Materials Research on High-Entropy Alloy Superconductors

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 Mn 5 Si 3 -type HEA superconductors. This hexagonal structure offers various intermetallic compounds, which often undergo a superconducting state. The Mn 5 Si 3 -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 Mn 5 Si 3 -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.


Introduction
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 [3], high strength at elevated temperatures [4], strong resistance to corrosion and oxidation [5], 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 (Mg 0.2 Co 0.2 Ni 0.2 Cu 0.2 Zn 0.2 )Al 2 O 4 . The high-entropy type spinel oxide interestingly shows enhanced magnetic frustration [8]. 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 (Gd 1/6 Tb 1/6 Dy 1/6 Tm 1/6 Yb 1/6 Lu 1/6 ) 2 Si 2 O 7 . The outstanding thermal stability is ascribed to the high-entropy state at the rareearth site [9]. 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. Fe 15 Co 15 Ni 20 Mn 20 Cu 30 shows a spinodal decomposition after the heat treatment [10]. 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 [14]. Transition metal-based superconductors, forming simple crystalline structures, follow the so-called Matthias rule. When the superconducting critical temperature T c is plotted as a function of valence electron count per atom (VEC), this rule shows broad peak structures at the specified VEC [15]. On the other hand, transition metal amorphous superconductors do not follow this rule and frequently show relatively high T c values in the valley of the curve of the Matthias rule [16]. HEA superconductors with simple crystal structures have been found in bcc [17][18][19][20][21][22] and hcp [23][24][25][26]. The T c vs. VEC plots of these HEAs seem to fall between a crystalline curve and an amorphous one [27,28]. Thus, HEA superconductors will shed light on the study of the relationship between crystalline and amorphous compounds.
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 T c would be substantially reduced in the VEC dependence of T c observed in the Matthias rule. So it may be unrealistic to search for an fcc HEA superconductor. However, this is valuable to challenge because an fcc HEA superconductor would contribute to the deep understanding of HEA and/or the relationship between crystalline and amorphous compounds. In this chapter, we introduce our attempt at the search for an fcc HEA superconductor. Our strategy is to employ a rather high T c element because the HEA superconductors reported to date contain superconducting elements [28]. We focused on the Nb-containing HEAs.
The concept of HEA is now used in superconducting materials with the crystal structures possessing multiple Wyckoff positions. For example, CsCl-type, α-Mntype, A15, NaCl-type, σ-phase and CuAl 2 -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 Mn 5 Si 3 -type HEAs, possessing multiple Wyckoff positions. Recently, several superconductors with the Mn 5 Si 3type-or its ordered derivative Ti 5 Ga 4 -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 Mn 5 Si 3 -type compound represented by M 5 X 3 . The space group is P6 3 /mcm, and the M atoms occupy the 4d (for M1 atom) and 6 g (for M2 atom) Wyckoff positions and the X atom another 6 g one. The M2 atoms form a face-sharing octahedral chain along the c-axis. The X atoms also form another octahedron, which encloses the M1 atom forming a one-dimensional atomic chain along the c-axis.
In this chapter, we report the synthesis and characterization of the fcc and the Mn 5 Si 3 -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.

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 Mn 5 Si 3 -type HEAs were annealed at 800°C for four days in evacuated quartz tubes.
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  [47], and VEC are also listed.

Advances in High-Entropy Alloys -Materials Research, Exotic Properties and Applications
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 χ ac (T) was measured by a home-made system in a GM refrigerator (UW404, Ulvac cryogenics, Kyoto, Japan) between 3 and 300 K. The amplitude and the frequency of the AC field were 5 Oe and 800 Hz, respectively.

Nb-containing fcc HEAs
The starting compositions of prepared Nb-containing samples were determined, considering the conventional design rule [1,2]: a δ-value less than 5% and a VEC larger than 8.0. To realize the requirements, fcc elements were predominantly used (see also Tables 1 and 2). The parameters of δ and VEC were calculated as follows: where c i , r i , and VEC i are the atomic fraction, the atomic radius, and the VEC of element i, respectively, and r is the composition-weighted average atomic radius. The parameter δ means the degree of the atomic size difference among the constituent elements. The calculated parameters for the prepared samples are listed in 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 Cu 40 Nb 20 Pd 30 V 10 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.  (Figure 3(a)) and Cu 21 Ir 21 Nb 15 Pd 22 Rh 21 (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 Cu 21 Nb 15 Pd 22 Rh 21 Zr 21 (Figure 3(c)) or Cu 20 Nb 15 Pd 24 Rh 25 V 10 Zr 6 (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), Cu 40 Nb 20 Pd 30 V 10 possesses two phases, both of which would be fcc  20  phases taking into account the XRD results. Ir 10 Nb 17 Pd 33 Rh 28 Ru 12 displays two contrast areas (see phases I and II in Figure 3(f)). The shape of the main phase has a dendriticlike morphology. The compositions of all phases determined by EDX are listed in Table 2.

