On the Superconductivity in High-Entropy Alloy (NbTa)_{1-X}(HfZrTi)_{X} ()

Snehadri B. Ota^{}

Government of India, New Delhi, India.

**DOI: **10.4236/jmp.2023.144025
PDF
HTML XML
115
Downloads
535
Views
Citations

Government of India, New Delhi, India.

The superconductivity in (NbTa)_{1-X}(HfZrTi)_{X} high-entropy alloy is analyzed using the theory of strong-coupled superconductor. It is concluded that (NbTa)_{1-X}(HfZrTi)_{X }is a strong coupled superconductor. The variation in the superconducting transition temperature from 7.9 K to 4.6 K as x increases from 0.2 to 0.84 arises because of the decrease in electronic band width due to localization and broadening of the band. It is suggested that the decrease in electronic band width is due to crystalline randomness which gives rise to the mobility edge.

Keywords

High-Entropy Alloys, Disordered Metals, Strong-Coupled Superconductivity, Localization, Cocktail Effect

Share and Cite:

Ota, S. (2023) On the Superconductivity in High-Entropy Alloy (NbTa)_{1-X}(HfZrTi)_{X}. *Journal of Modern Physics*, **14**, 445-449. doi: 10.4236/jmp.2023.144025.

1. Introduction

The high-entropy alloys (HEA) have attracted considerable attention in recent years [1] [2] . These alloys consist of several principal elements that are stabilized due to high configurational entropy. The atoms in HEA are randomly distributed on ordered lattice as has been inferred from the sharp X-ray diffraction peaks. Distortion of the lattice of the order of 1 percent has also been concluded from theoretical calculations [3] . These alloys show better mechanical properties and superparamagnetism. Recently, superconductivity has been observed in transition metal based HEA (Nb_{0.33}Ta_{0.34})_{1}_{−}_{X}(Hf_{0.08}Zr_{0.14}Ti_{0.11})_{X}, which has bcc lattice structure [4] [5] [6] [7] . (Hereafter, we replace (Nb_{0.33}Ta_{0.34})_{1}_{−}_{X}(Hf_{0.08}Zr_{0.14}Ti_{0.11})_{X} by (NbTa)_{1}_{−}_{X}(HfZrTi)_{X}, for simplicity.) The superconducting transition temperature (*T _{C}*) has been found to vary from 7.9 K to 4.6 K as the atomic fraction x increases from 0.2 to 0.84. The elements Nb, Ta, Hf, Zr and Ti have

2. Superconductivity in (NbTa)_{1}_{−X}(HfZrTi)_{X} HEA

The effect of disorder on superconductivity has been studied before, for example, the universal degradation of *T _{C}* in A15 compounds ( [10] and the references in [10] ). Here, the effect of disorder in (NbTa)

Approximate solutions of the Gor’kov-Eliashberg form of the theory of strong-coupled superconductors has been of interest for a long time [9] . First, the *T _{C}* of (NbTa)

${T}_{C}=1.14\cdot {\Theta}_{D}\cdot \mathrm{exp}\left(\frac{-1}{\text{N}\left(0\right)\text{V}}\right)$ (1)

Table 1. Measured and calculated values of *T _{C}*,

where, N(0)V is a dimensionless electron-phonon coupling constant. It is noted that in the weak-coupling limit the frequency dependence of the interaction is ignored. The calculated values of N(0)V using Equation (1) are given in Table 1, which are nearly 0.3. N(0)V is found to increase with x until x = 0.3 and then decreases with further increase in x. The decrease of N(0)V with increase of x can be attributed primarily due to the reduction of N(0).

