Superconductivity and hardness of the equiatomic high-entropy alloy HfMoNbTiZr

Abstract

We have found that body-centered cubic (bcc) HfMoNbTiZr is a type-II BCS high-entropy alloy (HEA) superconductor with a superconducting critical temperature of $T_{\mathrm{c}}$=4.1 K. By employing a Debye temperature ${\theta }_{\mathrm{D}}$ of 263 K and $T_{\mathrm{c}}$, the electron-phonon coupling constant ${\lambda }_{\mathrm{e}-\mathrm{p}}$ is calculated to be 0.63. The electronic structure calculation revealed band broadening with energy uncertainties due to atomic disorders. The superconducting properties are compared among equiatomic quinary bcc HEA superconductors. $T_{\mathrm{c}}$ decreases with decreasing ${\lambda }_{\mathrm{e}-\mathrm{p}}$, which is negatively correlated with ${\theta }_D$. The negative correlation between ${\lambda }_{\mathrm{e}-\mathrm{p}}$ and ${\theta }_D$ would be caused by a shorter phonon lifetime at a higher ${\theta }_D$, which is based on phonon broadening due to atomic disorder and the uncertainty principle. The Vickers microhardness was measured for several bcc HEA superconductors. $T_{\mathrm{c}}$ is exceptionally low in a superconductor with relatively high hardness, because the hardness generally increases with increasing ${\theta }_{\mathrm{D}}$, and ${\theta }_{\mathrm{D}}$ is negatively correlated with $T_{\mathrm{c}}$ in the high-entropy state.

To appear in Journal of Alloys and Compounds