Superconductivity in HEA-Type Compounds

*Yoshikazu Mizuguchi and Aichi Yamashita*

## **Abstract**

Since the discovery of superconductivity in a high-entropy alloy (HEA) Ti-Zr-Nb-Hf-Ta in 2014, the community of superconductor science has explored new HEA superconductors to find the merit of the HEA states on superconducting properties. Since 2018, we have developed "HEA-type" compounds as superconductors or thermoelectric materials. As well known, compounds like intermetallic compounds or layered compounds are composed of multi crystallographic sites. In a HEA-type compounds, one or more sites are alloyed and total mixing entropy satisfies with the criterion of HEA. Herein, we summarize the synthesis methods, the crystal structural variation and superconducting properties of the HEA-type compounds, which include NaCl-type metal tellurides, CuAl2-type transition metal zirconides, high-*T*<sup>c</sup> cuprates, and BiS2-based layered superconductors. The effects of the introduction of a HEA site in various kinds of complicated compounds are discussed from the structural-dimensionality viewpoint.

**Keywords:** superconductor, layered compounds, material design, high entropy alloy

### **1. Introduction**

#### **1.1 Superconducting materials**

Superconductivity is a quantum phenomenon, which is characterized by zero-resistivity states in electrical resistivity and exclusion of magnetic flux from a superconductor [1, 2]. Superconductivity has provided many exotic research topics not only in the field of science but also in application of superconductors. The zero-resistivity states can achieve large-scale electricity transport with ultra-low energy loss, very high magnetic fields, which has been used in various devices like a magnetic resonance imaging (MRI) and a superconducting Maglev train. Although superconductor devises look perfect, the use of superconductors are regulated by temperature in reality because superconducting states are observed only at temperatures below a superconducting transition temperature (*T*c), which is a parameter unique to the superconductor. To use superconducting devices, the system must be cooled down to low temperatures lower than the *T*c of its superconducting components. Therefore, discovery of high-*T*c superconductors has been desired.

In 1986, superconductivity with a high *T*c in a Cu oxide (La,Ba)2CuO4 was discovered [3, 4]. Soon after the discovery, *T*c of the Cu-oxide superconductor (cuprate) family reached 90 K for *RE*Ba2Cu3O7-*d* (*RE*: rare earth) [5], which is higher than liquid nitrogen temperature, and finally reached 135 K in a Hg-Ba-Ca-Gu-O system [6]. After the discovery of the cuprate family, many layered compounds have been

searched for high-*T*c superconductivity. In 2001, superconductivity in MgB2 with a *T*<sup>c</sup> of 39 K was reported [7]. Furthermore, in 2008, FeAs-based layered superconductors *RE*FeAsO1-*x*Fx with a *T*c exceeding 50 K were discovered [8, 9]. Particularly, in the cuprates and FeAs-based families, unconventional (non-phonon-mediated) mechanisms of superconductivity has been proposed to explain their high *T*c [10].

A surprising discovery of superconductivity at very high *T*c of 203 K in H3S was reported in 2015 [11]. The phenomenon could be achieved at extremely high pressures above 150 GPa, the high *T*c and possible conventional (phonon-mediated) mechanisms have recently been attracting many researchers in the field of condensed matter physics. Furthermore, higher *T*cs have been reported in related hydrides, LaH10 (*T*c > 250 K at ~200 GPa) [12, 13] and a carbonaceous sulfur hydride system (*T*c = 287.7 K at 267 GPa) [14]. To use high-*T*c superconducting states in hydrides, discovery of new superconducting hydrides which become superconductive at ambient pressure. The possible strategy to realize that is the utilization of chemical pressure effects, which are applied via chemical substitutions and sometimes work like external pressure effects. Therefore, further investigations on chemical pressure effects in novel superconductors are needed, and high-entropy alloying of compounds would be one of the routs to chemically modify the crystal structure of superconductors.

#### **1.2 Superconductivity in high-entropy alloys**

Although layered compounds had been the central topic in searching high-*T*<sup>c</sup> and/or unconventional superconductors over the last three decades, recent works on new superconductors have focused on various kinds of materials, which includes complicated compounds and pure metals as well. Among them, high-entropy-alloy (HEA) superconductors have been a developing field of study [15].

HEA is an alloy possessing high configurational mixing entropy (Δ*S*mix), which is achieved by making the alloy with more than five constituent elements with an occupancy ranging 5 to 35 at% for each element [16, 17]. Typically, Δ*S*mix of HEA is calculated by Δ*S*mix = −*R* Σi *c*i ln *c*i, where *c*i and *R* are the compositional ratio and the gas constant [17], and reaches 1.5*R*. Due to high Δ*S*mix, HEAs exhibit stability or high performance in high temperature and/or extreme conditions [17]. Therefore, HEAs have been extensively studied in the fields of materials science and engineering.

In 2014, Koželj et al. reported superconductivity with *T*c = 7.3 K in a HEA Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 [18]. The HEA superconductor has a bcc structure with a space group of *Im*-3 *m*. In **Figure 1**, we compare the crystal structures of (a) a pure Nb metal (*T*c = 9.2 K), (b) a NbTi alloy (*T*c ~ 10 K), which is the mostly-used practical superconductor, and (c) HEA Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. All those materials show superconductivity and the crystal structure type is the same. The difference between them is the mixing entropy Δ*S*mix and *T*c. Although the *T*c of HEA is lower than that of the other two, it was surprising for researchers that such a disordered alloy exhibits superconductivity with bulk nature. After the discovery of Ref. [18], various HEA superconductors have been developed; material information [18–26] is listed in **Table 1**.

As shown in **Figure 2**, a superconducting transition was observed in Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 [18]. The temperature dependence of electrical resistivity (**Figure 2(a)**) shows metallic behavior but exhibits a relatively small residual resistivity ratio (*RRR*) at low temperatures. This would be due to the presence of disorder, and a similar trend has been observed in various HEA-type superconductors. Bulk superconductivity could be confirmed through specific heat measurement as shown in **Figure 2(b)**. From specific heat data, it has been found that most HEA superconductors exhibit conventional (phonon-mediated) pairing states.

*T*c of HEA superconductors show correlation with valence electron count (VEC) [15, 21, 27]. The type-A HEAs with lower VEC exhibit a dependence of *T*c on VEC

**5**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

**Figure 1.**

*Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 (HEA).*

similar to that for crystalline metals, alloys, and amorphous materials, and the *T*c of HEAs are intermediate between crystalline materials and amorphous. In contrast, the *T*c of the type-C HEAs with middle VEC shows opposite behavior to that for other forms. For the type-B HEAs, the trend of *T*c on VEC seems resembling that for other forms, but their *T*cs are clearly lower than that for crystalline and amorphous materials. As mentioned in Ref. [15], there would be a clear effect of crystallinity on *T*c at the same VEC range, but the origin of the different trends between type-A, type-B, and type-C regimes have not been clarified from physical viewpoint (**Figure 3**). Another notable character of HEA is a robustness of superconductivity to extremely high pressure. As reported in Ref. [20], the *T*c of Ta-Nb-Hf-Zr-Ti slightly increases by external pressure effect and the 10 K-class *T*c maintains under extreme pressures like 200 GPa. However, the robustness of superconductivity to extremely high pressure was reported for simpler NbTi with a clear increase in *T*c to 19.1 K at 261 GPa [28]. Therefore, the issue if HEA can improve the stability of superconduc-

*Schematic image of crystal structure of (a) Nb (pure metal), (b) NbTi (alloy), and (c)* 

As described in subsection 1–2, superconductivity in HEAs has been discovered

and been regarded as a new research field of superconductivity. However, the merit of HEA states for superconductors has not been fully understood. Therefore, development of new types of HEA superconductors is needed. The hint to expand

the material variation of HEA superconductors was proposed in Ref. [29], in which a HEA superconductor with a CsCl-type structure was reported. Since the CsCl structure contains two independent crystallographic sites, we have flexibility of elemental solution at the two sites. When calculating total Δ*S*mix of (ScZrNbTa)0.65(RhPd)0.35 by taking the sum of Δ*S*mixs for site-1 and site-2, it appears to reach very high Δ*S*mix of 1.79*R*. A similar site separation has been observed in (Nb0.11Re0.56)(HfZrTi)0.33 [30]. Motivated by those studies on HEAs with site separation, we have tried to synthesize various "*HEA-type compounds*", which contain NaCl-type metal chalcogenides [31–33], CuAl2-type tetragonal *Tr*Zr2 (*Tr*: Fe, Co, Ni, Cu, Rh, Ir) [34, 35], high-*T*c RE123 cuprates [36], and BiS2-based layered superconductors [37, 38]. The concept of HEA-type compounds it that we achieve a high Δ*S*mix by site-selective alloying. As shown in **Figure 4**, HEA-type compounds have a HEA-type site, in which five or more elements are solving and a normal site, which is not in the HEA state. The list of superconducting HEA-type compounds is shown in **Table 2**. By studying HEA effects to crystal structure and

tor under extremely high pressures has not been clarified.

