Abstract
We report the crystal structure and superconducting properties of new V5+2xNb35−xMo35−xIr10Pt15 high-entropy alloys (HEAs) for x in the range of 0 x 10. These HEAs are found to crystallize in a cubic A15-type structure and have a weakly coupled, fully gapped superconducting state. A maximum Tc of 5.18 K and zero-temperature upper critical field (0) of 6.4 T are observed at x = 0, and both quantities decrease monotonically with the increase of V content x. In addition, Tc shows an increase with increasing valence electron concentration from 6.4 to 6.5, which is compared with other A15-type HEA and binary superconductors.
1 Introduction
High-entropy alloys (HEAs) consisting of five or more constituent elements have received a lot of attention as an emerging class of multicomponent alloys [1–5]. These alloys are stabilized by the high mixing entropy rather than the formation enthalpy, and often refereed to as metallic glasses on ordered lattices. Despite the presence of strong chemical disorder, some HEAs exhibit collective quantum phenomena such as superconductivity [6, 7]. So far, a number of HEA superconductors have been discovered and their crystal structures can be categorized into body-centered cubic (bcc)-type [8–11], a-Mn-type [12, 13], CsCl-type [14], hcp-type [15–17], A15-type [18], and s-type [19]. In particular, the A15-type HEA has a Tc of 10.2 K and a disorder-enhanced upper critical field of 20.1 T [18], both of which are the highest among HEA superconductors. It is worthy noting that, for binary A15-type superconductors, the Tc values exhibit two maxima at valence electron concentrations (VECs) of 4.7 and 6.5, respectively [20]. Since the VEC of the V–Nb–Mo–Al–Ga HEAs is limited below around 5, it is desirable to search for other A15-type HEA superconductors with VEC close to 6.5.
Motivated by this, we replace Al and Ga in the V–Nb–Mo–Al–Ga HEAs with Ir and Pt to form new V5+2xNb35−xMo35−xIr10Pt15 HEAs. A nearly single A15 phase is found for 0 x 10, which corresponds to a VEC range of 6.4–6.5. Physical property measurements indicate that these A15-type HEAs are weakly coupled, fully gapped superconductors with Tc and (0) up to 5.18 K and 6.4 T, respectively. In addition, their Tc increases with increasing VEC, in contrast to the V–Nb–Mo–Al–Ga HEAs. A comparison of the Tc vs. VEC plots is made between the A15-type HEA and binary superconductors, and its implication is discussed.
2 Materials and Methods
The V5+2xNb35−xMo35−xIr10Pt15 HEAs were prepared by the arc melting method. Stoichiometric amounts of high purity V (99.99%), Nb (99.999%), Mo (99.995%), Ir (99.99%), Pt (99.99%) elements were mixed thoroughly and pressed into pellets in an argon-filled glove box. The pellets were then melted in an arc furnace under high-purity argon atmosphere. To ensure homogeneity, the melts were flipped several times, followed by rapid cooling on a water-chilled copper plate. The phase purity of as-cast HEAs was checked by powder x-ray diffraction (XRD) at room temperature using a Bruker D8 Advance x-ray diffractometer with Cu-Kα radiation. The structural refinements were performed using the JANA2006 program [21]. The morphology and elemental composition were examined by a Zeiss field emission scanning electron microscope (SEM) equipped with an energy dispersive x-ray (EDX) spectrometer. The four-probe resistivity and specific heat were measured in a Quantum Design Physical Property Measurement System (PPMS-9 Dynacool). The dc magnetization measurements were carried out in a commercial SQUID magnetometer (MPMS3).
