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

Abstract

We have characterized the superconducting critical temperature ($T_\mathrm{c}$), the Debye temperature ($θ_\mathrm{D}$), 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 ($λ_\mathrm{e-p}$) and $θ_\mathrm{D}$ to a reduced phonon lifetime at higher $θ_\mathrm{D}$, 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 $λ_\mathrm{e-p}$ and $θ_{D}$. 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 $θ_{D}$ and may serve as a rapid screening metric for identifying bcc alloys with desired properties.

Figures (7)

• Figure 1: XRD patterns of HfNbTiVZr, NbTiZr, HfNbTi, HfNbZr, and HfNbTa. The origin of each XRD pattern is vertically offset for the clarity.
• Figure 2: SEM images and corresponding elemental mappings of (a) HfNbTiVZr, (b) NbTiZr, (c) HfNbTi, (d) HfNbZr, and (e) HfNbTa.
• Figure 3: (a) Temperature-dependent magnetization of HfNbTiVZr, NbTiZr, HfNbTi, HfNbZr, and HfNbTa measured under zero-field-cooled (ZFC) and field-cooled (FC) conditions. $M$ is normalized by the absolute value of the ZFC magnetization at 2.0 K. (b) Temperature-dependent electrical resistivity of HfNbTiVZr, NbTiZr, HfNbTi, HfNbZr, and HfNbTa, with the inset displaying the low-temperature region. (c) $C_\mathrm{p}/T$ versus $T^{2}$ plots of HfNbTiVZr, NbTiZr, HfNbTi, HfNbZr, and HfNbTa. The dashed lines represent the fitting results using the relation $C_\mathrm{p}/T=\gamma +\beta T^{2}$. The($\gamma$ (mJ/mol$\cdot$K$^{2}$), $\beta$(mJ/mol$\cdot$K$^{4}$)) datasets are (6.24, 0.2115) for HfNbTiVZr, (8.12, 0.2134) for NbTiZr, (5.74, 0.2828) for HfNbTi, (5.28, 0.3640) for HfNbZr, and (3.18, 0.2877) for HfNbTa, respectively.
• Figure 4: $\lambda_\mathrm{e-p}$ versus $\theta_{D}$ plot for equimolar quinary and ternary alloys.
• Figure 5: $\lambda_\mathrm{e-p}$ versus $\theta_{D}$ plot for (a) senary and quinary bcc alloys, (b) quaternary bcc alloys, (c) ternary bcc alloys, (d) binary bcc alloys, and (e) all bcc alloys.