**1.3 Concept of HEA-type compounds**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

**Figure 1.**

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

**1.2 Superconductivity in high-entropy alloys**

searched for high-*T*c superconductivity. In 2001, superconductivity in MgB2 with a *T*<sup>c</sup> of 39 K was reported [7]. Furthermore, in 2008, FeAs-based layered superconductors *RE*FeAsO1-*x*Fx with a *T*c exceeding 50 K were discovered [8, 9]. Particularly, in the cuprates and FeAs-based families, unconventional (non-phonon-mediated) mechanisms of superconductivity has been proposed to explain their high *T*c [10]. A surprising discovery of superconductivity at very high *T*c of 203 K in H3S was reported in 2015 [11]. The phenomenon could be achieved at extremely high pressures above 150 GPa, the high *T*c and possible conventional (phonon-mediated) mechanisms have recently been attracting many researchers in the field of condensed matter physics. Furthermore, higher *T*cs have been reported in related hydrides, LaH10 (*T*c > 250 K at ~200 GPa) [12, 13] and a carbonaceous sulfur hydride system (*T*c = 287.7 K at 267 GPa) [14]. To use high-*T*c superconducting states in hydrides, discovery of new superconducting hydrides which become superconductive at ambient pressure. The possible strategy to realize that is the utilization of chemical pressure effects, which are applied via chemical substitutions and sometimes work like external pressure effects. Therefore, further investigations on chemical pressure effects in novel superconductors are needed, and high-entropy alloying of compounds would be one of the routs to chemically modify the crystal structure of superconductors.

Although layered compounds had been the central topic in searching high-*T*<sup>c</sup> and/or unconventional superconductors over the last three decades, recent works on new superconductors have focused on various kinds of materials, which includes complicated compounds and pure metals as well. Among them, high-entropy-alloy

HEA is an alloy possessing high configurational mixing entropy (Δ*S*mix), which is achieved by making the alloy with more than five constituent elements with an occupancy ranging 5 to 35 at% for each element [16, 17]. Typically, Δ*S*mix of HEA is calculated by Δ*S*mix = −*R* Σi *c*i ln *c*i, where *c*i and *R* are the compositional ratio and the gas constant [17], and reaches 1.5*R*. Due to high Δ*S*mix, HEAs exhibit stability or high performance in high temperature and/or extreme conditions [17]. Therefore, HEAs have been extensively studied in the fields of materials science and engineering. In 2014, Koželj et al. reported superconductivity with *T*c = 7.3 K in a HEA Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 [18]. The HEA superconductor has a bcc structure with a space group of *Im*-3 *m*. In **Figure 1**, we compare the crystal structures of (a) a pure Nb metal (*T*c = 9.2 K), (b) a NbTi alloy (*T*c ~ 10 K), which is the mostly-used practical superconductor, and (c) HEA Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. All those materials show superconductivity and the crystal structure type is the same. The difference between them is the mixing entropy Δ*S*mix and *T*c. Although the *T*c of HEA is lower than that of the other two, it was surprising for researchers that such a disordered alloy exhibits superconductivity with bulk nature. After the discovery of Ref. [18], various HEA superconductors have been developed; material information [18–26] is listed in **Table 1**.

(HEA) superconductors have been a developing field of study [15].

As shown in **Figure 2**, a superconducting transition was observed in

Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 [18]. The temperature dependence of electrical resistivity (**Figure 2(a)**) shows metallic behavior but exhibits a relatively small residual resistivity ratio (*RRR*) at low temperatures. This would be due to the presence of disorder, and a similar trend has been observed in various HEA-type superconductors. Bulk superconductivity could be confirmed through specific heat measurement as shown in **Figure 2(b)**. From specific heat data, it has been found that most HEA superconductors exhibit conventional (phonon-mediated) pairing states.

*T*c of HEA superconductors show correlation with valence electron count (VEC) [15, 21, 27]. The type-A HEAs with lower VEC exhibit a dependence of *T*c on VEC

**4**

*Schematic image of crystal structure of (a) Nb (pure metal), (b) NbTi (alloy), and (c) Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 (HEA).*

similar to that for crystalline metals, alloys, and amorphous materials, and the *T*c of HEAs are intermediate between crystalline materials and amorphous. In contrast, the *T*c of the type-C HEAs with middle VEC shows opposite behavior to that for other forms. For the type-B HEAs, the trend of *T*c on VEC seems resembling that for other forms, but their *T*cs are clearly lower than that for crystalline and amorphous materials. As mentioned in Ref. [15], there would be a clear effect of crystallinity on *T*c at the same VEC range, but the origin of the different trends between type-A, type-B, and type-C regimes have not been clarified from physical viewpoint (**Figure 3**).

Another notable character of HEA is a robustness of superconductivity to extremely high pressure. As reported in Ref. [20], the *T*c of Ta-Nb-Hf-Zr-Ti slightly increases by external pressure effect and the 10 K-class *T*c maintains under extreme pressures like 200 GPa. However, the robustness of superconductivity to extremely high pressure was reported for simpler NbTi with a clear increase in *T*c to 19.1 K at 261 GPa [28]. Therefore, the issue if HEA can improve the stability of superconductor under extremely high pressures has not been clarified.

### **1.3 Concept of HEA-type compounds**

As described in subsection 1–2, superconductivity in HEAs has been discovered and been regarded as a new research field of superconductivity. However, the merit of HEA states for superconductors has not been fully understood. Therefore, development of new types of HEA superconductors is needed. The hint to expand the material variation of HEA superconductors was proposed in Ref. [29], in which a HEA superconductor with a CsCl-type structure was reported. Since the CsCl structure contains two independent crystallographic sites, we have flexibility of elemental solution at the two sites. When calculating total Δ*S*mix of (ScZrNbTa)0.65(RhPd)0.35 by taking the sum of Δ*S*mixs for site-1 and site-2, it appears to reach very high Δ*S*mix of 1.79*R*. A similar site separation has been observed in (Nb0.11Re0.56)(HfZrTi)0.33 [30]. Motivated by those studies on HEAs with site separation, we have tried to synthesize various "*HEA-type compounds*", which contain NaCl-type metal chalcogenides [31–33], CuAl2-type tetragonal *Tr*Zr2 (*Tr*: Fe, Co, Ni, Cu, Rh, Ir) [34, 35], high-*T*c RE123 cuprates [36], and BiS2-based layered superconductors [37, 38]. The concept of HEA-type compounds it that we achieve a high Δ*S*mix by site-selective alloying. As shown in **Figure 4**, HEA-type compounds have a HEA-type site, in which five or more elements are solving and a normal site, which is not in the HEA state. The list of superconducting HEA-type compounds is shown in **Table 2**. By studying HEA effects to crystal structure and


#### **Table 1.**

*List of HEA superconductors and HEA-type superconducting compounds; composition, mixing entropy, Tc, and structural type are summarized.*

physical properties in various crystal structures, we could identify the merit of HEA states in those compounds. In section 2, we review the material synthesis, crystal structure, and physical properties of newly synthesized HEA-type compounds.

