron concentration (VEC) > ~9.5 e-/f.u., to populate bonding metallic d-d states at the Fermi level -- for selecting elemental compositions that can form rock-salt structured (B1) high-entropy refractory ceramics with both high hardness and inherent resistance to fracture (enhanced toughness). As a proof of concept, we synthesize and mechanically-test single-phase B1 (HfTaTiWZr)C and (MoNbTaVW)C, chosen as representative high-entropy carbide (HEC) systems due to their specific VEC values. Nanoindentation arrays at various loads and depths statistically demonstrate that (HfTaTiWZr)C (VEC=8.6 e-/f.u.) is very hard but brittle, whilst (MoNbTaVW)C (VEC=9.4e-/f.u.) is hard and considerably more resistant to fracture than (HfTaTiWZr)C. Extensive ab initio molecular dynamics (AIMD) simulations of tensile and shearing deformation at room temperature reveal that local lattice transformations, activated in (MoNbTaVW)C by loading beyond its yield point, allow dissipating accumulated stresses, thus explaining its superior toughness. Additional AIMD simulations, carried out to follow the evolution in mechanical properties as a function of temperature, show that (MoNbTaVW)C may retain outstanding toughness up to ~900-1200K, whereas (HfTaTiWZr)C is predicted to maintain high hardness, but intrinsic brittleness at all investigated temperatures.