High-Entropy Alloys with Hexagonal Close-Packed Structure in Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 Alloys Designed by Sandwich Strategy for the Valence Electron Concentration of Constituent Elements in the Periodic Chart

Abstract

High-entropy alloys (HEAs) with a single hexagonal close-packed (hcp) structure were found in Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys annealed at 2373 K for 1 h. These HEAs were designed based on a sandwich strategy for valence electron concentration (VEC) of the constituent elements and by referring to their crystallographic structures in the periodic chart. The initial component and composition of these alloys were determined by considering exact and near equiatomic sub binary phase diagrams, followed by optimizing the composition by Thermo-Calc with the TCHEA3 database for HEAs as well as the SSOL5 database for solid solutions. The X-ray diffraction analysis, scanning electron microscopy observation, and energy-dispersive X-ray spectroscopy analysis revealed that the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys annealed at 2373 K for 1 h were formed in an hcp single phase. The formation of the hcp structure was principally evaluated by the VEC values of 7.855 and 7.865 for Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys, respectively, such that these values were close to VEC = 8 for pure elements Ru and Os with an hcp structure. It is considered that Ru is a strong hcp-forming element under this strategy because the other pure constituent elements have different crystallographic structures. The formation of Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 HEAs with an hcp structure is unique because these alloys, which consist of only transition metals, can be produced without applying high pressure, similar to a CrMnFeCoNi HEA with an hcp structure.

Property diagram calculated with Thermo-Calc 2018b and TCHEA3 database for (top) Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and (bottom) Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys, where inserts are (a) SEM image and (b–f) element-mapping images of the alloys annealed at 2373 K for 1 h and as-prepared samples.

1. Introduction

In this paper, we have described two alloys—Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5—that are different from conventional high-entropy alloys (HEAs)^1,2) because of the simultaneous achievement of the following four features during alloy formation:

1. (1)    A hexagonal close-packed (hcp) structure
2. (2)    Only transition metals as constituent elements
3. (3)    Ease of manufacture by conventional procedures, in that at ambient atmospheric pressure, without applying high pressure, and by a method of arc melting/high-frequency melting without involving a chemical reaction.

Moreover, feature (2) can be supplemented by another feature: (4) all components include 4d and 5d transition metals. Historically, conventional HEAs have been developed as the exact or near-equiatomic crystalline alloys consisting of five or more elements combined into a single body or face-centered cubic (bcc or fcc) or their mixed structure.^1,2) Thus, as described in feature (1), the presence of an hcp structure is the distinguishing factor for HEAs. In fact, only a few HEAs with the hcp structure have been reported till date by Takeuchi et al.,³⁾ Feuerbacher et al.,⁴⁾ Youssef et al.,⁵⁾ and Tracy et al.⁶⁾ In particular, the YGdTbDyLu and GdTbDyTmLu alloys³⁾ and Ho–Dy–Y–Gd–Tb alloy⁴⁾ comprising heavy lanthanide elements can be produced to exhibit an hcp structure. In addition, Youssef et al.⁵⁾ reported that the Al₂₀Li₂₀Mg₁₀Sc₂₀Ti₃₀ alloy prepared by a mechanical alloying process exhibits a single hcp structure from an initial fcc structure on annealing. These previously reported HEAs with an hcp structure cannot be categorized for possessing feature (2) of having only transition metals as their constituents.

More recently,⁶⁾ the synthesis of a CrMnFeCoNi HEA with an hcp structure under high pressure has been reported. The CrMnFeCoNi HEA with an hcp structure is unique, but it requires high pressure for its formation, i.e., it does not possess feature (3). Furthermore, a similar exception for feature (3) was reported by Yusenko et al.⁷⁾ for the Ir–Os–Re–Rh–Ru alloy comprising transition metals with near equiatomicity when it was produced as a HEA with a single phase by chemical reaction. The CrMnFeCoNi HEA with an hcp structure is composed of 3d transition metals only, and hence differs from the feature (4) as the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys consist of 4d or 5d transition metals. Thus, the revelation of HEAs with the simultaneous achievement of features (1) to (4) provided the motivation for the present study.

The purpose of this study was to determine hcp-structure-bearing HEAs comprising 4d and/or 5d transition metals that can be produced at atmospheric pressure by referring to binary phase diagrams and physical and thermodynamic quantities.

