Correlation between mechanical properties and valence electron concentration for NbTiZrM (M = Hf, Ta, W) refractory high entropy alloys: an ab initio study

On basis of systematical ab initio study of mechanical properties of body-centered cubic NbTiZrM (M = Hf, Ta, W) refractory high entropy alloys, the correlation between mechanical properties and valence electron concentration (VEC) is appreciably revealed. The present investigation demonstrates that both the single-crystal elastic parameters and the elastic moduli of NbTiZrM alloys increase for M from Hf to W, similar to the variation trend of VEC. Hence, the strength and hardness of NbTiZrM alloys exhibit apparent correlation with the VEC. Because the Poisson's ratio and the Pugh’s ratio suggest the alloys are more ductile for M from W to Hf, the lower VEC obviously correlates with the better ductility of NbTiZrM alloys. Moreover, with increasing VEC, the elastic anisotropies of NbTiZrM alloys are predicted to decrease, whereas the Debye temperatures of these alloys show increasing tendency. Noticeably, the VEC is an effective adjusting parameter to obtain excellent mechanical properties.