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 ($\lambda_\mathrm{e-p}$) 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 $\lambda_\mathrm{e-p}$ 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.