The theory of strong-coupled superconductors includes frequency dependences of phonon-induced interaction and instantaneous Coulomb repulsion. In order to understand the influence of Coulomb interaction on the phonon induced interaction, the strong-coupling case is considered. In the strong-coupling case, *T _{C}* is obtained as a function of electron-phonon and electron-electron coupling constants, which is given by (aka McMillan equation) [15] :

${T}_{C}=\frac{{\Theta}_{D}}{1.45}\cdot \mathrm{exp}\left(\frac{-1.04\left(1+\lambda \right)}{\lambda -{\mu}^{*}\left(1+0.62\lambda \right)}\right)$ (2)

where *λ* is the electron-phonon coupling constant and *μ*^{*} is the Coulomb pseudopotential. The Coulomb pseudopotential is given by [14] :

${\mu}^{*}=\frac{\mu}{1+\mu \mathrm{ln}\frac{{E}_{B}}{{\omega}_{0}}}$ (3)

where *E _{B}* and

Figure-1. *E _{B}* as a function of (e/a) in superconducting (Nb

3. Discussion and Conclusions

It is seen that *E _{B}* is of the order of μeV, which is considerably smaller than

In conclusion, the experimental results on superconductivity in (NbTa)_{1}_{−}_{X}(HfZrTi)_{X} have been analyzed using the Gor’kov-Eliashberg form of the theory for strong-coupled superconductors. The variation in the superconducting transition temperature from 7.9 K to 4.6 K as x increases from 0.2 to 0.84 is explained in terms of decrease in electronic band width due to localization and broadening of the band. The formation of the mobility edge is found to reduce the effective band width in these alloys. The cocktail effect in this HEA is explained in terms of the enhancement of *T _{C}*, when

Acknowledgements

The author is benefited from his visit to Europe in 1988-92 for HTSC research; Xiamen, China, during 1995 for STATPHYS19 conference and New Orleans and Dallas, USA during 2008 and 2011, respectively, for APS March meeting. The author thanks the referee for several helpful suggestions. The author thanks Joseph for constant encouragement.

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.

[1] |
Ye, Y.F., et al. (2016) Materials Today, 19, 349. https://doi.org/10.1016/j.mattod.2015.11.026 |

[2] |
Chen, S., Tong, Y. and Liaw, P.K. (2018) Entropy, 20, 937. https://doi.org/10.3390/e20120937 |

[3] | Song, H., et al. (2017) Physical Review Materials, 1, 23404. |

[4] |
Koželj, P., et al. (2014) Physical Review Letters, 113, Article ID: 107001. https://doi.org/10.1103/PhysRevLett.113.107001 |

[5] | von Rohr, F., et al. (2016) Proceedings of the National Academy of Sciences of the United States of America, 113, E7144-E7150. |

[6] |
Wu, K.Y., Chen, S.K. and Wu, J.M. (2018) Natural Science, 10, 110-124. https://doi.org/10.4236/ns.2018.103012 |

[7] |
Ishizu, N. and Kitagawa, J. (2019) Results in Physics, 13, Article ID: 102275. https://doi.org/10.1016/j.rinp.2019.102275 |

[8] | Kittel, C. (1976) Introduction to Solid State Physics. 5th Edition, Wiley Eastern Limited, New Delhi. |

[9] | Lynn, J.W. (1991) High Temperature Superconductivity. World Publishing Corporation, Beijing, Ch. 9, 303. |

[10] |
Ota, S.B. (1987) Physical Review B, 35, 8730. https://doi.org/10.1103/PhysRevB.35.8730 |

[11] |
Thouless, D.J. (1974) Physics Reports, 13, 93-142. https://doi.org/10.1016/0370-1573(74)90029-5 |

[12] |
Liu, Z.H. and Shang, J.X. (2011) Rare Metals, 30, 354-358. https://doi.org/10.1007/s12598-011-0302-9 |

[13] |
Skipetrov, S.E. and Sokolov, I.M. (2018) Physical Review B, 98, 64207. https://doi.org/10.1103/PhysRevB.98.064207 |

[14] |
Morel, P. and Anderson, P.W. (1962) Physical Review, 125, 1263. https://doi.org/10.1103/PhysRev.125.1263 |

[15] |
McMillan, W.L. (1968) Physical Review, 167, 331. https://doi.org/10.1103/PhysRev.167.331 |

[16] |
Sundqvist, B. (2022) Journal of Physics and Chemistry of Solids, 165, Article ID: 110686. https://doi.org/10.1016/j.jpcs.2022.110686 |

Journals Menu

Contact us

+1 323-425-8868 | |

customer@scirp.org | |

+86 18163351462(WhatsApp) | |

1655362766 | |

Paper Publishing WeChat |

Copyright © 2024 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.