**7**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

*(a) Temperature dependence of electrical resistivity (ρ) of Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. (b) T2*

*where C is specific heat of Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. The figures were reproduced under permission by the authors of Ref. [18] (DOI: 10.1103/PhysRevLett.113.107001) and APS. Copyright 2014 by American Physical Society.*

*Valence electron count (VEC) dependence of Tc for classic crystalline alloys, amorphous alloys, and HEAs. The figure was reproduced under permission by the authors of Ref. [15] (10.1103/PhysRevMaterials.3.090301) and* 

> *ΔS***mix/***R* **(site2)**

(Nb0.11Re0.56)(HfZrTi)0.33 0.73 0.57 1.30 4.4 hcp [30]

(ScZrNbTa)0.65(RhPd)0.35 1.18 0.61 1.79 9.3 CsCl

(Ag0.2In0.2Sn0.2Pb0.2Bi0.2)Te 1.61 0 1.61 2.8 NaCl

*ΔS***mix/***R* **(Total)**

1.60 0 1.60 1.2 NaCl

1.59 0 1.59 1.4

1.59 0 1.59 0.7

1.61 0 1.61 1.0

1.60 0 1.60 1.0

1.61 0 1.61 1.0

**(site1)**

(ScZrNb)0.63(RhPd)0.37 1.16 0.62 1.79 7.5 (ScZrNb)0.62(RhPd)0.38 1.16 0.63 1.79 6.4 (ScZrNb)0.60(RhPd)0.40 1.14 0.64 1.78 3.9  *dependence of C/T,* 

*T***c (K) Structure Ref.**

*Pm*3*m*

*Fm*-3 *m*

*Fm*-3 *m*

[29]

[31]

[32]

**Figure 2.**

**Figure 3.**

Te1.05

Te1.03

Te1.02

Te1.03

Te1.00

Te0.97

*APS. Copyright 2019 by American Physical Society.*

**Composition** *ΔS***mix/***R*

(Ag0.20Cd0.20Sn0.20Sb0.15Pb0.20)

(Ag0.24In0.22Sn0.18Sb0.14Pb0.19)

(Ag0.22Cd0.22In0.23Sn0.17Sb0.14)

(Ag0.19Cd0.19Sn0.20Pb0.18Bi0.21)

(Ag0.21Cd0.19In0.25Pb0.16Bi0.18)

(Ag0.21Cd0.21In0.24Sn0.19Bi0.19)

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

**Figure 2.**

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

(TaNb)0.7(ZrHfTi)0.33 1.24 7.8 bcc (TaNb)0.7(ZrHfTi)0.4 1.31 7.6 bcc (TaNb)0.7(ZrHfTi)0.5 1.39 6.5 bcc (TaNb)0.7(ZrHfTi)0.84 1.60 4.5 bcc (TaNb)0.67(Hf)0.33 1.10 7.3 bcc (TaNb)0.67(HfZr)0.33 1.33 6.6 bcc Nb0.67(HfZrTi)0.33 1.00 9.2 bcc (NbV)0.67(HfZrTi)0.33 1.46 7.2 bcc (TaV)0.67(HfZrTi)0.33 1.46 4.0 bcc (TaNb)0.67(HfZrTi)0.33 1.46 7.3 bcc (TaNbV)0.67(HfZrTi)0.33 1.73 4.3 bcc

**Composition** *ΔS***mix/***R T***c (K) Structure Ref.** Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11 1.45 7.3 bcc [18, 19] (TaNb)0.67(HfZrTi)0.33 1.46 7.7 bcc [20] (TaNb)0.7(ZrHfTi)0.3 1.43 8.0 bcc [21]

Hf0.21Nb0.25Ti0.15V0.15Zr0.24 1.59 5.3 bcc [22] Ta0.35Nb0.35Zr0.15Ti0.15 1.30 8.0 bcc [23] (ZrNb)0.2(MoReRu)0.8 1.52 4.2 bcc [24]

(ZrNb)0.1(MoReRu)0.9 1.38 5.3 bcc (HfTaWIr)0.6Re0.4 1.50 1.9 bcc + hcp (HfTaWIr)0.5Re0.5 1.39 2.7 bcc + hcp (HfTaWIr)0.4Re0.6 1.23 4.0 bcc (HfTaWIr)0.3Re0.7 1.03 4.5 bcc (HfTaWIr)0.2Re0.8 0.78 5.7 bcc (HfTaWPt)0.5Re0.5 1.39 2.2 bcc + hcp (HfTaWPt)0.4Re0.6 1.23 4.4 bcc (HfTaWPt)0.3Re0.7 1.03 5.7 bcc (HfTaWPt)0.25Re0.75 0.91 6.1 bcc

physical properties in various crystal structures, we could identify the merit of HEA states in those compounds. In section 2, we review the material synthesis, crystal structure, and physical properties of newly synthesized HEA-type compounds.

(TaNb)0.31(TiUHf)0.69 1.59 3.2 bcc [26]

*List of HEA superconductors and HEA-type superconducting compounds; composition, mixing entropy, Tc, and* 

Nb26.1Ta25.1Ti23.4Zr0.254 1.39 8.3 bcc [25]

Nb0.198Ta0.189Ti0.208Zr0.187Hf0.218 1.61 7.1 bcc Nb0.163Ta0.157Ti0.169Zr0.171Hf0.175V0.165 1.79 5.1 bcc Nb0.2Ta0.2Ti0.2Zr0.2Fe0.2 1.61 6.9 bcc Nb0.2Ta0.2Ti0.2Zr0.2Ge0.2 1.61 8.4 bcc Nb0.2Ta0.2Ti0.2Zr0.2Si0.2V0.2 1.79 4.3 bcc Nb0.2Ta0.2Ti0.2Zr0.2Si0.2Ge0.2 1.79 7.4 bcc

**6**

**Table 1.**

*structural type are summarized.*

*(a) Temperature dependence of electrical resistivity (ρ) of Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. (b) T2 dependence of C/T, where C is specific heat of Ta0.34Nb0.33Hf0.08Zr0.14Ti0.11. The figures were reproduced under permission by the authors of Ref. [18] (DOI: 10.1103/PhysRevLett.113.107001) and APS. Copyright 2014 by American Physical Society.*

#### **Figure 3.**

*Valence electron count (VEC) dependence of Tc for classic crystalline alloys, amorphous alloys, and HEAs. The figure was reproduced under permission by the authors of Ref. [15] (10.1103/PhysRevMaterials.3.090301) and APS. Copyright 2019 by American Physical Society.*


#### *Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*


#### **Table 2.**

*List of HEA-type superconducting compounds; composition, mixing entropy (site-1, site-2, total), Tc, and structural type are summarized.*

### **2. NaCl-type metal chalcogenides** *MCh*

#### **2.1 Metal tellurides** *M***Te**

The NaCl-type metal telluride family is one of the hot systems because it includes thermoelectric PbTe [40] and a topological crystalline insulator SnTe [41]. For superconducting tellurides, high-pressure synthesis was used to stabilize the NaCltype structure [42–44]. For example, the low-pressure phase of InTe has a TlSe-type structure, but the high-pressure phase of InTe has a NaCl-type structure. The highpressure phase can be obtained by high-pressure synthesis [43, 44]. Motivated by

**9**

**Figure 5.**

**Figure 4.**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

**2.2 Hybrid high-entropy alloying in** *MCh*

these facts, we tried to synthesize HEA-type tellurides *M*Te where the *M* site is in the

HEA state (see **Figure 4(b)** for crystal structure) by high-pressure synthesis. **Figure 5(a)** shows the temperature dependence of electrical resistivity for AgInSnPbBiTe5, in which the *M* site is evenly occupied by Ag, In, Sn, Pb, and Bi (five metals) [31]. Very small *RRR* was observed, which is a similar trend to that in HEA superconductors [18]. In addition, four different *M*Te (*M*: Ag, In, Cd, Sn, Sb, Pb, Bi) superconductors with a HEA-type site has been obtained [32]. Interestingly, there is a correlation between the lattice constant and *T*c in HEA-type *M*Te. In **Figure 5(b)**, the data for typical *M*Te superconductors are plotted. It is found that the trend that *T*c increases with increasing lattice constant is common among the plotted *M*Te. The *T*cs of HEA-type are, however, lower than those of low-entropy tellurides, such as InTe and (In,Sn)Te. Therefore, the introduction of the HEA-type *M* site is found to negatively work for *T*c in MTe. This negative effect would be due to the direct effect

of strong disorder to the *M*-Te bonding states and hence electronic states.

