High-Entropy Alloys Including 3d, 4d and 5d Transition Metals from the Same Group in the Periodic Table

Akira Takeuchi*, Kenji Amiya, Takeshi Wada and Kunio Yubuta

Institute for Materials Research, Tohoku University, Sendai 980–8577, Japan

Exact equi-atomic senary alloys including three elements from 3d, 4d and 5d transition metals (TMs) were investigated for their ability to form solid solutions as high-entropy alloys (HEAs). Three alloys of CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt were selected by fo-cusing on (Ti, Zr, Hf) from Early-TMs, and (Cu, Ag, Au) and/or (Ni, Pd, Pt) from Late-TMs based on an alloy design with a help of Pettifor map for binary compounds with several stoichiometries and binary phase diagrams, together with a marginal Al4CoNiPdPt alloy. The XRD analysis revealed that the CoCuPdTiZrHf alloy was formed into a bcc, whereas both the CoCuFeTiZrHf and Al4CoNiPdPt alloys were a CsCl, and the AgAuCuNiPdPt alloy was dual fcc structures. The observations with optical and scanning-electron microscopes and analysis with ener-gy dispersive X-ray for chemical composition revealed the homogeneous morphologies of these alloys in micrometer scale. The types of crys-tallographic structures of the CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt HEAs and the Al4CoNiPdPt alloy can be principally ex-plained by valence electron concentration. Three constituent elements from TMs in the same group enhance the increase in the number of complete solid solutions in the constituent binary systems, leading to forming these HEAs.　[doi:10.2320/matertrans.M2016121]

(Received April 1, 2016; Accepted April 25, 2016; Published June 3, 2016)

Keywords:　 high-entropy alloys, alloy design, phase stability

1.　 Introduction

The present study deals with high-entropy alloys (HEAs)1–3) in a class of multicomponent alloys with either exact or near equi-atomicity4) or compositions of constituent elements ranging 5 to 35 at%2). From crystallographic viewpoints, the HEAs are formed into solid solutions in chemically disor-dered and ordered phases with simple structures, such as bcc, fcc or their mixture3) when the constituent elements are se-lected carefully and appropriately. For instance, it was report-ed that NbTaTiZrHf5) and CoCrFeMnNi4,6) HEAs exhibit bcc and fcc single phases, respectively, whereas AlxCoCrCuFeNi HEAs exhibit fcc, bcc + fcc and bcc structures with increas-ing Al content from x =  0 to 31). In addition, recent reports include HEAs with hcp structure7,8) comprised mainly heavy-lanthanide elements. Furthermore, it was reported that exact equi-atomic quinary CuNiTiZrHf9), BeCuTiZrHf10) and PdPtCuNiP11) alloys are formed into non-crystalline structure in a form of bulk metallic glasses as high-entropy BMGs (HE-BMGs). According to literature3), the number of HEAs formed into disordered and ordered solid solutions is amount-ed to be no less than 200 species. However, these alloy com-ponents are not truly independent to each other among the HEAs, since substituting similar elements in the periodic ta-ble is frequently utilized for multicomponent alloying. In re-ality, HEAs and their relevant alloys possess the same constit-uent elements, such as Ti, Zr and Hf in the NbTaTiZrHf5) HEA and the CuNiTiZrHf9) and BeCuTiZrHf10) HE-BMGs. In the framework of multicomponent alloying strategy for al-loy designing, the authors have recently reported that a senary exact equi-atomic ScYLaTiZrHf alloy is formed into dual hcp structures12) by replacing Nb and Ta as bcc-formers from the NbTaTiZrHf5) HEA with bcc structure by Sc, Y and La from hcp-formers. Thus, the present study focuses on 3d, 4d and 5d transition metals (TMs), e.g. (Ti, Zr, Hf), (Cu, Ag, Au) and (Ni, Pd, Pt), to investigate the effects of these TMs on the

crystallographic structures of HEAs. In selecting candidates, the authors have decided to utilize the crystallographic data from Pettifor map for binary compounds13) and binary phase diagrams14,15) in accordance with the authors’ previous work16). The purpose of the present study is to develop novel HEAs including elements of (Ti, Zr, Hf), (Cu, Ag, Au) or (Ni, Pd, Pt) from 3d, 4d and 5d TMs from the same group in the periodic table by referring to crystallographic information from Pettifor map for binary compounds with several stoichi-ometries as well as constituent binary phase diagrams.

