Materials used in this study. The supply company, purity, crystal structure at room temperature, atomic radius , and VEC are also listed.
The first purpose of this chapter is materials research on face-centered-cubic (fcc) high-entropy alloy (HEA) superconductors, which have not yet been reported. We have investigated several Nb-containing multicomponent alloys. Although we succeeded in obtaining Nb-containing samples with the dominant fcc phases, no superconducting signals appeared in these samples down to 3 K. The microstructure analyses revealed that all samples were multi-phase, but the existence of several new Nb-containing HEA phases was confirmed in them. The second purpose is the report of materials research on the Mn5Si3-type HEA superconductors. This hexagonal structure offers various intermetallic compounds, which often undergo a superconducting state. The Mn5Si3-type HEA is classified into the multisite HEA, which possesses the high degree of freedom in the materials design and is good platform for studying exotic HEA superconductors. We have successfully found a single-phase Mn5Si3-type HEA, which, however, does not show a superconducting property down to 3 K. The attempt of controlling the valence electron count was not successful.
- high-entropy alloys
High-entropy alloys (HEAs) are a new class of materials and have attracted a great deal of attention [1, 2]. The concept of HEA was originally proposed for a face-centered-cubic (fcc), body-centered-cubic (bcc), or hexagonal-closed packing (hcp) structure. The most prominent feature of a HEA is that more than five elements, each having an atomic percentage between 5% and 35%, randomly occupy one crystallographic site (see also Figure 1(a)). This produces a large mixing entropy, and HEAs exhibit the combination of high yield strength and ductility , high strength at elevated temperatures , strong resistance to corrosion and oxidation , and so on. The high-entropy concept is extensively adapted in various materials such as oxides, chalcogenides, and halides [6, 7].
One of the novelties of HEAs is a cocktail effect, which indicates an enhancement of physical properties beyond the simple mixture of those of components. For example, several bcc HEAs show superior mechanical properties compared to conventional hard materials. Another example is found in magnetic spinel oxide (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)Al2O4. The high-entropy type spinel oxide interestingly shows enhanced magnetic frustration . The cocktail effect is also reported in the structural stability of high-entropy-type materials. A γ-type disilicate structure is stable from room temperature to 1900°C in (Gd1/6Tb1/6Dy1/6Tm1/6Yb1/6Lu1/6)2Si2O7. The outstanding thermal stability is ascribed to the high-entropy state at the rare-earth site . The other novelty of HEAs is the tuning of physical properties via the change of microstructure. The manufacturing process of HEAs considerably affects their microstructures, which are often deeply related to their physical properties. Fe15Co15Ni20Mn20Cu30 shows a spinodal decomposition after the heat treatment . The spinodally decomposed sample exhibits enhanced Curie temperature and magnetization compared to the homogenized single-phase sample. The tuning of magnetic properties is also reported in dual-phase HEAs [11, 12, 13].
One of the new research topics in HEA is the superconductivity found in 2014 . Transition metal-based superconductors, forming simple crystalline structures, follow the so-called Matthias rule. When the superconducting critical temperature
In the typical HEAs with fcc, bcc, or hcp structure, the superconductivity seems to appear in bcc or hcp HEAs. According to the classification by VEC, single-phase fcc HEA is stabilized for VEC larger than 8.0 [1, 2], where
The concept of HEA is now used in superconducting materials with the crystal structures possessing multiple Wyckoff positions. For example, CsCl-type, α-Mn-type, A15, NaCl-type, σ-phase and CuAl2-type HEA superconductors are reported [29, 30, 31, 32, 33, 34, 35, 36, 37]. High degree-of-freedom in such a multisite HEA design would promote the investigations of multisite HEA superconductors. The second purpose of this chapter is the materials research on the hexagonal Mn5Si3-type HEAs, possessing multiple Wyckoff positions. Recently, several superconductors with the Mn5Si3-type—or its ordered derivative Ti5Ga4-type—structure have been found and attract much attention [38, 39, 40, 41, 42, 43, 44]. Besides, many intermetallic compounds are crystallizing into these crystal structures [45, 46]. Figure 1(b) shows the crystal structure of the Mn5Si3-type compound represented by M5X3. The space group is
In this chapter, we report the synthesis and characterization of the fcc and the Mn5Si3-type HEA samples. The measurement of AC magnetic susceptibility checked the superconducting state. We also present the phase analyses of both kinds of samples. Finally, the future direction of materials research on superconducting HEAs is mentioned.