*Crystal structure images of conventional HEA (a) and HEA-type compounds (b–e).*

*M site. Original data has been published in Ref. [32]. Copyright 2020 by IOP.*

The Te site of *M*Te can be substituted by S and Se. The flexibility of both *M* and Te sites to element substitution enables us to design "*hybrid HEA*", in which both sites are alloyed [33]. **Figure 6(a)** shows the X-ray diffraction patterns for

*(a) Temperature dependence of the electrical resistivity of AgInSnPbBiTe5. Original data has been published in Ref. [31]. Copyright 2019 by the Physical Society of Japan. (b) Relationship between lattice constant and Tc for metal tellurides including HEA-type tellurides. The elements written in the figure indicate compositions of the* 

#### *Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

(Ag0.24In0.22Pb0.27Bi0.26)Te1.02 1.37 0.00 1.37 2.7 NaCl

(Co0.2Ni0.1Cu0.1Rh0.3Ir0.3)Zr2 1.47 0 1.47 7.8 CuAl2

*ΔS***mix/***R* **(site2)**

1.38 0.51 1.89 2.5

1.35 0.65 2.00 2.0

1.48 0 1.48 6.7

1.61 0 1.61 5.4

1.52 0 1.52 4.8

1.77 0 1.77 93.0

1.50 0.69 2.20 4.7

1.50 0.69 2.20 4.9

1.49 0 1.49 4.3

1.60 0 1.60 3.3

1.52 0 1.52 4.6

*ΔS***mix/***R* **(Total)**

1.50 0 1.50 7.8 CuAl2

1.59 0 1.59 93.0 Layered

1.61 0.69 2.30 4.3 Layered

1.50 0.69 2.20 3.4 Layered

1.50 0 1.50 3.4 Layered

*T***c (K) Structure Ref.**

*Fm*-3 *m*

*I*4/*mcm*

*I*4/*mcm*

*Pmmm*

*P*4/*nmm*

*P*4/*nmm*

*P*4/*nmm*

[33]

[34]

[35]

[36]

[37, 38]

[37]

[39]

**(site1)**

**Composition** *ΔS***mix/***R*

(Ag0.29In0.26Pb0.22Bi0.24) (Te0.78Se0.20)

(Ag0.34In0.15Pb0.24Bi0.29) (Te0.65Se0.34)

(Fe0.093Co0.194Ni0.113Rh0.271Ir0

(Fe0.108Co0.297Ni0.202Rh0.073

(Fe0.190Co0.190Ni0.200Rh0.212

(Fe0.293Co0.190Ni0.300Rh0.093

(Y0.28Nd0.16Sm0.18Eu0.18Gd0.20)

(Y0.18La0.24Nd0.14Sm0.14Eu0.15 Gd0.15)Ba2Cu3O7-*<sup>d</sup>*

(La0.2Ce0.2Pr0.2Nd0.2Sm0.2)

(La0.3Ce0.3Pr0.2Nd0.1Sm0.1)

(La0.1Ce0.1Pr0.3Nd0.3Sm0.2)

(La0.1Ce0.1Pr0.2Nd0.3Sm0.3)

(La0.28Ce0.32Pr0.21Nd0.09Sm0.10)

(La0.10Ce0.29Pr0.33Nd0.19Sm0.09)

(La0.23Ce0.21Pr0.19Nd0.19Sm0.17)

(La0.09Ce0.29Pr0.12Nd0.21Sm0.29)

.329)Zr2

Ir0.320)Zr2

Ir0.208)Zr2

Ir0.124)Zr2

Ba2Cu3O7-*<sup>d</sup>*

O0.5F0.5BiS2

O0.5F0.5BiS2

O0.5F0.5BiS2

O0.5F0.5BiS2

BiS2

BiS2

BiS2

BiS2

**Table 2.**

**8**

**2. NaCl-type metal chalcogenides** *MCh*

The NaCl-type metal telluride family is one of the hot systems because it includes

thermoelectric PbTe [40] and a topological crystalline insulator SnTe [41]. For superconducting tellurides, high-pressure synthesis was used to stabilize the NaCltype structure [42–44]. For example, the low-pressure phase of InTe has a TlSe-type structure, but the high-pressure phase of InTe has a NaCl-type structure. The highpressure phase can be obtained by high-pressure synthesis [43, 44]. Motivated by

*List of HEA-type superconducting compounds; composition, mixing entropy (site-1, site-2, total), Tc, and* 

**2.1 Metal tellurides** *M***Te**

*structural type are summarized.*

these facts, we tried to synthesize HEA-type tellurides *M*Te where the *M* site is in the HEA state (see **Figure 4(b)** for crystal structure) by high-pressure synthesis.

**Figure 5(a)** shows the temperature dependence of electrical resistivity for AgInSnPbBiTe5, in which the *M* site is evenly occupied by Ag, In, Sn, Pb, and Bi (five metals) [31]. Very small *RRR* was observed, which is a similar trend to that in HEA superconductors [18]. In addition, four different *M*Te (*M*: Ag, In, Cd, Sn, Sb, Pb, Bi) superconductors with a HEA-type site has been obtained [32]. Interestingly, there is a correlation between the lattice constant and *T*c in HEA-type *M*Te. In **Figure 5(b)**, the data for typical *M*Te superconductors are plotted. It is found that the trend that *T*c increases with increasing lattice constant is common among the plotted *M*Te. The *T*cs of HEA-type are, however, lower than those of low-entropy tellurides, such as InTe and (In,Sn)Te. Therefore, the introduction of the HEA-type *M* site is found to negatively work for *T*c in MTe. This negative effect would be due to the direct effect of strong disorder to the *M*-Te bonding states and hence electronic states.

## **2.2 Hybrid high-entropy alloying in** *MCh*

The Te site of *M*Te can be substituted by S and Se. The flexibility of both *M* and Te sites to element substitution enables us to design "*hybrid HEA*", in which both sites are alloyed [33]. **Figure 6(a)** shows the X-ray diffraction patterns for

**Figure 4.**

*Crystal structure images of conventional HEA (a) and HEA-type compounds (b–e).*

#### **Figure 5.**

*(a) Temperature dependence of the electrical resistivity of AgInSnPbBiTe5. Original data has been published in Ref. [31]. Copyright 2019 by the Physical Society of Japan. (b) Relationship between lattice constant and Tc for metal tellurides including HEA-type tellurides. The elements written in the figure indicate compositions of the M site. Original data has been published in Ref. [32]. Copyright 2020 by IOP.*

#### **Figure 6.**

*(a) X-ray diffraction patterns for hybrid-HEA-type (Ag0.25In0.25Pb0.25Bi0.25)Te1-xSex. (b) Schematic image of the crystal structure and mixing entropy for x = 0.25 (c) temperature dependences of electrical resistivity (Ag0.25In0.25Pb0.25Bi0.25)Te1-xSex under magnetic fields. (d) Temperature dependence of magnetic susceptibility. The inset shows the magnetization-field curves. Original data has been published in Ref. [33]. Copyright 2020 by the Royal Society of Chemistry.*

(Ag0.25In0.25Pb0.25Bi0.25)Te1-*x*Sex. Notably, mixing many elements at two sites does not result in phase separation, and a single-phase sample was obtained for *x* = 0.25, while small impurity phases were detected for *x* = 0.5. For *x* = 0.25, as displayed in **Figure 6(b)**, the Δ*S*mix for the *M* and *Ch* sites are 1.38*R* and 0.51*R*, and the total Δ*S*mix reaches 1.89*R*. Furthermore, the total Δ*S*mix for *x* = 0.5 reaches 2.00*R*. These Δ*S*mix values are clearly higher than that for HEAs (**Table 1**). Therefore, alloying at two or more sites (hybrid high-entropy alloying) results in very high total Δ*S*mix.

