Insight into high-entropy effect in body-centered cubic superconducting alloys

We have characterized the superconducting critical temperature ($T_{\mathrm{c}}$), the Debye temperature (${\theta }_{\mathrm{D}}$), the electronic specific heat coefficient, and the Vickers microhardness of HfNbTiVZr, NbTiZr, HfNbTi, HfNbZr, and HfNbTa, all possessing a body-centered cubic (bcc) structure. By compiling a comparable dataset for other equiatomic quinary bcc high-entropy alloy (HEA) superconductors, we have examined the validity of the hypothesis regarding the high-entropy effect in bcc HEA superconductors, as proposed in our previous work. This hypothesis attributes the observed negative correlation between the electron-phonon coupling constant (${\lambda }_{\mathrm{e}-\mathrm{p}}$) and ${\theta }_{\mathrm{D}}$ to a reduced phonon lifetime at higher ${\theta }_{\mathrm{D}}$, arising from the uncertainty principle in highly disordered quinary alloys. However, a pronounced change in this negative correlation is not evident in equiatomic ternary alloys with a lower degree of atomic disorder, thereby providing limited support for the hypothesis. Alternatively, by assembling the full dataset of bcc alloys spanning binary through senary systems, we have identified a universal negative correlation between ${\lambda }_{\mathrm{e}-\mathrm{p}}$ and ${\theta }_D$. This result would be useful for the materials design of bcc superconducting alloys. We further propose that the Vickers microhardness offers an alternative means to evaluate ${\theta }_D$ and may serve as a rapid screening metric for identifying bcc alloys with desired properties.