2. Materials and methods
All samples were synthesized by a home-made arc furnace in an Ar atmosphere. The constituent elements as listed in Table 1 were arc-melted on a water-cooled Cu hearth. The samples were turned over and melted several times. The Mn5Si3-type HEAs were annealed at 800°C for four days in evacuated quartz tubes.
|Element||Supply company||Purity (%)||Crystal structure||Atomic radius (Å)||VEC|
|Zr||Soekawa Chemicals, Tokyo, Japan||99||A3 (hcp)||1.6025||4|
|Nb||Nilaco, Tokyo, Japan||99.9||A2 (bcc)||1.429||5|
|V||Kojundo Chemical Laboratory, Sakado, Japan||99.9||A2 (bcc)||1.316||5|
|Ru||Soekawa Chemicals, Tokyo, Japan||99.9||A3 (hcp)||1.3384||8|
|Ir||Furuya Metal, Tokyo, Japan||99.99||A1 (fcc)||1.3573||9|
|Rh||Soekawa Chemicals, Tokyo, Japan||99.9||A1 (fcc)||1.345||9|
|Pd||Tanaka Kinzoku Kogyo, Tokyo, Japan||99.9||A1 (fcc)||1.3754||10|
|Cu||Soekawa Chemicals, Tokyo, Japan||99.99||A1 (fcc)||1.278||11|
|Sc||Furuya Metal, Tokyo, Japan||99.9||A3 (hcp)||1.641||3|
|Ti||Nilaco, Tokyo, Japan||99.9||A3 (hcp)||1.4615||4|
|Ga||Kojundo Chemical Laboratory, Sakado, Japan||99.99||All||1.392||3|
|Si||Soekawa Chemicals, Tokyo, Japan||99.999||A4||1.153||4|
|Ge||Soekawa Chemicals, Tokyo, Japan||99.999||A4||1.24||4|
|Pt||Tanaka Kinzoku Kogyo, Tokyo, Japan||99.9||A1 (fcc)||1.387||10|
A powder X-ray diffractometer (XRD-7000 L, Shimadzu, Kyoto, Japan) with Cu-Kα radiation was employed to detect the X-ray diffraction (XRD) patterns of prepared samples. The microstructure of each sample was examined by a field emission scanning electron microscope (FE-SEM, JSM-7100F; JEOL, Akishima, Japan). The atomic compositions of the samples were checked by an energy dispersive X-ray (EDX) spectrometer equipped to the FE-SEM.
To confirm the diamagnetic signal due to the superconducting state, the temperature dependence of the AC magnetic susceptibility
3. Results and discussion
3.1 Nb-containing fcc HEAs
The starting compositions of prepared Nb-containing samples were determined, considering the conventional design rule [1, 2]: a
|No.||Sample||Composition of Phase I, II or III||VEC|
|Phase I||Cu21.1(2)Nb27.6(2)Pd39.7(7)V11 5(7)||4.05||8.25|
Shown in Figure 2 is the XRD patterns of prepared samples. In the upper five samples, all containing Nb, Pd, and Cu atoms, Cu20Nb15Pd25Rh30V10 and Cu21Ir21Nb15Pd22Rh21 possess dominant fcc phases. On the other hand, the XRD patterns of Zr-containing samples (Cu21Nb15Pd22Rh21Zr21 and Cu20Nb15Pd24Rh25V10Zr6) cannot be characterized by fcc phases. These results suggest that Zr is unfavorable for the formation of an fcc structure. In order to further investigate the formation condition of the single fcc phase, the quaternary alloy Cu40Nb20Pd30V10 was synthesized. As shown in Figure 2, this sample exhibits two fcc phases with quite different lattice parameters. The XRD pattern of the sample with no Cu atom (see the bottom of Figure 2) can be explained by an fcc phase. The lattice parameters of all fcc phases were obtained by the least-square method [48, 49] and are shown in Figure 2.