3 Results and Discussion
3.1 X-Ray Diffraction and Chemical Composition
The XRD patterns for the V5+2xNb35−xMo35−xIr10Pt15 HEAs are displayed in Figure 1A. For all x values, the major diffraction peaks can be well indexed on a cubic lattice with the n space group, indicative of a dominant A15 phase. With increasing x, the (004) peak shifts toward higher 2θ values. This points to a decrease of the a-axis with the increase of V content, in consistent with its smaller atomic radius compared with those of Nb and Mo [22]. In addition to the A15 phase, small impurity peaks are observed in the vicinity of main (102) diffraction and probably comes from the NbAl2-type sigma phase [18]. In the A15 structure, there are two crystallographic sites (0, 0, 0) and (0.25, 0, 0.5). Following Reference [18], all the five constituent elements are assumed to be distributed randomly on these sites for the structural refinement (see the inset of Figure 1A), and their occupancies are fixed by the stoichiometry. This assumption is based on the previous studies of binary A15 compounds, which show that the antisite disorder is the most common point defects [23]. In Nb3Sn, it has been argued that the Nb and Sn atoms occupy randomly the two sites after a certain period of mechanical milling [24]. The refinement profiles are shown in Figures 1B–D and the statistics are listed in Table 1. Both the difference plot and () factor indicate a reasonably good agreement between the observed and calculated XRD patterns, which supports the validity of the employed structural model. Note that a more definitive conclusion requires atomic-level spectroscopies in future. The refined lattice parameter a = 5.0324, 5.0130, and 4.9848 Å for x = 0, 5 and 10, respectively, close to those of the A15-type V-Nb-Mo-Al-Ga HEAs. Figures 2A–C show the typical SEM images for the HEAs, all of which appear to be dense and homogeneous. Indeed, EDX elemental mapping reveals the uniform distribution of V, Nb, Mo, Ir, and Pt, and, as an example, the results for x = 0 are shown in Figures 2D–H. Furthermore, the EDX measurements allow us to determine the chemical compositions to be V7.1Nb33.8Mo37.1Ir10.7Pt11.3, V17.0Nb28.9Mo29.2Ir11.2Pt13.7 and V26.3Nb25.4Mo26.0Ir10.5Pt11.8 for the HEAs with x = 0, 5, and 10, respectively. These agree well with the nominal compositions within the experimental error of ±2.5 at%.
FIGURE 1
TABLE 1
| Parameter | Unit | x = 0 | x = 5 | x = 10 |
| V Content | – | 7.1% | 17.0% | 26.3% |
| Nb content | – | 33.8% | 28.9% | 25.4% |
| Mo content | – | 37.1% | 29.2% | 26.0% |
| Ir content | – | 10.7% | 11.2% | 10.5% |
| Pt content | – | 11.3% | 13.7% | 11.8% |
| A | Å | 5.0324 | 5.0130 | 4.9848 |
| – | 11.8% | 11.2% | 10.9% | |
| – | 8.4% | 7.5% | 7.3% | |
| Tc | K | 5.18 | 4.49 | 3.61 |
| γ | 4.59 | 4.94 | 5.03 | |
| K | 419 | 440 | 393 | |
| – | 0.59 | 0.56 | 0.55 | |
| (0) | T | 6.4 | 5.7 | 4.4 |
| nm | 7.2 | 7.6 | 8.7 |
Structural and physical parameters of the V5+2xNb35−xMo35−xIr10Pt15 HEAs.
FIGURE 2
3.2 Resistivity and Magnetic Susceptibility
Figures 3A,B show the temperature dependencies of resistivity (ρ) and magnetic susceptibility (χ) for the V5+2xNb35−xMo35−xIr10Pt15 HEAs, respectively. For each x value, a sharp drop in ρ and strong diamagnetic χ are observed, signifying a superconducting transition. As indicated by the vertical dashed line, the midpoint of ρ drop coincides well with the onset of diamagnetic transition. By this criterion, Tc is determined to be 5.18, 4.49, and 3.61 K for the HEAs with x = 0, 5, and 10, respectively. Below Tc, there is a clear bifurcation between the zero-field cooling (ZFC) and field cooling (FC) χ data measured under an applied field of 1 mT, which is characteristic of a type-II superconductor. At 1.8 K, the data correspond to superconducting shielding fractions ranging from 101 to 174%. Although the demagnetization effect is difficult to correct due to irregular sample shapes, these large values suggest bulk superconductivity in these HEAs.