**11**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

suppression of *T*c could be solved.

**3. CuAl2-type** *Tr***Zr2**

The superconducting properties for (Ag0.25In0.25Pb0.25Bi0.25)Te1-*x*Sex are shown in **Figure 6(c)**. A superconducting transition with *T*c > 2 K was observed for *x* = 0 and 0.25. By focusing on these two phases, interesting trend was found. Although the *T*c for *x* = 0.25 is lower than that for *x* = 0, the suppression of *T*c for *x* = 0.25 under magnetic fields is clearly smaller than that for *x* = 0. From the estimation of upper critical field (*H*c2), it was found that the *H*c2 (0 K) for *x* = 0.25 is higher than that for *x* = 0. In addition, from the measurements of the magnetization-field loop, it was confirmed that the critical current density (*J*c) at 1.8 K for *x* = 0.25 is larger than that for *x* = 0. These results suggest that an increase in Δ*S*mix may be useful to improve *H*c2 and/or *J*c characteristics of superconductors if the problem on the

As shown in the last section, high-entropy alloying of a compound, which possesses two or more crystallographic sites, is a route to develop new superconductors with a high mixing entropy. In addition, in HEA-type compounds, not only the site entropy but also the entropy of chemical bonding states should be higher than normal alloys or compounds. To discover new HEA-type superconductors, the use of material database is quite useful. SuperCon (NIMS database) [45] is a database of superconductors and contain information of composition, structural type, *T*c, and reference of the material. To achieve the material design of HEA-type superconductors, we have to find a system in which compositional variation is rich within the same structural type, and superconducting transition has been observed. Herein, we introduce an example of material design for new HEA-type superconductors. *Tr*Zr2 (*T*r: transition metal) with a tetragonal CuAl2-type structure (**Figure 4(c)**) is a superconducting system. For *Tr* = Fe, Co, Ni, Rh, Ir, superconductivity was reported. Among them, CoZr2, RhZr2, and IrZr2 exhibits a higher *T*c of 5.5, 11.3, and 7.5 K, respectively [46]. Furthermore, the *Tr* site can be partially substituted by Sc, Cu, Ga, Pd, and Ta [34, 45]. These facts suggest that the *Tr* site of *Tr*Zr2 can be modified into a HEA-type site. We synthesized Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 by arc melting and observed superconductivity with a *T*c of 8 K [34]. The *Tr* site of Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 contains five transition metals, and the Δ*S*mix for the *Tr* site is about 1.5*R*. In addition, (Fe,Co,Ni,Rh,Ir) Zr2 superconductors were also synthesized and exhibited superconductivity [35]. Interestingly, the resulting *T*c in HEA-type phases was very close to the weightedaverage *T*c of pure *Tr*Zr2 systems. Although the origin of the unexpected behavior is still unclear, the effects of disordering by the HEA-type site to superconducting properties seem very limited. The difference in the HEA effects between *MCh* and

*Tr*Zr2 may be caused by the different structural complexity.

local phase separation in HEA-type superconducting compounds.

As shown in **Figure 7(a)**, the temperature dependence of resistivity exhibits a relatively large *RRR* as compared to other HEA-type superconductors. However, a large *RRR* of ~30 was reported for CoZr2 single crystals [47], which is clearly larger than that for HEA-type *Tr*Zr2. Therefore, the HEA effects (disordering effects) to transport properties would be a common trend. **Figure 7(b)** shows the temperature dependences of the specific heat for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 in the form of *C*/*T*. Although a clear jump of *C*/*T* at the *T*c is seen, the transition is broader as compared to the case of CoZr2. The trend of broad transition in specific heat at *T*<sup>c</sup> was not observed in a HEA superconductor but observed in HEA-type compounds. Because the superconducting transitions observed in resistivity and magnetization were sharp, the broad transition in the specific heat would suggest microscopic

The superconducting properties for (Ag0.25In0.25Pb0.25Bi0.25)Te1-*x*Sex are shown in **Figure 6(c)**. A superconducting transition with *T*c > 2 K was observed for *x* = 0 and 0.25. By focusing on these two phases, interesting trend was found. Although the *T*c for *x* = 0.25 is lower than that for *x* = 0, the suppression of *T*c for *x* = 0.25 under magnetic fields is clearly smaller than that for *x* = 0. From the estimation of upper critical field (*H*c2), it was found that the *H*c2 (0 K) for *x* = 0.25 is higher than that for *x* = 0. In addition, from the measurements of the magnetization-field loop, it was confirmed that the critical current density (*J*c) at 1.8 K for *x* = 0.25 is larger than that for *x* = 0. These results suggest that an increase in Δ*S*mix may be useful to improve *H*c2 and/or *J*c characteristics of superconductors if the problem on the suppression of *T*c could be solved.

## **3. CuAl2-type** *Tr***Zr2**

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

*(a) X-ray diffraction patterns for hybrid-HEA-type (Ag0.25In0.25Pb0.25Bi0.25)Te1-xSex. (b) Schematic image of the crystal structure and mixing entropy for x = 0.25 (c) temperature dependences of electrical resistivity (Ag0.25In0.25Pb0.25Bi0.25)Te1-xSex under magnetic fields. (d) Temperature dependence of magnetic susceptibility. The inset shows the magnetization-field curves. Original data has been published in Ref. [33]. Copyright 2020* 

(Ag0.25In0.25Pb0.25Bi0.25)Te1-*x*Sex. Notably, mixing many elements at two sites does not result in phase separation, and a single-phase sample was obtained for *x* = 0.25, while small impurity phases were detected for *x* = 0.5. For *x* = 0.25, as displayed in **Figure 6(b)**, the Δ*S*mix for the *M* and *Ch* sites are 1.38*R* and 0.51*R*, and the total Δ*S*mix reaches 1.89*R*. Furthermore, the total Δ*S*mix for *x* = 0.5 reaches

2.00*R*. These Δ*S*mix values are clearly higher than that for HEAs (**Table 1**). Therefore, alloying at two or more sites (hybrid high-entropy alloying) results in

**10**

**Figure 6.**

*by the Royal Society of Chemistry.*

very high total Δ*S*mix.

As shown in the last section, high-entropy alloying of a compound, which possesses two or more crystallographic sites, is a route to develop new superconductors with a high mixing entropy. In addition, in HEA-type compounds, not only the site entropy but also the entropy of chemical bonding states should be higher than normal alloys or compounds. To discover new HEA-type superconductors, the use of material database is quite useful. SuperCon (NIMS database) [45] is a database of superconductors and contain information of composition, structural type, *T*c, and reference of the material. To achieve the material design of HEA-type superconductors, we have to find a system in which compositional variation is rich within the same structural type, and superconducting transition has been observed. Herein, we introduce an example of material design for new HEA-type superconductors.