Figures 3(a)–(f) display the SEM images of samples, all indicating multi-phases. In Cu20Nb15Pd25Rh30V10 (Figure 3(a)) and Cu21Ir21Nb15Pd22Rh21 (Figure 3(b)), three contrast phases I, II and III were detected. In each case, the brightest area (phase I) showed a dendritic morphology, which is surrounded by phase II with the median contrast. The darkest area (phase III) would be the precipitate that formed in the final solidification process. A part of Cu21Nb15Pd22Rh21Zr21 (Figure 3(c)) or Cu20Nb15Pd24Rh25V10Zr6 (Figure 3(d)) showed a eutectic-like structure formed by phase I and phase II (see, for example, the green elliptic closed-curve). As shown in Figure 3(e), Cu40Nb20Pd30V10 possesses two phases, both of which would be fcc phases taking into account the XRD results. Ir10Nb17Pd33Rh28Ru12 displays two contrast areas (see phases I and II in Figure 3(f)). The shape of the main phase has a dendritic-like morphology. The compositions of all phases determined by EDX are listed in Table 2.
Here, we discuss the fcc phase stability, viewed from the parameters of
3.2 Mn5Si3-type HEAs
We have prepared five Mn5Si3-type HEAs as listed in Table 3, and the XRD patterns are given in Figure 4. All XRD patterns are well indexed by the hexagonal Mn5Si3-type structure, and the determined lattice parameters are displayed in Figure 4. The SEM images of all samples are presented in Figures 5 and 6, and
|No.||Sample||Composition of main phase||Composition of minor phase||VEC|
|2||(Nb1.25Sc1.25Ti1.25Zr1.25) (Ge1.8Si1.2)||(Nb17(1)Sc14(1)Ti16(1)Zr17(1)) (Ge22(1)Si14(1))||—||4|
|3||(Nb1.25Sc1.25Ti1.25Zr1.25) (Ge1.55Ru0.47Si0.98)||(Nb18.0(2)Sc13.5(4)Ti12.3(5)Zr20.5(6)) (Ge21.4(2)Si14.3(4))||Nb28(4)Ru31(4)Sc6(2)T31(3)Zr4(1)||4.234|
|4||(Nb1.4ScTiZr1.6) (Ge1.6Pt0.3Si1.1)||(Nb20.8(3)Sc8.4(5)Ti10.9(3)Zr24(1)) (Ge19.9(5)Pt1.0(4) Si15.0(5))||Ge5.5(7)Sc37(2)Si1.7(2)Ti15(1)Pt40.7(7)||4.275|
|5||(Nb1.4ScTiZr1.6) (Ge1.6Ir0.3Si1.1)||(Nb20.4(2)Sc8.9(5)Ti10.9(1)Zr24.5(4)) (Ge20.3(3)Si15.0(2))||Ge5.3(5)Ir27.7(9)Nb9.3(5) Sc20.5(9)Si4.0(6)Ti16.4(5) Zr16.7(8)||4.238|
We have started from (NbScTiVZr)(GaGeSi), which shows a diamagnetic signal (see Figure 7). However, as shown in Figure 5(a), the elemental mapping has revealed the inhomogeneous distribution of constituent elements, which is obviously signaled by the V atom. The atomic compositions determined by EDX are (Nb13.0(1)Sc15.5(1)Ti11.2(1)V4.6(2) Zr19.0(1))(Ga4.4(2)Ge19.3(1)Si13.1(1)) for the V-poor phase and Ga7(1)Ge6(1)Nb19(1)Sc8(1)Si7(1)Ti17(1)V28(1) Zr8(1) for the V-rich phase, respectively. The separately synthesized latter phase crystallizes into a bcc structure. This compound also shows the diamagnetic signal at approximately 5 K, which is identical to that of (NbScTiVZr)(GaGeSi). Therefore, (NbScTiVZr)(GaGeSi) would be an intrinsically normal state down to 3 K. The result of the chemical composition of the Mn5Si3-type phase in (NbScTiVZr)(GaGeSi) suggests the difficulty of incorporation of V and Ga atoms in a Mn5Si3-type HEA. Taking into account this experimental result, we have synthesized (Nb1.25Sc1.25Ti1.25Zr1.25)(Ge1.8Si1.2). As shown in Figure 4, the sample is almost single phase, which is also supported by homogeneous elemental mapping (see also Figure 5(b)). The determined atomic composition is (Nb17(1)Sc14(1)Ti16(1)Zr17(1))(Ge22(1)Si14(1)), which agrees well with the starting composition. While the single-phase Mn5Si3-type HEA is successfully obtained, the diamagnetic signal cannot be confirmed down to 3 K, as shown in Figure 7.
