Structural evolution and superconductivity tuned by valence electron concentration in the Nb-Mo-Re-Ru-Rh high-entropy alloys

doi:10.1016/j.jmst.2021.02.002

Abstract

Abstract:

The crystal structure and physical properties of Nb₂₅Mo₅₊_xRe₃₅Ru₂₅_-xRh₁₀ (0 ≤ x ≤ 10) and Nb₅Mo₃₅_-yRe₁₅₊_yRu₃₅Rh₁₀ (0 ≤ y ≤ 15) high-entropy alloys (HEAs) have been studied by X-ray diffraction, electrical resistivity, magnetic susceptibility, and specific heat measurements. The results show that the former HEAs with valence electron concentration (VEC) values of 6.7-6.9 crystallize in a noncentrosymmetric cubic α-Mn structure, while the latter ones with VEC values of 7.1-7.25 adopt a centrosymmetric hexagonal close-packed (hcp) structure. Despite different structures, both series of HEAs are found to be bulk superconductors with a full energy gap, and the superconducting transition temperature T_c tends to decrease with the increase of VEC. Nevertheless, the T_c values of the hcp-type HEAs are higher than those of the α-Mn-type ones, likely due to a stronger electron phonon coupling. Furthermore, we show that VEC and electronegativity difference are two key parameters to control the stability of α-Mn and hcp-type HEAs. These results not only are helpful for the design of such HEAs, but also represent the first realization of structurally different HEA superconductors without changing the constituent elements.

Key words: High-entropy alloys, Hcp to α-Mn structural evolution, Superconducting properties, Valence electron concentration, Electronegativity difference

Bin Liu, Jifeng Wu, Yanwei Cui, Qinqing Zhu, Guorui Xiao, Siqi Wu, Guang-han Cao, Zhi Ren. Structural evolution and superconductivity tuned by valence electron concentration in the Nb-Mo-Re-Ru-Rh high-entropy alloys[J]. J. Mater. Sci. Technol., 2021, 85: 11-17.

Figures/Tables 10

Fig. 1. (a) XRD patterns for the Nb-Mo-Re-Ru-Rh HEAs with increasing VEC from 6.7 to 7.25 (from topto bottom). The upper three and lower four patterns correspond to Nb25Mo5+xRe35Ru25-xRh10 (0 ≤ x ≤ 10) HEAs with a cubic α-Mn structure and Nb5Mo35-yRe15+yRu35Rh10(0 ≤ x ≤ 15) HEAs with an hcp structure, respectively. Small impurity peaks are marked by the asterisks. In between these data sets, the pattern for with VEC = 7.05 shows coexistence of the α-Mn and hcp phases. (b, c) Structure-refinement profiles for the cubic Nb25Mo5+xRe35Ru25-xRh10 with x = 10 andthe hexagonal Nb5Mo35-yRe15+yRu35Rh10HEA with y = 15, respectively. (d, e) Compositional dependence of the lattice parameters for the series of Nb25Mo5+xRe35Ru25-xRh10 and Nb5Mo35-yRe15+yRu35Rh10 HEAs, respectively. Note that, in the latter case, the c-axis values are divided by a factor of 1.6.

Table 1 Representative structure-refinement results of the α-Mn-type Nb25Mo5+xRe35Ru25-xRh10 and hcp-type Nb5Mo35-yRe15+yRu35Rh10 HEAs.

	Nb₂₅Mo₅₊_xRe₃₅Ru₂₅_-xRh₁₀Nb₅Mo₃₅_-y Re₁₅₊_yRu₃₅Rh₁₀
Parameter	x = 0	x = 5	x = 10	y = 0	y = 5	y = 10	y = 15
Nb (at.%)	25.5	23.9	26.4	5.8	5.5	6.2	5.6
Mo (at.%)	5.6	10.0	14.6	34.6	30.1	25.1	20.9
Re (at.%)	36.6	33.8	32.9	13.9	18.7	20.2	29.4
Ru (at.%)	25.4	22.1	16.6	38.0	38.3	37.4	34.4
Rh (at.%)	7.2	10.2	9.5	7.7	7.4	11.0	9.7
VEC	6.9	6.8	6.7	7.1	7.15	7.2	7.25
T_c (K)	4.66	5.10	5.10	7.54	6.69	6.51	5.46
γ (mJ molatom^-¹ K^-²)	3.36	3.63	3.46	3.70	3.93	4.15	3.32
Θ_D (K)	327	309	359	338	467	393	378
λep	0.61	0.64	0.61	0.70	0.62	0.64	0.61
Bc2(0) (T)	7.5	8.3	7.9	8.9	7.5	7.5	6.1
ξGL (nm)	6.6	6.3	6.4	6.1	6.6	6.6	7.3