2.　 Methods

First, target alloys were selected computationally as candi-dates with home-build program by utilizing crystallographic data of Pettifor map13) in digitalized formats16) for com-pounds with a set of stoichiometries of 1:1, and 1:2, 1:3, 2:3, 3:4 and 3:5 and their opposite ratios. After the initial candi-dates had been selected, then the target alloys were subse-quently selected based on the thermodynamic knowledge of binary phase diagrams14). Eventually, these procedures in al-loy design gave CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt alloys as �nal candidates. In addition, the authors also focused on n-element alloys (n: integer > 1) for-mulated as An−1X (X  =  BCDE...), such as AB, A2BC and A3BCD where the number of elements excepting for “A” is n −  1 and the fraction of A-element is kept to be 0.5 (50 at%). The An−1X alloys cannot be classi�ed into HEAs rigidly even if they are formed into a solid solution because the content of the element A is 50 at%. However, the authors keep on paying attention to the An−1X alloys because of the following rea-sons. First, the An−1X alloys locate in a multicomponent com-position diagram along the line to connect two exact equi- atomic alloys: A2BC is on the line connecting BC and ABC, A3BCD is BCD and ABCD, and A4BCDE is BCDE and ABCDE16). Second, mixture of An−1X and A’n−1X alloys has a potential to yield new HEAs, which can be represented by Cu4GdTbDyY  +  Ag4GdTbDyY  =  Cu2Ag2GdTbDyY where * Corresponding author, E-mail: takeuchi@imr.tohoku.ac.jp

Materials Transactions, Vol. 57, No. 7 (2016) pp. 1197 to 1201 ©2016 The Japan Institute of Metals and Materials

the Cu2Ag2GdTbDyY is HEA with CsCl structure16). Here, it should be noted that each An−1X (or A’n−1X) alloy requires n ≥  7.25 to achieve the HEAs that satisfy their most rigid de�nition: exact equi-atomicity and constituent elements of �ve or more. In addition, note that the most rigid de�nition is given by evaluating con�guration entropy (Scon�g.) normal-ized with gas constant (R) as Scon�g./R ≥  ln 5 (~ 1.609). As for the An−1X (or A’n−1X) alloy, the value of Scon�g./R of the Cu4GdTbDyY and Ag4GdTbDyY (n =  4) was evaluated to be Scon�g./R  ~  1.386, which is considerably smaller than Scon�g./R ~  ln 5 (~ 1.609). In other words, the An−1X alloys that require as many elements as n ≥  7.25 are not ef�cient alloys solely to yield HEAs. However, Scon�g./R ≥  ln 5 was easily achieved by mixing two types of An−1X alloys by equi-mole of alloy strategy as Cu4GdTbDyY +  Ag4GdTbDyY =  Cu2Ag2GdTbDyY where the Cu2Ag2GdTbDyY alloy has Scon�g./R ~  1.733. These relationships suggest that the An−1X alloys can be supplemental and marginal alloys against HEAs with exact equi-atomicity, and thus, the An−1X alloys should be worth investigating in a framework of the researches on HEAs.

Alloy ingots with nominal compositions of each 16.67 at% for the CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt and the Al4CoNiPdPt (Al50Co12.5Ni12.5Pd12.5Pt12.5) with an approximate mass of 10 g were prepared via arc-melting of commercially obtained raw materials (99.9 mass% pure) in an Ar atmosphere with paying attention to keep a homogene-ity in chemical composition. Eventually, ingots were formed approximately 12 mmϕ and 5 mm height in a hemisphere shape. In necessary, pieces of an ingot were loaded in a quarts tube evacuated and sealed and were homogenized at a high temperature. The samples were analyzed with X-ray diffrac-tion (XRD) to identify crystalline phases. Optical microscope (OM) and scanning electron microscope (SEM) were used to observe the microstructures of the samples. The chemical compositions of samples and phases were analyzed by energy dispersive X-ray spectroscopy (EDX) equipped with SEM.

The alloys were evaluated for their physical, thermody-namic and electronic quantities: delta parameter (δ)17), mix-ing enthalpy (ΔHmix)18) and valence electron concentration (VEC)19). The details of the calculation methods for δ and ΔHmix can be acquired from authors’ previous literature20), whereas VEC from original literature, in which (VEC)i =  3 for Al is empirically adopted19). Here, it should be noted that (VEC)i is a VEC value of constituent pure element (i-th ele-ment), and is different from VEC value of the alloy of inter-est.