One of the conceivable reasons for no superconductivity in the samples mentioned above is that the VEC value is slightly less than the optimal value (see also Table 3). As pointed out in the review , multisite HEA superconductors follow the respective Matthias rule, which means the important role of the density of states at the Fermi level. The VEC values of Mn5Si3-type superconductors Zr5Sb3 and Zr5Ge2.5Ru0.5 are 4.375 and 4.25, respectively [40, 42], while the VEC value of (NbScTiVZr)(GaGeSi) or (Nb1.25Sc1.25Ti1.25Zr1.25)(Ge1.8Si1.2) is 4. Thus, aiming at increasing the VEC, we substituted Ru, Pt, or Ir atoms at the Si site of Mn5Si3-type HEA. The prepared samples were (Nb1.25Sc1.25Ti1.25Zr1.25)(Ge1.55Ru0.47Si0.98), (Nb1.4ScTiZr1.6)(Ge1.6Pt0.3Si1.1), and (Nb1.4ScTiZr1.6)(Ge1.6Ir0.3Si1.1) with the respective VEC value of 4.234, 4.275, and 4.238. In each sample, the main phase of XRD pattern is well characterized by the Mn5Si3-type structure (see Figure 4). However, the atomic composition, deviating from the starting one, as shown in Table 3, indicates that Ru, Pt, or Ir atoms cannot replace the atoms at the Si site. The SEM images of these samples show the precipitation of impurity phases at the grain boundaries of hexagonal-shaped main phases (see Figure 6(a)–(c)).
We have carried out materials research on the fcc and the Mn5Si3-type HEA superconductors. In the study of fcc HEA superconductors, we employed the Nb element, taking into account that the inclusion of rather high
The conclusions regarding the manufacturing process or microstructure in HEA superconductors are bulleted below.
If one wants to obtain a single-phase sample with bcc, hcp, or fcc type structure by the arc-melting method, it would be a rather hard task due to an appearance of secondary phase and/or of phase with a slightly different composition.
Eutectic HEAs receive much attention due to the rich functions arising from the microstructures . In some cases, eutectic superconductors show enhanced superconducting critical temperatures. Therefore, the study of the eutectic phase in HEA superconductors might be interesting.
Mechanical alloying has been widely used to produce HEAs . The mechanical alloying process is different from the arc-melting one. So this is another route to obtain single-phase HEA superconductors.
5. Future directions
The formation of single-phase fcc HEA is realized at VEC larger than 8.0. According to the Matthias rule of transition metal alloys,
Nb5Ir3O, crystallizing into the Ti5Ga4-type structure, which is the ordered derivative of Mn5Si3-type structure, is well known as a two-band superconductor . By substituting Pt into Ir, the crossover to single-band superconductivity is observed , which is a rare phenomenon. This result promotes us to investigate multisite HEA superconductors for further search of the crossover phenomenon, and the high-entropy state may be a new route of controlling the superconducting band. Another interesting aspect of HEA is the cocktail effect. In bcc HEA superconductors, we have shown that the peculiar enhancement of
J.K. is grateful for the support provided by Comprehensive Research Organization of Fukuoka Institute of Technology.
Conflict of interest
The authors declare no conflict of interest.
Gao M C, Yeh J W, Liaw P K, Zhang Y. High-entropy alloys: fundamentals and applications Swizerland: Springer; 2015.
Murty B S, Yeh J W, Ranganathan S, Bhattacharjee P P. High-Entropy Alloys. 2nd ed. Amsterdam: Elsevier; 2019.
Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Tsau C H, Chang S Y. Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater. 2004;6:299-303. DOI: 10.1002/adem.200300567
Otto F, Yang Y, Bei H, George E P. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys. Acta Mater. 2013;61:2628-2638. DOI: 10.1016/j.actamat.2013.01.042
Rost C M, Sachet E, Borman T, Moballegh A, Dickey E C, Hou D, Jones J L, Curtarolo S, Maria J P. Entropy-stabilized oxides. Nat. Commun. 2015;6:8485. DOI: 10.1038/ncomms9485
Musicό B L, Gilbert D, Ward T Z, Page K, George E, Yan J, Mandrus D, Keppens V. The emergent field of high entropy oxides: Design, prospects, challenges, and opportunities for tailoring material properties. APL Materials 2020;8:040912. DOI: 10.1063/5.0003149
Ying T, Yu T, Shiah Y-S, Li C, Li J, Qi Y, Hosono H. High-entropy van der Waals materials formed from mixed metal dichalcogenides, halides, and phosphorus trisulfides. J. Am. Chem. Soc. 2021;143:7042-7049. DOI: 10.1021/jacs.1c01580
Marik S, Singh D, Gonano B, Veillon F, Pelloquin D, Bréard Y. Enhanced magnetic frustration in a new high entropy diamond lattice spinel oxide. Scr. Mater. 2020;186:366-369. DOI: 10.1016/j.scriptamat.2020.04.027
Sun L, Luo Y, Ren X, Gao Z, Du T, Wu Z, Wang J. A multicomponent γ-type (Gd1/6Tb1/6Dy1/6Tm1/6Yb1/6Lu1/6)2Si2O7 disilicate with outstanding thermal stability. Mater. Res. Lett. 2020;8:424-430. DOI: 10.1080/21663831.2020.1783007
Rao Z, Dutta B, Körmann F, Lu W, Zhou X, Liu C, Kwiatkowski da Silva A, Wiedwald U, Spasova M, Farle M, Ponge D, Gault B, Neugebauer J, Raabe D, Li Z. Beyond solid solution high-entropy alloys: tailoring magnetic properties via spinodal decomposition. Adv. Funct. Mater. 2021;31:2007668. DOI: 10.1002/adfm.202007668
Quintana-Nedelcos A, Leong Z, Morley N A. Study of dual-phase functionalisation of NiCoFeCr-Alx multicomponent alloys for the enhancement of magnetic properties and magneto-caloric effect. Mater. Today: Energy 2021;20:100621. DOI: 10.1016/j.mtener.2020.100621
Jung C, Kang K, Marshal A, Gokuldoss Pradeep K, Seol J–B, Lee H M, Choi P–P. Effects of phase composition and elemental partitioning on soft magnetic properties of AlFeCoCrMn high entropy alloys. Acta Mater. 2019;171:31-39. DOI: 10.1016/j.actamat.2019.04.007
BaBa K, Ishizu N, Nishizaki T, Kitagawa J. Magnetic and transport properties of new dual-phase high-entropy alloy FeRhIrPdPt. Materials 2021;14:2877. DOI: 10.3390/ma14112877
Koželj P, Vrtnik S, Jelen A, Jazbec S, Jagličić Z, Maiti S, Feuerbacher M, Steurer W, Dolinšek J. Discovery of a superconducting high-entropy alloy. Phys. Rev. Lett. 2014;113:107001. DOI: 10.1103/PhysRevLett.113.107001
Matthias B T. Empirical relation between superconductivity and the number of valence electrons per atom. Phys Rev 1955;97:74-76. DOI: 10.1103/PhysRev.97.74
Collver M M, Hammond R H. Superconductivity in “amorphous” transition-metal alloy films. Phys Rev Lett 1973;30:92-95. DOI: 10.1103/PhysRevLett.30.92
von Rohr F O, Winiarski M J, Tao J, Klimczuk T, Cava R J. Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor. Proc. Natl. Acad. Sci. 2016;113:E7144-E7150. DOI: 10.1073/pnas.1615926113
von Rohr F O, Cava R J. Isoelectronic substitutions and aluminium alloying in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor. Phys. Rev. Mater. 2018;2:034801. DOI: 10.1103/PhysRevMaterials.2.034801
