Polymorphism and superconductivity in the V-Nb-Mo-Al-Ga high-entropy alloys

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  • ReceivedNov 21, 2019
  • AcceptedDec 19, 2019
  • PublishedJan 10, 2020


Funded by

the National Key Research Development Program of China(2017YFA0303002)


This work was financially supported by the National Key Research & Development Program of China (2017YFA0303002).

Interest statement

The authors declare no conflict of interest.

Contributions statement

Wu J conceived the idea, synthesized the samples and did the physical property measurements with the assistance from Liu B, Cui Y, Zhu Q, Xiao G. Wang H helped in the EDX analyses. Wu S and Cao G contributed to the magnetic susceptibility measurements. Ren Z supervised the project and wrote the paper.

Author information

Jifeng Wu is currently a PhD student in the Department of Physics at Fudan University. He received his bachelor degree from Liaoning Shihua University in 2013, and then received his master degree from Xiamen University in 2016. He worked at GCL Nano for perovskite solar cells, China, from 2016 to 2017. His research interests include the syntheses and characterizations of novel superconductors and supercapacitor materials.

Zhi Ren is currently a research fellow in the School of Science at Westlake University since 2017. He received his bachelor and doctoral degrees from Zhejiang University in 2004 and 2009, respectively. He was a specially appointed researcher in Osaka University from 2009 to 2012 and a postdoctoral assistant in the University of Geneva from 2013 to 2017. His research interests include superconductivity and topological quantum state of materials.


Supplementary information

Chemical composition of the HEAs, analysis of the specific heat data for x = 0.2, and resistivity under various field for x ≥ 0.4 are available in the online version of the paper.


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  • Figure 1

    (a, b) Powder XRD patterns at room temperature for the as-cast and annealed (V0.5Nb0.5)3xMoxAl0.5Ga0.5 HEAs. The major diffraction peaks for the as-cast HEAs with x ≤ 0.4 are indexed to the bcc structure. While for x ≥ 0.6, the major peaks are indexed to the A15 structure. For annealed HEAs, the major peaks are indexed to the A15 structure, and the small impurity peaks for x ≤ 0.6 are marked by the asterisks. The inset between (a) and (b) shows the lattice parameter of the A15 phase for the as-cast and annealed HEAs plotted as a function of the Mo content x.

  • Figure 2

    (a, b) The structural refinement profiles for the as-cast and annealed (V0.5Nb0.5)3−xMoxAl0.5Ga0.5 HEAs with x = 0.2. The small impurity peak in (b) is marked by asterisks. (c, d) Electron diffraction patterns for the bcc and A15 polymorphs, respectively. (e) Temperature dependence of resistivity for the two different polymorphs. The inset shows the corresponding low-temperature specific heat data plotted as Cp/T versus T2.

  • Figure 3

    (a–c) Temperature dependence of resistivity, magnetic susceptibility and specific heat below 12 K for the series of A15-type (V0.5Nb0.5)3−xMoxAl0.5Ga0.5 HEAs. The left-handed arrow indicates the direction of increasing x, and the vertical dashed line is a guide to the eyes. In panel (a), the horizontal line denotes the midpoint of the resistive transition. In panel (c), the red solid lines are the fits by the Debye model to the normal-state data. (d) Temperature dependence of resistivity for x = 0.2 under magnetic fields up to 9 T in increments of 1 T. The dashed line marks the midpoint of the resistive transition. (e) Temperature dependence of the upper critical fields determined for the series of HEAs. The solid lines are fitted from the WHH model to the data. (f) Tc/ΘD plotted as a function of γ. The solid line is a guide to the eyes, and the arrow marks the γ value for the bcc polymorph with x = 0.2. (g) Logarithm of Tc plotted as a function of −1/λep for the HEAs, together with the data of Nb3Sn. The solid lines are a guide to the eyes. (h) Mo content x dependence of Bc2(0)/Tc. The dashed and dashed-dotted lines denote the values for the Pauli limiting field BP(0)/Tc = 1.86 T/K and Nb3Sn, respectively.

  • Figure 4

    Dependence of Tc on the average number of valence electrons per atom ratio for A15-type (V0.5Nb0.5)3−xMoxAl0.5Ga0.5 HEAs. The data for binary A15 [41] and other structurally different HEA [1720] superconductors are also included for comparison. The solid lines are a guide to the eyes, and the two Tc maxima for binary A15 compounds are marked by the arrows.

  • Table 1   Refined crystallographic data of the as-cast and annealed (VNb)MoAlGa HEAs with = 0.2



    Structural type



    Space group



    Lattice parameter

    3.163 Å

    5.014 Å

    Rwp factor



    Rp factor


























  • Table 2   Normal-state and superconducting parameters of A15-type (VNb)MoAlGa HEAs

    x = 0.2

    x = 0.4

    x = 0.6

    x = 0.8

    x = 1.0

    x = 1.2

    x = 1.4

    Tc (K)








    γ (mJ mol−1 K−2)
















    ΘD (K)
















    Bc2(0) (T)








    ξGL (nm)









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