2. Methods

The HEAs with the hcp structure were mainly designed with the assistance of crystallographic structures of each constituent element, periodic chart, and sub binary phase diagrams. Moreover, the alloys were evaluated for the following thermodynamic and physical parameters: configuration entropy normalized with gas constant (S_config./R), delta (δ) parameter,⁸⁾ mixing enthalpy (ΔH_mix), and valence electron concentration (VEC).⁹⁾

2.1 Alloy design

The phase stability is first described by Miedema¹⁰⁾ and Friedel^11,12) models, followed by a process before selecting a sandwich strategy. A practical strategy for selecting an Ir₃₀Mo_22.5Rh₂₅Cr_12.5W₁₀ alloy as the first candidate is then described. Finally, the process of determining Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys as the final candidates is described along with the alloy design using thermodynamic calculations.

The alloy design started by focusing on the stability of the hcp phase. This study began with the selection of the HEA candidates with the hcp structure by identifying the pure elements from transition metals with the hcp structure at room temperature and by referring to the crystallographic structures of elements illustrated in the periodic chart.^13,14) As a result, Sc, Ti, Co, Tc, Ru, Re, and Os were initially selected as the constituent elements for alloying. Next, sub binary phase diagrams¹⁵⁾ of the above-selected constituent elements were examined carefully to determine the first candidates. In particular, special attention was paid to the presence of the hcp phase in the constituent binary phase diagrams near equiatomic composition. This attention for exact equiatomicity was previously examined as the Pettifor map for binary compounds with 1:1 stoichiometry.¹⁶⁾ Similarly, exact and near equiatomicity in the present study was regarded for a sandwich strategy in terms of the VEC of the constituent elements in the periodic chart and based on sub binary phase diagrams. The concept of this strategy from Miedema’s model^10,17) as shown in Fig. 1, was based on the structural stabilities, E_σ(Z), of paramagnetic transition metals in the three main crystallographic structures—hcp, fcc, and bcc—plotted versus Z, the average number of valence electrons per atom. As shown in Fig. 1, stable phases for integer values of Z are hcp (Z = 3 and 4), bcc (Z = 5 and 6), hcp (Z = 7 and 8), and fcc (Z = 9 and 10). YGdTbDyLu and GdTbDyTmLu HEAs with hcp structure³⁾ have been found by referring to Z = 3, and the present study aimed to find another type of HEA with an hcp structure in accordance with hcp (Z = 7 and 8). The hcp (Z = 7 and 8) is located in Fig. 1 in the region between bcc (Z = 5 and 6) and fcc (Z = 9 and 10), indicating that exact- or near-equiatomic alloys could be formed into alloys with the hcp structure by appropriately mixing the elements with bcc and fcc structure. This implication is a fundamental concept of the sandwich strategy and is partially supported by the Friedel model,^11,12) which states that the stability of the hcp structure is achieved when the number of d-electrons (n_d) is in the range^18,19) of 2.6 < n_d < 3.5 and 6.5 < n_d < 7.4 where n_d is its definition of wide sense including the number of outer s electrons and is equivalent to VEC.

Fig. 1

Structural stabilities, E_σ(Z), of paramagnetic transition metals in the three main crystallographic structures hcp, fcc and bcc plotted versus Z, the average number of valence electrons per atom.^10,17) Pure transition metals possess integer values of Z, whereas alloys can have decimal values of Z as well as integer values as the average number of valence electrons per atom from constituent elements. Reproduced with permission.¹⁷⁾