Fig. 2. (a) SEM image of the α-Mn-type Nb25Mo5+xRe35Ru25-xRh10 HEA with x = 10. (b) EDX elemental mapping of the Nb, Mo, Re, Ru, Rh elements for the HEA. (c) TEM image of the HEA. The two insets show the zoom of the lattice fringes and electron diffraction pattern, respectively. The yellow lines are a guide to the eyes. The same set of data for the hcp-type Nb5Mo35-yRe15+yRu35Rh10 HEA with y = 10 are shown in (d-f).

Table 2 Chemical composition and physical parameters of the α-Mn- and hcp-type Nb-Mo-Re-Ru-Rh HEAs.

		x = 10			y = 15
Structural type		α-Mn			hcp
Space group		Ī43m			P63/mmc
Lattice parameter		a = 9.659 Å			a=2.757Å,c=4.427Å
Unit-cell volume		901.4Å³			29.2Å³
R_wp factor		8.7%			9.3%
R_p factor		6.4%			6.6%
Atoms	x	y	z	Occ.	x y z	Occ.
Nb1/Mo1/Re1/Ru1/Rh1	0	0	0	0.25/0.15/0.35/0.15/0.1	0 0 0	0.05/0.2/0.3/0.35/0.1
Nb2/Mo2/Re2/Ru2/Rh2	0.316	0.316	0.316	0.25/0.15/0.35/0.15/0.1	2/3 1/3 1/2	0.05/0.2/0.3/0.35/0.1
Nb3/Mo3/Re3/Ru3/Rh3	0.356	0.356	0.034	0.25/0.15/0.35/0.15/0.1
Nb4/Mo4/Re4/Ru4/Rh4	0.089	0.089	0.282	0.25/0.15/0.35/0.15/0.1

Fig. 3. (a, b) Temperature dependence of resistivity and magnetic susceptibility for the series of α-Mn-type Nb25Mo5+xRe35Ru25-xRh10 HEAs, respectively. (c, d) Temperature dependence of resistivity and magnetic susceptibility for the series of hcp-type Nb5Mo35-yRe15+yRu35Rh10 HEAs, respectively. (e, f) Low temperature specific heat data plotted as Cp/T versus T2 for the two series of HEAs, respectively. The red lines are best fits to the normal-state data by the Debye model.

Fig. 4. (a-c) Temperature dependence of normalized electronic specific data for the series of α-Mn-type Nb25Mo5+xRe35Ru25-xRh10 HEAs. (d-g) The normalized electronic specific data for the series of hcp-type Nb5Mo35-yRe15+yRu35Rh10 HEAs. In each panel, the red line is a theoretical curve calculated from a modified BCS model.

Fig. 5. (a, b) Temperature dependence of resistivity under various fields for the α-Mn-type Nb25Mo5+xRe35Ru25-xRh10 HEA with x = 10 and hcp-type Nb5Mo35-yRe15+yRu35Rh10 HEA with y = 0, respectively. The field increment is 1 T and the two dashed lines are a guide to the eyes. (c, d) Upper critical field versus temperature phase diagram for the two series of HEAs.The solid lines are WHH fits to the data.

Fig. 6. (a-f) Compositional dependence of Tc, γ,and λep for the α-Mn- and hcp-type Nb-Mo-Re-Ru-Rh HEAs, respectively. (g) VEC dependence of Tc for known cubic α-Mn type and hexagonal HEA superconductors. The data for crystalline 4d metals and Tc-based hcp-type binary alloys are also included for comparison.

Table 3 Physicochemical properties of the elements Nb,Mo, Re, Ru, and Rh. The data are taken from Refs. [31,41].

Element	Atomic radius (Å)	Pauling electronegativity
Nb	1.457	1.60
Mo	1.396	2.16
Re	1.38	1.90
Ru	1.35	2.20
Rh	1.344	2.28

Fig. 7. (a, b) Dependence of electronegative difference Δχ and VEC on the atomic size difference δ, respectively, for all superconducting HEAs with the α-Mn and hcp structures. The dashed lines are a guide to the eyes.

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