Marik S, Varghese M, Sajilesh K P, Singh D, Singh R P. Superconductivity in equimolar Nb-Re-Hf-Zr-Ti high entropy alloy. J. Alloys Compd. 2018;769:1059-1063. DOI: 10.1016/j.jallcom.2018.08.039
Ishizu N, Kitagawa J. New high-entropy alloy superconductor Hf21Nb25Ti15V15Zr24. Res. Phys. 2019;13:102275. DOI: 10.1016/j.rinp.2019.102275
Zhang X, Winter N, Witteveen C, Moehl T, Xiao Y, Krogh F, Schilling A, von Rohr F O. Preparation and characterization of high-entropy alloy (TaNb)1−x(ZrHfTi)x superconducting films. Phys. Rev. Res. 2020;2:013375. DOI: 10.1103/PhysRevResearch.2.013375
Harayama Y, Kitagawa J. Superconductivity in Al-Nb-Ti-V-Zr multicomponent alloy. J. Supercond. Nov. Magn. 2021 DOI: 10.1007/s10948-021-05966-z
Lee Y S, Cava R J. Superconductivity in high and medium entropy alloys based on MoReRu. Physica C 2019;566:1353520. DOI: 10.1016/j.physc.2019.1353520
Marik S, Motla K, Varghese M, Sajilesh K P, Singh D, Breard Y, Boullay P, Singh R P. Superconductivity in a new hexagonal high-entropy alloy. Phys. Rev. Mater. 2019;3:060602(R). DOI: 10.1103/PhysRevMaterials.3.060602
Liu B, Wu J, Cui Y, Zhu Q , Xiao G, Wu S, Cao G, Ren Z. Superconductivity in hexagonal Nb-Mo-Ru-Rh-Pd high-entropy alloys. Scr. Mater. 2020;182:109-113. DOI: 10.1016/j.scriptamat.2020.03.004
Liu B, Wu J, Cui Y, Zhu Q , Xiao G, Wu S, Cao G-h, Ren Z. Structural evolution and superconductivity tuned by valence electron concentration in the Nb-Mo-Re-Ru-Rh high-entropy alloys. J. Mater. Sci. Technol. 2021;85:11-17. DOI: 10.1016/j.jmst.2021.02.002
Sun L, Cava R J. High-entropy alloy superconductors: Status, opportunities, and challenges. Phys. Rev. Mater. 2019;3:090301. DOI: 10.1103/PhysRevMaterials.3.090301
Kitagawa J, Hamamoto S, Ishizu N. Cutting edge of high-entropy alloy superconductors from the perspective of materials research. Metals 2020;10:1078. DOI: 10.3390/met10081078
Stolze K, Tao J, von Rohr F O, Kong T, Cava R J. Sc−Zr−Nb−Rh−Pd and Sc−Zr−Nb−Ta−Rh−Pd high-entropy alloy superconductors on a CsCl-type lattice. Chem. Mater. 2018;30:906-914. DOI: 10.1021/acs.chemmater.7b04578
Stolze K, Cevallos F A, Kong T, Cava R J. High-entropy alloy superconductors on an α-Mn lattice. J. Mater. Chem. C 2018;6:10441-10449. DOI: 10.1039/C8TC03337D
Wu J, Liu B, Cui Y, Zhu Q , Xiao G, Wang H, Wu S, Cao G, Ren Z. Polymorphism and superconductivity in the V-Nb-Mo-Al-Ga high-entropy alloys. Sci. China Mater. 2020;63:823-831. DOI: 10.1007/s40843-019-1237-5
Mizuguchi Y. Superconductivity in high-entropy-alloy telluride AgInSnPbBiTe5. J. Phys. Soc. Jpn. 2019;88:124708. DOI: 10.7566/JPSJ.88.124708
Kasem M R, Hoshi K, Jha R, Katsuno M, Yamashita A, Goto Y, Matsuda T D, Aoki Y, Mizuguchi Y. Superconducting properties of high-entropy-alloy tellurides M-Te (M: Ag, In, Cd, Sn, Sb, Pb, Bi) with a NaCl-type structure. Appl. Phys. Express 2020;13:033001. DOI: 10.35848/1882-0786/ab7482
Yamashita A, Jha R, Goto Y, Matsuda T D, Aoki Y, Mizuguchi Y. An Efficient way of increasing the total entropy of mixing in high-entropy-alloy compounds: a case of NaCl-type (Ag,In,Pb,Bi)Te1-xSex (x = 0.0, 0.25, 0.5) superconductors. Dalton Trans. 2020;49:9118-9122. DOI: 10.1039/D0DT01880E
Liu B, Wu J, Cui Y, Zhu Q , Xiao G, Wu S, Cao G-h, Ren Z. Superconductivity and paramagnetism in Cr-containing tetragonal high-entropy alloys. J. Alloys Compd. 2021;869:159293. DOI: 10.1016/j.jallcom.2021.159293