In practice, the application of the sandwich strategy was adopted as follows. First, the authors referred to binary phase diagrams¹⁵⁾ and found a solid solution with an hcp structure in Ir₆₀Mo₄₀, Ir₆₀W₄₀, Cr₅₀Rh₅₀, Mo₅₀Rh₅₀, etc. Neither Cr, Mo, and W with VEC (or Z) = 6 nor Ir and Rh with VEC = 9 from the periodic chart possess the hcp structure as pure elements. However, from Fig. 1, we can deduce that a possible reason for the Ir₆₀Mo₄₀, Ir₆₀W₄₀, Cr₅₀Rh₅₀, and Mo₅₀Rh₅₀ alloys to form the hcp structure is that the average value of Z was calculated to be 7.8 for the Ir₆₀Mo₄₀ and Ir₆₀W₄₀ alloys and 7.5 for the Cr₅₀Rh₅₀ and Mo₅₀Rh₅₀ alloys. Consequently, all four binary alloys are located in a region in Fig. 1 where the hcp structure is stable, as shown in dotted curves. Assembling the above four binary alloys with exact and near equiatomicity simply into a quaternary alloy led to an Ir₃₀Mo_22.5Rh₂₅Cr_12.5W₁₀ alloy as the first candidate. None of the constituent elements of the Ir₃₀Mo_22.5Rh₂₅Cr_12.5W₁₀ possesses the hcp structure as pure elements. Then, thermodynamic calculations were performed with Thermo-Calc 2017a with the SSOL5 database for solid solutions. The SSOL5 database was initially used instead of TCHEA2 in the database for HEA, because it was not possible to deal with Ir and Rh using the TCHEA2 database in April 2018. After that, the succeeding database to TCHEA2, TCHEA3 (Ver. 3.0), which was released in May 2018, was used as it could handle Ir and Rh. The first candidate was optimized by monitoring the appearance of a single hcp phase by varying the content of the alloys using the property diagram, as shown in Fig. 2, with axes of temperature and amount of all phases in mol. As a result, an optimized alloy composition was obtained in Ir₃₅Mo_22.5Rh₂₅Cr_12.5W₅. Figure 2(a) depicts the first candidate (Ir₃₀Mo_22.5Rh₂₅Cr_12.5W₁₀), whereas Fig. 2(b) demonstrates its optimized alloy (Ir₃₅Mo_22.5Rh₂₅Cr_12.5W₅); both the alloys demonstrated that an hcp phase can exist at T ∼ 2000 K, but they were different as the former alloy is a mixture of hcp and bcc, whereas the latter is a single hcp phase. Thus, there is a possibility that the Ir₃₅Mo_22.5Rh₂₅Cr_12.5W₅ alloy can be formed into a single hcp phase at a high-temperature of approximately 2000 K. However, the calculation showed that the Ir₃₅Mo_22.5Rh₂₅Cr_12.5W₅ alloy was stable only within a limited temperature range of 100 K: 2045–1945 K. Furthermore, it also became evident that the Ir₃₅Mo_22.5Rh₂₅Cr_12.5W₅ alloy was experimentally difficult to melt homogeneously because of the differences in vapor pressure and melting temperatures between Cr and W. Hence, we considered a third candidate by replacing Cr with Ru.

Fig. 2

Property diagram of (a) Ir₃₀Mo_22.5Rh₂₅Cr_12.5W₁₀ and (b) Ir₃₅Mo_22.5Rh₂₅Cr_12.5W₅ alloys calculated with Thermo-Calc 2017a and SSOL5 database for solid solutions: Ir–Mo–Rh–Cr–W alloys were not prepared in the present study, but their thermal stability is shown for comparison.

The sandwich strategy still works somehow in exact- or near-equiatomic Ir–Mo–Rh–Ru–W alloys regardless of the replacement of Ru with Cr, because Ru with a VEC (or Z) of 8 is put in Mo and W with VEC = 6 and Rh and Ir with VEC = 9. Besides, Ru has an hcp structure element, but other constituent elements in the Ir–Mo–Rh–Ru–W alloys possess other crystallographic structures, such as Mo and W have bcc and Ir and Rh have fcc structures. The difference in the combinations of VEC in the Ir₃₀Mo_22.5Rh₂₅Cr_12.5W₁₀ alloy and Ir–Mo–Rh–Ru–W alloys, was that VEC = 6 (Cr, Mo, and W) and VEC = 9 (Ir and Rh) in the former alloy as two-layered VECs, whereas the latter alloy was three-layered VECs with VEC = 6 (Mo and W), VEC = 8 (Ru), and VEC = 9 (Rh and Ir). Following the thermodynamic calculations, which are described in the next section, an Ir₃₀Mo₂₀Rh₂₀Ru₂₅W₅ alloy was successfully selected as the third candidate. Furthermore, TCHEA3, which successfully deals with Ir and Rh, was released and hence the further and precise optimization was conducted using Thermo-Calc 2018b with the TCHEA3 database. As a result, an Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloy was selected as a final candidate and an additional final candidate, Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 alloy, was selected from a prototypical Ir₂₀Mo₂₀Rh₂₀Ru₂₀W₂₀ alloy with exact equiatomicity.