Back-scattered electron (15 keV) images of (a) Cu
χ ac (T) measurements of all prepared samples suggested no superconductivity down to 3 K, which means that a Nb-containing fcc-HEA might be an inadequate strategy for searching fcc HEA superconductors. The appearance of superconductivity in a Nb-containing fcc compound might be a rare event because almost all Nb-based superconductors form bcc-related structures. NbN or NbC superconductor is a rare example, crystallizing into a NaCl-type structure related to the fcc structure [50,51]. Although our results would be negative for the research of Nb-containing fcc HEA superconductors, it is to be noted that phase II in sample no. 1, phase I in sample no. 6 and possibly phases I and II in sample no. 4 are new members of HEA.
Here, we discuss the fcc phase stability, viewed from the parameters of δ and VEC, which is summarized in Table 2. We also calculate these parameters for the phases detected by EDX. The values of δ were very large in Cu 21  In each case, going from phase I to phase III, the VEC value increases, which accompanies the decrease (increase) of the Nb (Cu) atomic fraction. This suggests that the combination of Nb and Cu is not recommended even with a reduced δ, because an Nb-rich phase and a Cu-rich phase are stabilized for a smaller VEC and a larger VEC, respectively. Probably due to this reason, quaternary Cu 40 Nb 20 Pd 30 V 10 does not show a single fcc phase. We note here that the addition of Cu leads to the breakdown of single-phase fcc CoCrFeNi into two fcc phases. This is ascribed to the positive enthalpy of mixing between the Cu and several elements [52]. Ir 10 Nb 17 Pd 33 Rh 28 Ru 12 with substantially suppressed δ and no Cu atom was expected to show a single fcc phase; however, two phases were detected in the sample. The detected phases possess reduced δ values and a similar VEC. Thus, it may not be easy to synthesize a single-phase Nb-containing fcc HEA.

Mn 5 Si 3 -type HEAs
We have prepared five Mn 5 Si 3 -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 Mn 5 Si 3 -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 χ ac (T) of each sample is 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 [28], 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 Mn 5 Si 3 -type superconductors Zr 5 Sb 3 and Zr 5 Ge 2.5 Ru 0.5 are 4.375 and 4.25, respectively [40,42], while the VEC value of (NbScTiVZr)(GaGeSi) or (Nb 1. 25  In each sample, the main phase of XRD pattern is well characterized by the Mn 5 Si 3 -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)). χ ac (T) measurements of these Mn 5 Si 3 -type HEA do not show a superconducting signal down to 3 K.

Summary
We have carried out materials research on the fcc and the Mn 5 Si 3 -type HEA superconductors. In the study of fcc HEA superconductors, we employed the Nb element, taking into account that the inclusion of rather high T c elements is advantageous. Although some Nb-containing samples showed dominant fcc phases, single-phase ones could not be obtained. While we have found several new Nb-containing HEA phases in the multi-phase samples, no superconductivity Thus Ru, Ir, or Pt element was substituted at the Si site to increase VEC, resulting in the unsuccessful attempt. We need a strategy to adjust the VEC value for the Mn 5 Si 3 -type HEAs.
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 [53]. 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 [54]. The mechanical alloying process is different from the arc-melting one. So this is another route to obtain single-phase HEA superconductors.

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, T c at such a large VEC value is substantially reduced. Therefore, the measurement of physical properties at much lower than 3 K is desired. Because the synthesis of quinary alloy with the single-phase might be a hard task, research on ternary or quarternary fcc multicomponent superconductor would be necessary. In the research area of HEAs, the CALPHAD (calculation of phase diagram) method is rapidly used for the prediction of HEAs or the study of the phase relation between HEAs and other alloys. If the thermodynamic data of various compounds in the present Nb-containing multicomponent systems are sufficiently collected, the CALPHAD method will elucidate the stability of a HEA in this system. Thus, our results will greatly assist in the evaluation of the CALPHAD method in the future. Nb 5 Ir 3 O, crystallizing into the Ti 5 Ga 4 -type structure, which is the ordered derivative of Mn 5 Si 3 -type structure, is well known as a two-band superconductor [41]. By substituting Pt into Ir, the crossover to single-band superconductivity is observed [44], 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 T c by introducing the high-entropy state is not observed [28]. It would be interesting to pursue the cocktail effect of T c in multisite HEAs.

Author details
Jiro Kitagawa*, Naoki Ishizu and Shusuke Hamamoto Department of Electrical Engineering, Faculty of Engineering, Fukuoka Institute of Technology, Fukuoka, Japan *Address all correspondence to: j-kitagawa@fit.ac.jp