Mizuguchi Y, Kasem M R, Matsuda T D. Superconductivity in CuAl2-type Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 with a high-entropy-alloy transition metal site. Mater. Res. Lett. 2020:9;141-147. DOI: 10.1080/21663831.2020.1860147
Kasem M R, Yamashita A, Goto Y, Matsuda T D, Mizuguchi Y. Synthesis of high-entropy-alloy-type superconductors (Fe,Co,Ni,Rh,Ir)Zr2 with tunable transition temperature. J. Mater. Sci. 2021;56:9499-9505. DOI: 10.1007/s10853-021-05921-2
Cort B, Giorgi A L, Stewart G R. Low temperature specific heats of H(NbIrO) and R(NbPtO). J. Low. Temp. Phys. 1982;47:179-185. DOI: 10.1007/BF00682027
Waterstrat R M, Kuentzler R, Muller J. Structural instabilities and superconductivity in quasi-binary Mn5Si3-type compounds. J. Less Common Met. 1990;167:169-178. DOI: 10.1016/0022-5088(90)90302-Z
Lv B, Zhu X Y, Lorenz B, Wei F Y, Xue Y Y, Yin Z P, Kotliar G, Chu C W. Superconductivity in the Mn5Si3-type Zr5Sb3 system. Phys. Rev. B 2013;88:134520. DOI: 10.1103/PhysRevB.88.134520
Zhang Y, Wang B, Xiao Z, Lu Y, Kamiya T, Uwatoko Y, Kageyama H, Hosono H. Electride and superconductivity behaviors in Mn5Si3-type intermetallics. npj Quantum Materials 2017;2:45. DOI: 10.1038/s41535-017-0053-4
Li S, Liu X, Anand V, Lv B. Superconductivity from site-selective Ru doping studies in Zr5Ge3 compound. New J. Phys. 2018;20:013009. DOI: 10.1088/1367-2630/aa9ccd
Hamamoto S, Kitagawa J. Superconductivity in oxygen-added Zr5Pt3. Mater. Res. Express 2018;5:106001. DOI: 10.1088/2053-1591/aad9cf
Xu Y, Jöhr S, Das L, Kitagawa J, Medarde M, Shiroka T, Chang J, Shang T. Crossover from multiple- to single-gap superconductivity in Nb5Ir3−xPtxO alloys. Phys. Rev. B 2020;101:134513. DOI: 10.1103/PhysRevB.101.134513
Corbett J D, Garcia E, Guloy A M, Hurng W M, Kwon Y U, Leon-Escamilla E A. Widespread interstitial chemistry of Mn5Si3-type and related phases. Hidden impurities and opportunities. Chem. Mater. 1998;10:2824-2836. DOI: 10.1021/cm980223c
Kitagawa J, Hamamoto S. Superconductivity in Nb5Ir3−xPtxO. JPS Conf. Proc. 2020;30:011055. DOI: 10.7566/JPSCP.30.011055
Miracle D B, Senkov O N. A critical review of high entropy alloys and related concepts. Acta Mater. 2017;122:448-511. DOI: 10.1016/j.actamat.2016.08.081
Izumi F, Momma K. Three-dimensional visualization in powder diffraction. Solid State Phenom. 2007; 130:15-20. DOI: 10.4028/www.scientific.net/SSP.130.15
Tsubota M, Kitagawa J. A necessary criterion for obtaining accurate lattice parameters by Rietveld method. Sci. Rep. 2017;7:15381. DOI: 10.1038/s41598-017-15766-y
Giorgi A L, Szklarz E G, Storms E K, Bowman A L, Matthias B T. Effect of Composition on the superconducting transition temperature of tantalum carbide and niobium carbide. Phys. Rev. 1962;125:837-838. DOI: 10.1103/PhysRev.125.837
Matthias B T. Transition temperatures of superconductors. Phys. Rev. 1953;92:874-876. DOI: 10.1103/PhysRev.92.874
Otto F, Yang Y, Bei H, George E P. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys. Acta Materialia 2013;61:2628-2638. DOI: 10.1016/j.actamat.2013.01.042
Lu Y, Dong Y, Guo S, Jiang L, Kang H, Wang T, Wen B, Wang Z, Jie J, Cao Z, Ruan H, Li T. A promising new class of high-temperature alloys: Eutectic high-entropy alloys. Sci. Rep. 2015;4:6200. DOI: 10.1038/srep06200
Vaidya M, Muralikrishna G M, Murty B S. High-entropy alloys by mechanical alloying: A review. J. Mater. Res. 2019;34:664-686. DOI: 10.1557/jmr.2019.37