FIGURE 3
3.3 Specific Heat
To confirm the bulk nature of superconductivity, the V5+2xNb35−xMo35−xIr10Pt15 HEAs were further characterized by specific heat () measurements, whose results are shown in Figure 4. As can be seen in Figures 4A, a Cp jump is indeed detected around Tc for these HEAs. Above Tc, the data are analyzed by the Debye modelwhere γ and β(δ) are the Sommerfeld and phonon specific heat coefficients, respectively. With β, the Debye temperature is calculated aswhere R is the molar gas constant 8.314 J/molK2. This gives γ = 4.59, 4.94, and 5.03 mJ/molatomK2, and = 419, 440, and 393 K for x = 0, 5, and 10, respectively. Figure 4B shows the normalized electronic specific heat Cel/γT after subtraction of the phonon contribution. For all HEAs, the ΔCel/γT are significantly smaller than the BCS value of 1.43 [25]. Nevertheless, the Cel/γT data can still be fitted by a modified BCS model or the α-model [26] with α = 1.39, 1.41 and 1.56 for x = 0, 5 and 10, respectively, where α = Δ0/Tc and Δ0 is the gap size at 0 K. These results suggest that the V5+2xNb35−xMo35−xIr10Pt15 HEAs are BCS-like superconductors in the weak coupling regime. This is corroborated by their electron-phonon coupling constants in the range of 0.55–0.59, as calculated using the inverted McMillan formula [27],with = 0.13 being the Coulomb repulsion pseudopotential. In passing, it is pointed out that the decrease in Tc with increasing x is accompanied by the decrease in but the increase in γ. Hence the Tc in the V5+2xNb35−xMo35−xIr10Pt15 HEAs is mainly governed by the electron-phonon coupling strength rather than the density of states at the Fermi level. In passing, it is worth noting that the Tc, γ and values of the V–Nb–Mo–Pt–Ir HEAs are very similar to those of the ()3−x Mox HEAs for x 1.2 [18], pointing to a common phonon-mediated pairing mechanism.
FIGURE 4
3.4 Upper Critical Field
The upper critical fields of these HEAs were investigated by resistivity measurements under magnetic fields. As an example, the result for the HEA with x = 0 is shown in Figure 5A. The resistive transition is gradually suppressed to low temperatures as the field increases. For each field, the Tc is determined using the same criterion as above, and the obtained vs. T phase diagrams are displayed in Figure 5B. Extrapolating the (T) data to 0 K using the Wathamer-Helfand-Hohenberg model [28] yields (0) = 6.4, 5.7 and 4.4 T for the HEAs with x = 0, 5, and 10, respectively. These values are well below the corresponding Pauli limiting fields [29] of ∼9.6, ∼8.4, and ∼6.7 T, suggesting that in these HEAs is orbitally limited. In addition, the Ginzburg–Landau coherence lengths can be calculated using the equationwhere = 2.07 Wb is the flux quantum. This yields = 7.2, 7.6 and 8.7 nm for the HEAs with x = 0, 5, and 10, respectively. The above results are summarized in Table 1.
FIGURE 5
3.5 VEC Dependence of Tc
Figure 6 shows the VEC dependence of Tc for the V5+2xNb35−xMo35−xIr10Pt15 HEAs, together with the data for A15-type V-Nb-Mo-Al-Ga HEA [18] and binary [20] superconductors for comparison. One can see that superconductivity in all these materials occurs near the VEC values of 4.7 and 6.5, consistent with the expectation from the Matthias rule [30]. Compared with the V–Nb–Mo–Al–Ga HEAs, the V–Nb–Mo–Ir–Pt HEAs have higher VEC values in the range of 6.4–6.5 and their VEC dependence of Tc is in the opposite trend, increasing monotonically with the increase of VEC. Nevertheless, the maximum Tc is considerably lower for the V–Nb–Mo–Ir–Pt HEAs than for the V-Nb-Mo-Al-Ga ones. This indicates that optimal VEC for Tc in A15-type HEA superconductors is around 4.7, which is reminiscent of the case in binary A15 compounds [20]. Moreover, for similar VEC values, the Tc values for V–Nb–Mo–Al–Ga and V–Nb–Mo–Ir–Pt HEAs are always no more than half those of the binary compounds. It is thus reasonable to speculate that the upper limit of Tc for A15-type HEA superconductors is about one-half the highest Tc in binary A15 superconductors.
