Local lattice distortions and the structural instabilities in bcc Nb–Ta–Ti–Hf high-entropy alloys: An ab initio computational study

Local lattice distortions (LLD) and structural stability of body-centered cubic (bcc) Nb-Ta-Ti-Hf high-entropy alloys (HEAs) are studied as functions of composition employing ab initio density-functional theory calculations, with specific focus on the role of the relative concentrations of group IV (Ti and Hf) versus group V (Nb and Ta) elements. Calculated results are presented as a function of composition x in NbxTa0.25Ti(0.75−x)/2Hf(0.75−x)/2 alloys, for elastic moduli, phonon spectral functions, LLD and structural energy differences for the bcc and competing hexagonal close-packed (hcp) and ω phases. The results highlight the important role of group V elements and LLD in stabilizing the bcc structure. They further reveal how composition x can be tuned to alter both the magnitude of the LLD and structural energy differences. Specifically, the magnitude of the structural energy differences, and elastic and dynamic stability of the bcc phase, are enhanced with increasing x, while the LLD increase in magnitude as this concentration is decreased. The results also show evidence of correlated LLD at lower values of x, reflecting local structural distortions toward the ω phase, but not hcp. The degree of ω-collapse is nevertheless partial, i.e., transformation towards this phase is not observed to be complete due to the presence of Ta and Nb. At lower values of x we further find an energy landscape characterized by multiple, nearly degenerate local energy minima for different values of the LLD.