2.2 Evaluation of quantities

The values of ΔH_mix were calculated based on eq. (1), in which its right-hand side has an assumption that ΔH_mix was calculated as a quadratic formula with a maximum or minimum at the equiatomic composition in an A–B alloy system. In reality, the equiatomic composition can be described as AB, A₅₀B₅₀, or A_0.5B_0.5, respectively, for the compound-, atomic-percentage-, or atomic-fraction-type. The factor four on the right-hand side of eq. (1) accounts for the value of ΔH_mix at the binary equiatomic alloy, A_0.5B_0.5, with c_i = c_j = 0.5,   

\begin{equation} \Delta H_{\text{mix}} = 4\sum_{\text{j}\neq\text{i}}^{\text{N}}\sum_{i = 1}^{\text{N}}\Delta H_{\text{ij}}c_{\text{i}}c_{\text{j}}. \end{equation} (1)

For calculating ΔH_mix, actual values of ΔH_ij were acquired from a previous work.²⁰⁾ However, δ was calculated using eqs. (2) and (3),⁸⁾   

\begin{equation} \delta = \sqrt{\sum_{\text{i} = 1}^{\text{N}}c_{\text{i}}\left(1 - \frac{r_{\text{i}}}{\bar{r}}\right)^{2}} \times 100, \end{equation} (2)

  

\begin{equation} \bar{r} = \sum_{i = 1}^{\text{N}}c_{\text{i}}r_{\text{i}}. \end{equation} (3)

Here, r_i is the atomic radius of the i-th constituent element and $\bar{r}$ is the average atomic radius of the alloy defined by eq. (3). The r_is of the 73 elements were acquired from the literature²¹⁾ and also from a previous work.²⁰⁾

In addition, the values of VEC⁹⁾ were calculated to clarify the characteristics of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys. The VEC was calculated by averaging the value assigned to each constituent element, (VEC)_i with c_i, as shown in eq. (4). The (VEC)_i assigned for each constituent element corresponds to the valence (Z) or group in the periodic chart.⁹⁾   

\begin{equation} \mathrm{VEC} = \sum_{i = 1}^{\text{N}}c_{\text{i}}(\mathrm{VEC})_{\text{i}} \end{equation} (4)

The calculated values of S_config./R, δ, ΔH_mix, and VEC for the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys are summarized in Table 1.

Table 1 Calculated values of S_config./R, ΔH_mix, δ, and VEC of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys.

2.3 Experiments

Alloy ingots of ∼5 g with nominal compositions of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5(at%) alloys were prepared by arc-melting from raw metals with industrial purity. The raw metals were commercially obtained and had a purity of 99.9 mass% with Ir, Rh, and Ru elements in powder form. Accordingly, these powders were consolidated separately in advance by arc melting to acquire a bulk form. The 5-g samples were solidified into button-shaped ingots of ∼10 mm^ϕ and ∼5-mm height, such that their button shape was similar to the hemispheroid shape achieved by conventional arc melting. Samples were annealed at a high temperature to confirm the equilibrium phases. The as-prepared ingot was put into a magnesium oxide crucible and annealed in a high-temperature furnace with a graphite heater. The chamber of the furnace was once vacuumed (∼10⁻² Pa) and then filled with high-purity Ar gas at ambient pressure. After the homogenization annealing, the samples were furnace-cooled. These alloys were cut into two pieces perpendicular to the base, and their structures were examined by X-ray diffraction (XRD) to the cross-sectional area. The morphology of the sample was observed with a scanning electron microscope (SEM), and the chemical composition was analyzed by energy-dispersive X-ray spectroscopy (EDX) equipped with SEM.

3. Results

First, the thermal stability of the phases of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys as the final candidates was computed as a function of temperature. As shown in Fig. 3, the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys exhibit a stable hcp phase for a wide range from T ∼ 2500 to 1300–1400 K. This strongly supports the appearance of the hcp phase in the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloy ingots when they solidified even at a low cooling rate. Furthermore, it was expected that these alloys would homogenize when annealed at a high temperature of ∼2000 K. In addition, it was anticipated that the actual atomic diffusion would not be sufficient to produce the bcc and fcc phases at temperatures ranging from 1300–1400 to 600 K during solidification. The calculated result shown in Fig. 3 supports the experimental data that the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys are the stable HEAs with the hcp structure. The Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys formed in the hcp phase precipitate into fcc and bcc phases simultaneously as a eutectoid reaction occurs at T ∼ 1400 K in (a) Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and T ∼ 1250 K in (b) Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys. The occurrence of these eutectoid reactions would tend to increase the thermal stability of the hcp phase because the precipitation of multiple phases needs a higher driving force as compared with the precipitation of a single phase, and the growth of the precipitated phases competes in growing crystalline grains. The eutectoid reaction in Fig. 3 can be regarded as the confusion principle in terms of the equilibrated phases. Figure 3 indicates that Ru can be a strong hcp-forming element, as described in the previous section.