*Tr*Zr2 (*T*r: transition metal) with a tetragonal CuAl2-type structure (**Figure 4(c)**) is a superconducting system. For *Tr* = Fe, Co, Ni, Rh, Ir, superconductivity was reported. Among them, CoZr2, RhZr2, and IrZr2 exhibits a higher *T*c of 5.5, 11.3, and 7.5 K, respectively [46]. Furthermore, the *Tr* site can be partially substituted by Sc, Cu, Ga, Pd, and Ta [34, 45]. These facts suggest that the *Tr* site of *Tr*Zr2 can be modified into a HEA-type site. We synthesized Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 by arc melting and observed superconductivity with a *T*c of 8 K [34]. The *Tr* site of Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 contains five transition metals, and the Δ*S*mix for the *Tr* site is about 1.5*R*. In addition, (Fe,Co,Ni,Rh,Ir) Zr2 superconductors were also synthesized and exhibited superconductivity [35]. Interestingly, the resulting *T*c in HEA-type phases was very close to the weightedaverage *T*c of pure *Tr*Zr2 systems. Although the origin of the unexpected behavior is still unclear, the effects of disordering by the HEA-type site to superconducting properties seem very limited. The difference in the HEA effects between *MCh* and *Tr*Zr2 may be caused by the different structural complexity.

As shown in **Figure 7(a)**, the temperature dependence of resistivity exhibits a relatively large *RRR* as compared to other HEA-type superconductors. However, a large *RRR* of ~30 was reported for CoZr2 single crystals [47], which is clearly larger than that for HEA-type *Tr*Zr2. Therefore, the HEA effects (disordering effects) to transport properties would be a common trend. **Figure 7(b)** shows the temperature dependences of the specific heat for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 in the form of *C*/*T*. Although a clear jump of *C*/*T* at the *T*c is seen, the transition is broader as compared to the case of CoZr2. The trend of broad transition in specific heat at *T*<sup>c</sup> was not observed in a HEA superconductor but observed in HEA-type compounds. Because the superconducting transitions observed in resistivity and magnetization were sharp, the broad transition in the specific heat would suggest microscopic local phase separation in HEA-type superconducting compounds.

**Figure 7.**

*(a) Temperature dependence of resistivity for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2. (b) Temperature dependence of specific heat (C/T) for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 at 0 and 9 T. Original data has been published in Refs. [34] and [35]. Copyright 2020 by Taylor & Francis.*

## **4. Cuprate (high-***T***c) superconductors** *RE***Ba2Cu3O7-***<sup>d</sup>*

As mentioned in introduction, cuprates (Cu oxides) have been extensively studied in the fields of science and engineering because of its high *T*c. Among them, *RE*Ba2Cu3O7-*d* (*RE*123) system [5] is one of practical materials for superconductivity

#### **Figure 8.**

*Orthorhombicity parameter (2|a-b|/(a + b)) dependences of (a) Tc and (b) magnetic Jc (T = 2 K, B = 1 T) for REBa2Cu3O7-d. Original data has been published in Ref. [36]. Copyright 2020 by Elsevier.*

**13**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

cuprate superconductors.

BiS2-based compounds [51].

application. In addition, a high *J*c was reported in *RE*123 samples with three elements at the *RE* site [48]. Motivated by the fact, we synthesized polycrystalline samples of *RE*Ba2Cu3O7-*d* with different Δ*S*mix for the *RE* site [36] by standard solidstate reaction in air. In the study, two-step annealing was performed to optimize oxygen content (*d*) because oxygen content affect crystal structure (orthorhombicity) and superconducting properties of *RE*Ba2Cu3O7-*d*. A high superconducting property is generally achieved in an orthorhombic phase in the system, we estimated the orthorhombicity parameter (*OP*), which is given by 2|*a*-*b*|/(*a* + *b*), and plotted the estimated *T*c and magnetic *J*c (*T* = 2 K, *B* = 1 T) for *RE*Ba2Cu3O7-*d* as a function of *OP* as shown in **Figure 8**. Note that the data points are colored according to the number of elements contained at the RE site. From the plot, it is found that Tc does not show a remarkable correlation with Δ*S*mix (RE site) and exhibits a clear correlation with *OP*. *J*c also exhibits a trend of improvement with increasing *OP*. These facts suggest that disorder introduced by high-entropy alloying at the *RE* site (see **Figure 4(d)**) does not largely affect superconducting properties of *RE*Ba2Cu3O7-*d*, which is a two-dimensional layered compound. Because the trend is clearly different to that observed for cubic (NaCl-type) tellurides with a HEA-type site, crystal-structure dimensionality is a key factor to how the introduction of

HEA-type site affects superconducting properties in compounds.

**5. BiS2-based layered superconductors** *RE***(O,F)BiS2**

In **Figure 8(b)**, we found three data points for HEA-type samples show a *J*c larger than that for the other low-entropy samples at *OP* = 0.01–0.015. Although it has not been fully clarified whether the slightly large *J*cs in the HEA-type samples are caused by high-entropy alloying or not, the effect of high-entropy alloying for cuprates should be further studied to find the way to improve practical performance of

BiS2-based superconductor family is one of the layered superconductor families and was discover in 2012 [49–51]. The crystal structure is composed of alternate stacks of a conducting BiS2 bilayer and a blocking layer (for example, a *RE*O layer), which is similar to that of high-*T*c systems. Furthermore, unconventional superconductivity has been proposed from theoretical and experimental studies on the

A typical BiS2-based system is *RE*OBiS2 (see **Figure 4(e)**). Because non-doped REOBiS2 is a semiconductor, electron carrier doping is required to induce metallicity [50]. For *RE* = La, a superconducting transition was observed at 2.5 K after electron doping through partial substitution of O by F in LaO0.5F0.5BiS2. However, the superconductivity states in La(O,F)BiS2 is not bulk in nature. This is due to the presence of the local disorder due to Bi lone pairs, and the local disorder could be suppressed by in-plane chemical pressure effects [52–54]. In-plane chemical pressure can be generated by *RE*-site substitution by smaller *RE* ions or Se substitution for the S site. By increasing in-plane chemical pressure, local disorder is suppressed, and bulk superconductivity is induced [52, 53]. Therefore, one can say that *RE*(O,F) BiS2 is a useful system to investigate the effect of structural modification on local crystal structure and superconducting properties. This suggests that the investigation of the effects of introduction of a HEA site in *RE*(O,F)BiS2 would provide us with key information about interlayer interaction through the HEA states.

The HEA-type samples of *RE*O0.5F0.5BiS2 with *RE* = La, Ce, Pr, Nd, Sm were synthesized by solid-state reaction in an evacuated quartz tube [37]. **Figure 9(a)** and **(b)** show superconducting properties of four different HEA-type *RE*O0.5F0.5BiS2 samples. The *T*c varies depending on the *RE*-site composition. As shown in **Figure 9(c)**, these

#### *Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

**4. Cuprate (high-***T***c) superconductors** *RE***Ba2Cu3O7-***<sup>d</sup>*

*and [35]. Copyright 2020 by Taylor & Francis.*

As mentioned in introduction, cuprates (Cu oxides) have been extensively studied in the fields of science and engineering because of its high *T*c. Among them, *RE*Ba2Cu3O7-*d* (*RE*123) system [5] is one of practical materials for superconductivity

*(a) Temperature dependence of resistivity for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2. (b) Temperature dependence of specific heat (C/T) for Co0.2Ni0.1Cu0.1Rh0.3Ir0.3Zr2 at 0 and 9 T. Original data has been published in Refs. [34]* 

*Orthorhombicity parameter (2|a-b|/(a + b)) dependences of (a) Tc and (b) magnetic Jc (T = 2 K, B = 1 T) for* 

*REBa2Cu3O7-d. Original data has been published in Ref. [36]. Copyright 2020 by Elsevier.*

**12**

**Figure 8.**

**Figure 7.**

application. In addition, a high *J*c was reported in *RE*123 samples with three elements at the *RE* site [48]. Motivated by the fact, we synthesized polycrystalline samples of *RE*Ba2Cu3O7-*d* with different Δ*S*mix for the *RE* site [36] by standard solidstate reaction in air. In the study, two-step annealing was performed to optimize oxygen content (*d*) because oxygen content affect crystal structure (orthorhombicity) and superconducting properties of *RE*Ba2Cu3O7-*d*. A high superconducting property is generally achieved in an orthorhombic phase in the system, we estimated the orthorhombicity parameter (*OP*), which is given by 2|*a*-*b*|/(*a* + *b*), and plotted the estimated *T*c and magnetic *J*c (*T* = 2 K, *B* = 1 T) for *RE*Ba2Cu3O7-*d* as a function of *OP* as shown in **Figure 8**. Note that the data points are colored according to the number of elements contained at the RE site. From the plot, it is found that Tc does not show a remarkable correlation with Δ*S*mix (RE site) and exhibits a clear correlation with *OP*. *J*c also exhibits a trend of improvement with increasing *OP*. These facts suggest that disorder introduced by high-entropy alloying at the *RE* site (see **Figure 4(d)**) does not largely affect superconducting properties of *RE*Ba2Cu3O7-*d*, which is a two-dimensional layered compound. Because the trend is clearly different to that observed for cubic (NaCl-type) tellurides with a HEA-type site, crystal-structure dimensionality is a key factor to how the introduction of HEA-type site affects superconducting properties in compounds.

