On the influence of enthalpy of formation on lattice distortion and intrinsic ductility of concentrated refractory alloys

Abstract

Valence electron concentration (VEC), atomic size difference (δ), and Pugh’s ratio (B/G) are a few of the empirical parameters widely used to design ductile refractory alloys. Here, we used the intrinsic ductility parameter (D), which is the ratio of surface energy (γs) and unstable stacking fault energy (γusfe), to design ductile refractory alloy. We found that the D correctly captures the experimentally observed ductility in concentrated refractory alloys. Here, we studied the enthalpy of formation (ΔEf), lattice distortion, and D of 9 refractory metals and 36 equiatomic refractory alloys using density functional theory simulations. We found that the ΔEf strongly influences the D of concentrated refractory alloys. The positive ΔEf and δ lead to large lattice distortion in concentrated refractory alloys. However, we did not find a strong correlation between lattice distortion and D in the presently studied alloys. We found that the success of VEC and Pugh’s ratio in designing ductile refractory alloys has a strong dependence on the underlying ΔEf of the alloy. We have developed a bottom-up method, which drastically reduces the number of alloys to be studied, to design ductile concentrated refractory alloys that can be thermodynamically stable.