Fig. 3

Property diagram of (a) Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and (b) Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys calculated with Thermo-Calc 2018b and TCHEA3 database.

Figure 4 shows XRD patterns of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys annealed at 2373 K for 1 h. The annealing temperature of 2373 K was selected according to the thermal stability of the hcp structure of the alloys, as shown in Fig. 3. The XRD profiles demonstrate that the alloys exhibited distinct sharp peaks corresponding to the presence of crystalline grains. These XRD patterns were identified as the reflections of the hcp structure. The XRD spectra shown in Fig. 4 demonstrate the difference in the relative intensity against each primary reflection from (0002), but they can be indexed in the same manner as an hcp structure. The difference in the relative intensity of each reflection peak is caused by the difference between the crystallographic orientations of the crystalline planes and the sample face. The lattice constants were evaluated as a = 0.2736 nm, c = 0.4379 nm, and c/a = 1.601 for the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 alloy and as a = 0.2736 nm, c = 0.4371 nm, and c/a = 1.598 for the Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloy. These values of a, c, and c/a are close to those for Ru (a = 0.2706 nm, c = 0.4282 nm, and c/a = 1.5824), as summarized in Table 2. As a whole, Table 2 suggests that the metals and alloys with a VEC of 3 or 4 from the early-transition metals tend to have c/a < 1.6, whereas late-transition metals with a VEC of 7 or more have c/a > 1.6, except for Ru and Os (VEC = 8) having c/a < 1.6. This tendency supports the speculation that the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys can be regarded as the alloys with an hcp structure that possess c/a ∼ 1.6, which is a characteristic of the late-transition metals with VEC ≥ 7. As a preliminary experiment, the XRD analysis was also performed for the arc-melted Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys in as-prepared samples; their results are not shown in Fig. 4. Each as-prepared sample exhibited the hcp structure to similar to that of the corresponding annealed sample, wherein the as-prepared samples indicated slightly broad reflection peaks located toward higher angles by 2θ = 0.3 in the case of (0002) peaks in Fig. 4.

Fig. 4

XRD patterns of (a) Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and (b) Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys annealed at 2373 K for 1 h.

Table 2 Lattice constants of the hcp phase (a, c) and their ratio (c/a) of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys: data of other HEAs³⁾ and referential transition metals²¹⁾ with hcp structure are also shown for comparison.

Further investigations were performed by observing with SEM and analyzing the compositions with EDX. Figure 5(a) shows the SEM image and Figs. 5(b)–(f) demonstrate element mapping images of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 alloy prepared by arc melting. The SEM image demonstrates a well-developed grain-like or dendritic structure with an approximate size of ∼10 µm. This structure was presumably created from the collision of a primary crystalline phase during solidification, leaving a small amount of area with dark contrast in Fig. 5(a). The element mapping in Figs. 5(b)–(f) shows that the area is relatively rich in Mo, Rh, and Ru, poor in Ir, and faintly poor in W. The same investigations were also performed for the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 alloy annealed at 2373 K for 1 h, as shown in Fig. 6. The SEM image shown in Fig. 6(a) demonstrates that the alloy is completely homogeneous at a sub-millimeter scale. In contrast to Figs. 5(b)–(f), the constituent elements are homogeneously distributed in Figs. 6(b)–(f) without segregation, precipitating the secondary phase. The same morphology was observed in the Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloy for as-prepared and annealed samples, as shown in Figs. 7 and 8, respectively. The experimental results shown in Figs. 4, 6, and 8 indicate that the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys annealed at 2373 K for 1 h were formed in a single HEA with an hcp structure. Additionally, Fig. 5 reveals that the hcp structure created at high temperature from a melt kept its structure during cooling after arc melting because of the wide temperature range of the stabilized hcp structure, as demonstrated in Fig. 3. In a similar manner, Fig. 7 indicates the high stabilization of the hcp structure in comparison with Fig. 8.