FIGURE 6
4 Conclusion
In summary, we have studied the structure, electronic, magnetic and thermodynamic properties of the V5+2xNb35−xMo35−xIr10Pt15 HEAs with 0 x 10. In this x range, the HEAs adopt a cubic A15-type structure and exhibit bulk superconductivity. The analysis of their specific-heat jumps points to a weakly coupled, fully gapped superconducting state. The Tc and (0) reach 5.18 K and 6.4 T, respectively, at x = 0, and decrease monotonically with the increase of V content x. In addition, Tc increases with increasing VEC from 6.4 to 6.5 and its comparison with isostructural HEA and binary superconductors suggests that the upper limit of Tc for A15-type HEA superconductors is about half that for binary compounds. Our study helps to better understand the effect of chemical disorder in A15-type superconductors.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, upon reasonable request.
Author contributions
LB synthesized the samples and did the physical property measurements with the assistance from WJF, CYW, ZQQ, XGR. WSQ and CGH contributed in the magnetic measurements. RZ supervised the project and wrote the paper.
Funding
The authors thank the foundation of Westlake University and the National Key Research Development Program of China (No. 2017YFA0303002) for financial support.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
References
1.
YehJWChenSKLinSJGanJYChinSTShunTTet alNanostructured high-entropy alloys with multiple principal elements: novel alloy Design concepts and outcomes. Adv Eng Mater (2004) 6:299. 10.1002/adem.200300567
2.
YeYFWangQLuJLiuCTYangYHigh-entropy alloy: challenges and prospects. Mater Today (2016) 19:349. 10.1016/j.mattod.2015.11.026
3.
MiracleDBSenkovONA critical review of high entropy alloys and related concepts. Acta Mater (2017) 122:448. 10.1016/j.actamat.2016.08.081
4.
ZhangWRLiawPKZhangYScience and technology in high-entropy alloys. Sci China Mater (2018) 61:2. 10.1007/s40843-017-9195-8
5.
GeorgeEPRabbeDRitchieROHigh-entropy alloys. Nat Rev Mater (2019) 4:515. 10.1038/s41578-019-0121-4
6.
SunLLCavaRJHigh entropy alloy superconductors -status, opportunities and challenges. Phys Rev Mater (2019) 3:090301. 10.1016/j.mattod.2015.11.026
7.
KitagawaJHamamotoSIshizuNCutting edge of high-entropy alloy superconductors from the perspective of materials research. Metals (2020) 10:1078. 10.3390/met10081078
8.
KozeljKVrtnikSJelenAJazbecSJaglicicZMaitiSet alDiscovery of a superconducting high-entropy alloy. Phys Rev Lett (2014) 113:107001. 10.1103/PhysRevLett.113.107001
9.
vonn RohrFWiniarskiMJTaoJKlimczukTCavaRJThe effect of electron count and chemical complexity on the superconductivity of the Ta-Nb-Hf-Zr-Ti high-entropy alloy. Proc Nat Acad Sci USA (2016) 113:E7144. 10.1073/pnas.1615926113
10.
YuanYWuYLuoHQWangZSLiangXYangZet alSuperconducting Ti15Zr15Nb35Ta35 high-entropy alloy with intermediate electron-phonon coupling. Front Mater (2018) 5:72. 10.3389/fmats.2018.00072
11.
NelsonWLChemeyATHertzMChoiEGrafDELatturnerSet alSuperconductivity in a uranium containing high entropy alloy. Sci Rep (2020) 10:4717. 10.1038/s41598-020-61666-z
12.
StolzeKCevallosFAKongTCavaRJHigh-entropy alloy superconductors on an α-Mn lattice. J Mater Chem C (2018) 6:10441. 10.1039/C8TC03337D
13.
LiuBWuJFCuiYWZhuQQXiaoGRWangHDet alStructural evolution and superconductivity tuned by valence electron concentration in the Nb–Mo–Re–Ru–Rh high-entropy alloys. J Mater Sci Technol (2021) 85:11. 10.1016/j.jmst.2021.02.002
14.
StolzeKTaoJvon RohrFOKongTCavaRJSc–Zr–Nb–Rh–Pd and Sc–Zr–Nb–Ta–Rh–Pd high-entropy alloy superconductors on a CsCl-type lattice. Chem Mater (2018) 20:906. 10.1021/acs.chemmater.7b04578
15.
