A systematic investigation on quaternary NbTiZr-based refractory high entropy alloys using empirical parameters and first principles calculations

Quaternary NbTiZr-based refractory high entropy alloys (RHEAs) have been studied in present work systematically based on empirical parameters and first principles calculations. Firstly, some simple rules based on the elemental properties are applied to screen out all possible elements in the quaternary NbTiZr-based RHEAs. Then, several commonly used empirical parameters, such as atomic size mismatch, average mixing enthalpy, the parameter Ω, are used to screen out the alloys which have a great potential of forming a single-phase solid solution from the remaining alloys. Finally, first principles method is employed to calculate the elastic properties for all screened NbTiZr-based RHEAs, and the mechanical performance of each alloy is evaluated accordingly. The results show that the quaternary NbTiZr-based RHEAs containing Al, Cr, Hf, Mo, Ta, V, W are the most likely to form a single-phase solid solution with bcc structure. Furthermore, the alloys containing W, Ta, and Mo will have high strength, while the alloys containing Al, Hf, and V will have good ductility. This work can provide guidance for the selection of the fourth element in the quaternary NbTiZr-based alloy.