Fig. 5

(a) SEM image and (b–f) element-mapping images of Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 alloy prepared by arc melting.

Fig. 6

(a) SEM image and (b–f) element-mapping images of Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 alloy annealed at 2373 K for 1 h.

Fig. 7

(a) SEM image and (b–f) element-mapping images of Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloy prepared by arc melting.

Fig. 8

(a) SEM image and (b–f) element-mapping images of Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloy annealed at 2373 K for 1 h.

The formation of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 HEAs with an hcp structure was examined for their thermodynamic and physical values. The ΔH_mix, δ, and S_config./R of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys summarized in Table 1 were plotted out of the zone S for disordered HEAs, and S′ for ordered HEAs, in terms of chemically ordering in a δ–ΔH_mix diagram,⁸⁾ as shown in Fig. 9. Here, zone S is a trapezoid area surrounded by edges expressed by the following formulae:²²⁾   

\begin{equation} (0.7) < \delta < 4.6 \end{equation} (5)

and   

\begin{align} -2.685\cdot\delta - 2.54& < \Delta H_{\text{mix}}/\text{kJ$\,$mol$^{-1}$}\\ & < -1.28\cdot\delta + 5.44. \end{align} (6)

The location of the plots that are out of zone S is a characteristic of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 HEAs with an hcp structure. This suggests that zone S, and zone S′, in the δ–ΔH_mix diagram are merely a necessary condition for the formation of HEAs and that the new HEAs can be found by focusing on zones exterior to zones S and S′ in the future. However, the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys exhibit S_config./R ≥ 1.5, which satisfies a criterion of HEAs.

Fig. 9

Plot of Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys in the δ–ΔH_mix diagram⁸⁾ where zones S and S′ are the areas for disordered and ordered HEAs, and zone B₁ is for conventional bulk metallic glasses (BMGs), except for Mg- and Cu-based BMG for zone B₂. Reproduced with permission.³⁾

The VEC values of the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 alloys were calculated to be approximately 7.86–8, which agrees with the formation of the hcp phase. In particular, the formation of the hcp structure was fully and partially explained by the value of VEC and the number of d-electrons (n_d) of the Friedel model, respectively. A VEC of 7.86–8 agrees with that for Ru and Os with an hcp structure in the group 8 of the periodic chart, whereas a VEC of ∼8 mostly accounts for the stable hcp structure between the following ranges:^18,19) 6.5 < n_d < 7.4 and 2.6 < n_d < 3.5. In previous reports, it was reported that the GdTbDyTmLu and YGdTbDyLu HEAs with the hcp structure have VEC = 3. However, another earlier report⁹⁾ does not include VEC for hcp, and it just indicates that the VEC values of the bcc, bcc + fcc, and fcc are determined as follows: VEC < 6.87 (bcc), 6.87 ≤ VEC < 8.0 (bcc + fcc), and VEC ≥ 8 (fcc).

4. Discussion

This study is academically significant in terms of alloy design, sample preparation method, and the development of new HEA with the hcp structure. Subsequently, the effects of the present study on the development of the academic science of HEAs with fcc, bcc, and hcp solid solutions will be discussed below.

First, a feature of the present alloy design is highlighted by a unique alloy design based on a sandwiched strategy of VEC, which is accompanied by the optimization of the alloy systems and alloy compositions based on the computational prediction through the CALPHAD method and Gibbs free energy. There are some similar thermodynamic predictions for the formation of HEAs with hcp as well as refractory bcc structure and others made by other researchers, such as Gao et al.^23–25) However, almost all of these predictions have been made for alloys with exact equiatomicity, alloys with almost equiatomicity but for only one atomic pair with ratios other than 1:1, alloys with four or less constituent elements, and predictions without experimental proof even after the report. Thus, the present alloy design is completely different from these predictions by other researchers. The hcp structure of the HEAs was intentionally optimized, but this suggests that one can obtain HEAs with fcc or bcc structures when fcc or bcc is optimized. Accordingly, when focusing on a HEA with the fcc structure, the present study will lead to the quantitative analysis by thermodynamic approach based on Gibbs free energy to the stable phases of actual HEAs in terms of TRIP²⁶⁾ (Transformation-Induced Plasticity) that includes lamellar hcp phase in the fcc matrix containing high density stacking faults, twins introduced during deformation, and low stacking fault energy.