MarikSMoltaKVargheseMSajileshKPSinghDBreardYet alSuperconductivity in a new hexagonal high-entropy alloy. Phys Rev Mater (2019) 3:060602. 10.1103/PhysRevMaterials.3.060602
16.
LeeYSCavaRJSuperconductivity in high and medium entropy alloys based on MoReRu. Physica C. (2019) 566:1353520. 10.1016/j.physc.2019.1353520
17.
LiuBWuJFCuiYWZhuQQXiaoGRWuSQet alSuperconductivity in hexagonal Nb–Mo–Ru–Rh–Pd high-entropy alloys. Scripta Mater (2020) 182:109. 10.1016/j.scriptamat.2020.03.004
18.
WuJFLiuBCuiYWZhuQQXiaoGRWangHDet alPolymorphism and superconductivity in the V–Nb–Mo–Al–Ga high-entropy alloys. Sci China Mater (2020) 63:823. 10.1007/s40843-019-1237-5
19.
LiuBWuJFCuiYWZhuQQXiaoGRWangHDet alFormation and superconductivity of single-phase high-entropy alloys with a tetragonal structure. ACS Appl Electron Mater (2020) 2:1130. 10.1021/acsaelm.0c00108
20.
Dew-HughesDSuperconducting A-15 compounds: a review. Cryogenics (1975) 15:435. 10.1016/0011-2275(75)90019-3
21.
PetricekVDusekMPalatinusLCrystallographic computing system JANA2006: general features. Z Kristallogr (2014) 229:345. 10.1515/zkri-2014-1737
22.
TarutaniYKudoMAtomic radii and lattice parameters of the A15 crystal structure. J Less Common Met (1977) 55:221. 10.1016/0022-5088(77)90196-5
23.
BessonRGuyotSLegrisAAtomic-scale study of diffusion in A15 Nb3Sn. Phys Rev B (2007) 75:054105. 10.1103/PhysRevB.75.054105
24.
TakanoHSugiueTAmakaiYMomonoNMurayamaSSite random supercoductivity of A15 compound Nb3Sn induced by mechanical milling. J Phys Conf Ser (2010) 200:032073. 10.1088/1742-6596/200/3/032073
25.
BardeenJCooperLNSchreifferJRTheory of superconductivity. Phys Rev (1957) 108:1175. 10.1201/9780429495700
26.
JohnstonDCElaboration of the $\alpha$-model derived from the BCS theory of superconductivity. Supercond Sci Technol (2013) 26:115011. 10.1088/0953-2048/26/11/115011
27.
McMillanWLTransition temperature of strong-coupled superconductors. Phys Rev (1968) 167:331.
28.
WerthamerNRHelfandEHohenbergPCTemperature and Purity Dependence of the Superconducting Critical Field, $H_{\rm c2}$. III. Electron Spin and Spin-Orbit Effects. Phys Rev (1966) 147:295. 10.1103/PhysRev.147.295
29.
ClogstonAMUpper Limit for the Critical Field in Hard Superconductors. Phys Rev Lett (1962) 9:266. 10.1103/PhysRevLett.9.266
30.
MatthiasBTEmpirical Relation between Superconductivity and the Number of Valence Electrons per Atom. Phys Rev (1955) 97:74. 10.1103/PhysRev.97.74
Summary
Keywords
cubic A15 structure, high-entropy alloys, superconductivity, upper critical field, valence electron concentration
Citation
Liu B, Wu J, Cui Y, Zhu Q, Xiao G, Wu S, Cao G and Ren Z (2021) Superconductivity in Cubic A15-type V–Nb–Mo–Ir–Pt High-Entropy Alloys. Front. Phys. 9:651808. doi: 10.3389/fphy.2021.651808
Received
11 January 2021
Accepted
28 January 2021
Published
31 March 2021
Volume
9 - 2021
Edited by
Jiro Kitagawa, Fukuoka Institute of Technology, Japan
Reviewed by
Yoshikazu Mizuguchi, Tokyo Metropolitan University, Japan
Li Xiang, Florida State University, United States
Updates
Copyright
© 2021 Liu, Wu, Cui, Zhu, Xiao, Wu, Cao and Ren.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Zhi Ren, renzhi@westlake.edu.cn
This article was submitted to Condensed Matter Physics, a section of the journal Frontiers in Physics
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.