In **Figure 8(b)**, we found three data points for HEA-type samples show a *J*c larger than that for the other low-entropy samples at *OP* = 0.01–0.015. Although it has not been fully clarified whether the slightly large *J*cs in the HEA-type samples are caused by high-entropy alloying or not, the effect of high-entropy alloying for cuprates should be further studied to find the way to improve practical performance of cuprate superconductors.

## **5. BiS2-based layered superconductors** *RE***(O,F)BiS2**

BiS2-based superconductor family is one of the layered superconductor families and was discover in 2012 [49–51]. The crystal structure is composed of alternate stacks of a conducting BiS2 bilayer and a blocking layer (for example, a *RE*O layer), which is similar to that of high-*T*c systems. Furthermore, unconventional superconductivity has been proposed from theoretical and experimental studies on the BiS2-based compounds [51].

A typical BiS2-based system is *RE*OBiS2 (see **Figure 4(e)**). Because non-doped REOBiS2 is a semiconductor, electron carrier doping is required to induce metallicity [50]. For *RE* = La, a superconducting transition was observed at 2.5 K after electron doping through partial substitution of O by F in LaO0.5F0.5BiS2. However, the superconductivity states in La(O,F)BiS2 is not bulk in nature. This is due to the presence of the local disorder due to Bi lone pairs, and the local disorder could be suppressed by in-plane chemical pressure effects [52–54]. In-plane chemical pressure can be generated by *RE*-site substitution by smaller *RE* ions or Se substitution for the S site. By increasing in-plane chemical pressure, local disorder is suppressed, and bulk superconductivity is induced [52, 53]. Therefore, one can say that *RE*(O,F) BiS2 is a useful system to investigate the effect of structural modification on local crystal structure and superconducting properties. This suggests that the investigation of the effects of introduction of a HEA site in *RE*(O,F)BiS2 would provide us with key information about interlayer interaction through the HEA states.

The HEA-type samples of *RE*O0.5F0.5BiS2 with *RE* = La, Ce, Pr, Nd, Sm were synthesized by solid-state reaction in an evacuated quartz tube [37]. **Figure 9(a)** and **(b)** show superconducting properties of four different HEA-type *RE*O0.5F0.5BiS2 samples. The *T*c varies depending on the *RE*-site composition. As shown in **Figure 9(c)**, these

#### **Figure 9.**

*(a, b) Temperature dependences of (a) electrical resistivity and (b) magnetic susceptibility for HEA-type REO0.5F0.5BiS2. (c) Lattice constant a dependences of Tc and* Δ*4*π*χ (T = 2 K). Original data has been published in Ref. [37]. Copyright 2020 by IOP.*

four samples have different lattice constants *a*, which is corresponding to different in-plane chemical pressures. Therefore, the variation of *T*c can be understood with the in-plane chemical pressure scenario. When focusing on the samples with the same lattice constant *a* and different mixing entropy, we find that the superconducting properties (*T*c and Δ4πχ) of the HEA-type sample are higher than those of low-entropy samples (**Figures 9(c)** and **(d)**). The facts indicate that an increase in Δ*S*mix for the *RE* site may positively work in improving superconducting properties. Therefore, we systematically prepared *RE*O0.5F0.5BiS2 samples with the same lattice constant *a* and different Δ*S*mix to investigate the interlayer interaction [38].

As summarized in **Figure 10(a)**, we succeeded in preparation of a set of five *RE*O0.5F0.5BiS2 samples with almost the same *a* and systematically varied Δ*S*mix. Because the lattice constant *a* nearly corresponds to the degree of the in-plane chemical pressure, the set of samples have almost similar in-plane chemical pressure. Therefore, we could detect the effects of the increase in Δ*S*mix to superconducting properties and local structural disorder [38]. Through magnetic susceptibility measurements, we confirmed that shielding volume fraction increases with increasing Δ*S*mix while the *T*c does not change (**Figure 10(c)** and **(d)**). To understand the origin of the improvement of superconducting properties, local structure was analyzed using synchrotron X-ray diffraction. As summarized in **Figure 10(b)**, suppression of in-plane structural disorder, which was detected by anisotropic displacement parameter for the in-plane direction (*U*11), was achieved by the HEA effect at the *RE* site. Similar trend was observed in another set of *RE*O0.5F0.5BiS2 samples with larger lattice constant (comparable to that of CeO0.5F0.5BiS2). The results propose that high-entropy alloying at the blocking layer would modify

**15**

structure.

**Figure 10.**

**6. Conclusion**

*has been published in Ref. [38]. Copyright 2020 by Elsevier.*

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

the local structure at the conducting layer in BiS2-based layered compounds. This effect should be a new strategy to develop novel functional materials with a layered

*(a) Mixing entropy (*Δ*Smix) and lattice constant a are plotted as a function of the number of RE elements contained in the sample. (b) Schematic images of local structural disorder for low-entropy and HEA-type REO0.5F0.5BiS2. (c) Temperature dependences of 4*π*χ. (d)* Δ*Smix dependence of* Δ*4*π*χ (T = 2 K). Original data* 

In this chapter, we reviewed the works on HEA superconductors and HEA-type superconducting compounds, which have been developed applying the HEA concept in simple alloys to more complicated compounds. By introducing a HEA-type site (or alloying multi sites) in a compound, a high mixing entropy can be achieved. HEA-type compounds would have a high mixing entropy at the alloyed site and a highly (randomly) disordered bonding states. For a three-dimensional system, such as NaCl-type chalcogenides, introduction of the HEA-type *M* site in *MCh* resulted in suppression of *T*c, but, at the same time, slight enhancements of *H*c2 and *J*c were observed. For tetragonal (CuAl2-type) *Tr*Zr2, the introduction of the HEA-type site does not suppress *T*c. Furthermore, for layered systems, such as *RE*Ba2Cu3O7-*<sup>d</sup>* cuprates and BiS2-based *RE*0.5F0.5BiS2, high-entropy alloying rather improves their superconducting properties. Through investigations of the HEA effects to superconducting and structural properties for HEA-type compounds with different structural types, we conclude that the HEA effects are highly depending on the structural dimensionality. Hence, to effectively use the HEA effect to improve superconducting properties of compounds, target structure should be lower-symmetric, a layered *Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

#### **Figure 10.**

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

four samples have different lattice constants *a*, which is corresponding to different in-plane chemical pressures. Therefore, the variation of *T*c can be understood with the in-plane chemical pressure scenario. When focusing on the samples with the same lattice constant *a* and different mixing entropy, we find that the superconducting properties (*T*c and Δ4πχ) of the HEA-type sample are higher than those of low-entropy samples (**Figures 9(c)** and **(d)**). The facts indicate that an increase in Δ*S*mix for the *RE* site may positively work in improving superconducting properties. Therefore, we systematically prepared *RE*O0.5F0.5BiS2 samples with the same lattice

*(a, b) Temperature dependences of (a) electrical resistivity and (b) magnetic susceptibility for HEA-type REO0.5F0.5BiS2. (c) Lattice constant a dependences of Tc and* Δ*4*π*χ (T = 2 K). Original data has been published* 

constant *a* and different Δ*S*mix to investigate the interlayer interaction [38].