As for the sample preparation, the present method, arc melting, is superior to the other methods as it is a conventional method and subsequently anneals at high temperature to homogenize only in the processing. In the other researches, the HEAs with hcp structure were prepared by applying high pressure⁶⁾ for alloys comprising 3d transition metals, mechanical alloying for light-weighted alloys,⁵⁾ and chemical reaction⁷⁾ for alloys consisting of transition metals. The present method exhibits an advantage over the other methods as one can produce enough amount of samples for performing researches at a laboratory scale. As far as high temperature annealing is concerned, selecting high temperature is effective to maximize configurational entropy term, and to obtain a solid solution, but still, a temperature higher than 2000 K is disadvantageous in the processing. However, the present HEA does not always require such high-temperature for forming a single hcp phase due to the presence of a wide temperature range greater than 1000 K at which a single hcp phase can be present stably. This was demonstrated by the formation of the HEAs with hcp structure as almost a single phase in as-prepared samples. Thus, one can assure that the present study took the best method to prepare HEAs. As a result, the method of high-temperature annealing selected in the present study is affected by a characteristic of HEA, high-melting temperature alloys, which is represented by refractory HEAs with bcc structure.²⁷⁾

As for the findings of the HEAs with hcp structure, controlling ferromagnetism is significantly important. For instance, high pressure is required to obtain the hcp phase for alloys comprising 3d transition metals. It is specified in the report⁶⁾ that elements with ferromagnetism prevent the formation of alloys in an hcp phase under ambient pressure for alloys comprising 3d transition metals. Hence, for the present study, we selected 4d and 5d transition metals with paramagnetism in accordance with the alloy design illustrated in Fig. 1. Under the circumstances, the present paper provides that the structure of the solid solutions can be controlled to one’s heart content in accordance with the sandwich strategy for VEC for transition metals in 4d and 5d series with paramagnetism, which should be the inherent nature of the transition metals. Thus, the present paper will bring considerable progress in the fundamental researches for clarifying the formation mechanism of solid solutions in HEAs. It is noteworthy that the success in fabricating a HEA with the hcp structure by chemical reaction, as proposed by Yusenko,⁷⁾ also indicates the importance of selecting paramagnetic 4d and 5d transition metals. It is expected that HEAs with hcp structure containing ferromagnetic elements can be formed if the 3d ferromagnetic component of the transition metals can be controlled such that they do not exceed the critical concentration of site percolation.²⁸⁾

As a whole, the present results possess high significance in fundamental research. Furthermore, the present research will contribute in establishing the academic science of HEAs with solid solutions from fcc, bcc, and hcp structures. Moreover, the present study is highly evaluated as pioneer research leading to disclose the unprecedented alloys that originate from the unclearness of the central composition region in multi-component alloys.

5. Conclusions

The alloy design of HEAs, done by referring to exact and near equiatomicity, sub binary phase diagrams, and sandwich strategy in terms of the VEC of the constituent elements and their crystallographic structures in the periodic chart, led to the finding the Ir₂₆Mo₂₀Rh_22.5Ru₂₀W_11.5 and Ir_25.5Mo₂₀Rh₂₀Ru₂₅W_9.5 HEAs with an hcp structure. The formation of the HEAs with an hcp structure is enhanced by adding Ru as a strong hcp-forming element under the above alloy design. The formation of the hcp structure was explained by VEC ∼8 and was partially supported by the Friedel model in terms of the number of d-electrons (n_d) as 6.5 < n_d < 7.4 where n_d corresponds to VEC. These HEAs with hcp structure differ from a CrMnFeCoNi HEA as the former alloys are composed of 4d and 5d transition metals only and can be produced by a conventional solidification method without imposing high pressure. Semi-empirical alloy design based on experimental and computational phase diagrams is worth utilizing for the further development of new HEAs.

Acknowledgments

This research was primarily supported by Grant-in-Aids for Scientific Research from the Japan Society for the Promotion of Science (JSPS) through Grant Program of Scientific Research (B) (grant number 17H03375). In part, the research was also supported by Grant-in-Aids for Scientific Research on Innovative Areas on High Entropy Alloys through the grant number JP18H05452.

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