As summarized in **Figure 10(a)**, we succeeded in preparation of a set of five *RE*O0.5F0.5BiS2 samples with almost the same *a* and systematically varied Δ*S*mix. Because the lattice constant *a* nearly corresponds to the degree of the in-plane chemical pressure, the set of samples have almost similar in-plane chemical pressure. Therefore, we could detect the effects of the increase in Δ*S*mix to superconducting properties and local structural disorder [38]. Through magnetic susceptibility measurements, we confirmed that shielding volume fraction increases with increasing Δ*S*mix while the *T*c does not change (**Figure 10(c)** and **(d)**). To understand the origin of the improvement of superconducting properties, local structure was analyzed using synchrotron X-ray diffraction. As summarized in **Figure 10(b)**, suppression of in-plane structural disorder, which was detected by anisotropic displacement parameter for the in-plane direction (*U*11), was achieved by the HEA effect at the *RE* site. Similar trend was observed in another set of *RE*O0.5F0.5BiS2 samples with larger lattice constant (comparable to that of CeO0.5F0.5BiS2). The results propose that high-entropy alloying at the blocking layer would modify

**14**

**Figure 9.**

*in Ref. [37]. Copyright 2020 by IOP.*

*(a) Mixing entropy (*Δ*Smix) and lattice constant a are plotted as a function of the number of RE elements contained in the sample. (b) Schematic images of local structural disorder for low-entropy and HEA-type REO0.5F0.5BiS2. (c) Temperature dependences of 4*π*χ. (d)* Δ*Smix dependence of* Δ*4*π*χ (T = 2 K). Original data has been published in Ref. [38]. Copyright 2020 by Elsevier.*

the local structure at the conducting layer in BiS2-based layered compounds. This effect should be a new strategy to develop novel functional materials with a layered structure.

#### **6. Conclusion**

In this chapter, we reviewed the works on HEA superconductors and HEA-type superconducting compounds, which have been developed applying the HEA concept in simple alloys to more complicated compounds. By introducing a HEA-type site (or alloying multi sites) in a compound, a high mixing entropy can be achieved. HEA-type compounds would have a high mixing entropy at the alloyed site and a highly (randomly) disordered bonding states. For a three-dimensional system, such as NaCl-type chalcogenides, introduction of the HEA-type *M* site in *MCh* resulted in suppression of *T*c, but, at the same time, slight enhancements of *H*c2 and *J*c were observed. For tetragonal (CuAl2-type) *Tr*Zr2, the introduction of the HEA-type site does not suppress *T*c. Furthermore, for layered systems, such as *RE*Ba2Cu3O7-*<sup>d</sup>* cuprates and BiS2-based *RE*0.5F0.5BiS2, high-entropy alloying rather improves their superconducting properties. Through investigations of the HEA effects to superconducting and structural properties for HEA-type compounds with different structural types, we conclude that the HEA effects are highly depending on the structural dimensionality. Hence, to effectively use the HEA effect to improve superconducting properties of compounds, target structure should be lower-symmetric, a layered

structure or a one-dimensional structure. To obtain further knowledge about the presence/absence of local phase separations, pinning characteristics, and the HEA effect to superconducting pairing states, further investigations on HEA-type superconducting compounds using various probes are required.

## **Acknowledgements**

The author thanks R. Sogabe, Md. R. Kasem, Y. Shukunami, M. Katsuno, K. Hoshi, R. Jha, Y. Goto, T. D. Matsuda, and O. Miura who have contributed on the works reviewed here. The author would like to thank all the coauthors of the works. The works reviewed here were supported by JSPS-KAKENHI (Nos.: 16H04493, 15H05886, 18KK0076), JST-CREST (Nos.: JPMJCR16Q6, JPMJCR20Q4), and Tokyo Metropolitan Government Advanced Research (No.: H31-1).

## **Author details**

Yoshikazu Mizuguchi\* and Aichi Yamashita Department of Physics, Tokyo Metropolitan University, Hachioji, Japan

\*Address all correspondence to: mizugu@tmu.ac.jp

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**17**

*Superconductivity in HEA-Type Compounds DOI: http://dx.doi.org/10.5772/intechopen.96156*

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The author thanks R. Sogabe, Md. R. Kasem, Y. Shukunami, M. Katsuno, K. Hoshi, R. Jha, Y. Goto, T. D. Matsuda, and O. Miura who have contributed on the works reviewed here. The author would like to thank all the coauthors of the works. The works reviewed here were supported by JSPS-KAKENHI (Nos.: 16H04493, 15H05886, 18KK0076), JST-CREST (Nos.: JPMJCR16Q6, JPMJCR20Q4), and Tokyo

superconducting compounds using various probes are required.

Metropolitan Government Advanced Research (No.: H31-1).

**Acknowledgements**

**16**

**Author details**

Yoshikazu Mizuguchi\* and Aichi Yamashita

provided the original work is properly cited.

\*Address all correspondence to: mizugu@tmu.ac.jp

Department of Physics, Tokyo Metropolitan University, Hachioji, Japan

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[18] 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(1-5).

[19] Vrtnik S., Koželj P., Meden A., Maiti S., Steurer W., Feuerbacher M., Dolinšek J. Superconductivity in thermally annealed Ta-Nb-Hf-Zr-Ti high-entropy alloys. J. Alloy Compounds 2017;695 3530-3540.

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[33] 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

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Cava R. J. High-entropy alloy

**18**

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.

[34] Mizuguchi Y., Kasem Md. 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. 2021;9 141-147.

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[51] Mizuguchi Y. Material Development and Physical Properties of BiS2-Based Layered Compounds. J. Phys. Soc. Jpn. 2019;88 041001 (1-17).

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**21**

**Chapter 2**

**Abstract**

Mn5Si3-type

**1. Introduction**

Materials Research on

*Jiro Kitagawa, Naoki Ishizu and Shusuke Hamamoto*

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.

**Keywords:** high-entropy alloys, superconductivity, face-centered-cubic, niobium,

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

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

materials such as oxides, chalcogenides, and halides [6, 7].

High-Entropy Alloy

Superconductors

## **Chapter 2**

*Advances in High-Entropy Alloys - Materials Research, Exotic Properties and Applications*

[49] Mizuguchi Y., Fujihisa H.,

Demura S., Takano Y., Izawa H., Miura O. BiS2-based layered superconductor Bi4O4S3. Phys. Rev. B 2012;86

[50] Mizuguchi Y., Demura S., Deguchi K., Takano Y., Fujihisa H., Gotoh Y., Izawa H., Miura O. J. Phys. Soc. Jpn. 2012;81 114725(1-5).

2019;88 041001 (1-17).

Rep. 2015; 5 14968(1-8).

Jpn. 2018;87 023704 (1-4).

041004 (1-10).

220510(1-5).

Gotoh Y., Suzuki K., Usui H., Kuroki K.,

[51] Mizuguchi Y. Material Development and Physical Properties of BiS2-Based Layered Compounds. J. Phys. Soc. Jpn.

[52] Mizuguchi Y., Miura A., Kajitani J., Hiroi T., Miura O., Tadanaga K., Kumada N., Magome E., Moriyoshi C., Kuroiwa Y. In-plane chemical pressure essential for superconductivity in BiCh2 based (Ch: S, Se) layered structure. Sci.

[53] Mizuguchi Y., Hoshi K., Goto Y., Miura A., Tadanaga K., Moriyoshi C., Kuroiwa Y. Evolution of Anisotropic Displacement Parameters and Superconductivity with Chemical Pressure in BiS2-Based REO0.5F0.5BiS2 (RE = La, Ce, Pr, and Nd). J. Phys. Soc.

[54] Athauda A., Louca D. Nanoscale Atomic Distortions in the BiS2 Superconductors: Ferrodistortive Sulfur Modes. J. Phys. Soc. Jpn. 2019;88

**20**