3.　 Results and Discussion

Figure 1 shows the XRD pro�les of the CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt alloy ingots as-prepared as well as the Al4CoNiPdPt alloy that was subjected to be homogenized at 1273 K for 43.2 ks. These XRD analysis re-vealed that the CoCuPdTiZrHf alloy was formed into a bcc, the CoCuFeTiZrHf and Al4CoNiPdPt were into CsCl struc-tures, whereas the AgAuCuNiPdPt was into dual fcc struc-tures. The lattice constants (a) calculated from the diffraction peaks in Fig. 1 were (a) 0.320 nm for the CoCuPdTiZrHf, (b) 0.315 nm for the CoCuFeTiZrHf, (c) 0.395 and 0.378 nm for

the AgAuCuNiPdPt denoted by α and β, and (d) 0.298 nm for the Al4CoNiPdPt alloy. The OM photos of (a) CoCuPdTiZrHf, (b) CoCuFeTiZrHf and (c) AgAuCuNiPdPt alloys are shown in Fig. 2. Featureless contrast excepting for the presence of surface morphology appears in Fig. 2(a), whereas dendritic structures appear to evolve partially and fully in Figs. 2(b) and (c), respectively, in a micrometer scale. On the other hand, the Al4CoNiPdPt alloy exhibits a featureless contrast from SEM image and homogeneous distributions of elements were con�rmed over hundred micron scale as shown in Fig. 3.

These alloys were evaluated for ΔHmix, δ and VEC as sum-marized in Table 1. The evaluated values of the alloys are ΔHmix =  −34.4, −22.0, −44.2 and −2.2 kJmol−1, δ =  5.4, 10.5, 9.7 and 5.4, and VEC =  6.375, 6.67, 7 and 10.5, respectively, for the Al4CoNiPdPt alloy (CsCl) and the CoCuPdTiZrHf (bcc), CoCuFeTiZrHf (CsCl) and AgAuCuNiPdPt (fcc) HEAs. The VEC values of these alloys roughly exhibit a ten-dency to reproduce the report in an early study19): VEC <  6.87 (bcc), 6.87 ≤  VEC <  8.0 (bcc + fcc) and fcc for VEC ≥  8.0. In contrast, the alloys studied in the present work listed in Ta-ble 1 exhibit larger δ values than 4.6 and larger and negative ΔHmix than conventional HEAs that roughly possess values17)

Fig. 1　X-ray diffraction patterns of the alloy ingots of (a) CoCuPdTiZrHf, (b) CoCuFeTiZrHf and (c) AgAuCuNiPdPt alloys as prepared and (d) Al4CoNiPdPt alloy ingot homogenized at 1273 K for 43.2 ks.

Fig. 2　Optical micrographs of the alloy ingots of (a) CoCuPdTiZrHf, (b) CoCuFeTiZrHf and (c) AgAuCuNiPdPt alloys as prepared.

Fig. 3　SEM image (upper-left) and elemental-maps by EDX of the Al4C-oNiPdPt alloy ingot homogenized at 1273 K for 43.2 ks.

1198 A. Takeuchi, K. Amiya, T. Wada and K. Yubuta

of δ  ≤  4.6 and ΔHmix  ≥  −15 kJmol−1. Here, δ  =  4.6 and ΔHmix =  −15 kJmol−1 correspond to upper- and lower-limit values, respectively, of zone S in a δ–ΔHmix diagram17) for chemically disordered HEAs. More speci�cally, the zone S in a trapezoid shape for disordered HEAs in the δ–ΔHmix dia-gram is de�ned21) by eqs. (1) and (2), which were also re-ferred to in the authors’ previous study22).

(0.7 <) ≤ 4.6 (1)

−2.688 · δ − 2.54 ≤ ∆Hmix ≤ −1.28 · δ + 5.44 (2)

In spite of the large magnitude of δ and ΔHmix, Table 1 demonstrates that the values of VEC of the present work tend to explain difference in crystallographic structures between bcc (CsCl) and fcc.

The VEC values of the CoCuPdTiZrHf and CoCuFeTiZrHf HEAs with a bcc-derivative structures (bcc and CsCl) were evaluated to be 7 and 6.67, respectively, which are at the boundary of VEC < 6.87 (bcc) reported by literature19). How-

ever, the authors consider that the stability of bcc structure is much higher in the NbTaTiZrHf HEA5) with bcc structure (VEC  =  4.4) than the CoCuPdTiZrHf and CoCuFeTiZrHf HEAs. This is because the Cu, Co, Pd and Fe from Late-TMs (LTMs) in the CoCuPdTiZrHf and CoCuFeTiZrHf alloys possess higher (VEC)i values appointed for elements than 8, and thus, they increase the VEC values. Meanwhile, other quantities, such as δ and ΔHmix vary considerably ranging 1.6 to greater than 10 for the former and 11.4 to −44.2 kJmol−1 for the latter among the alloys listed in Table 1. In other words, VEC can be the most appropriate parameter for evalu-ating the structure of HEAs. Here, HE-BMGs comprising metallic elements only possess nearly the same VEC values to the alloys with bcc and CsCl structures, suggesting a struc-tural similarity between HE-BMG and bcc-derivative phases from VEC analysis.

The analysis with Pettifor map for binary compounds with 1:1 stoichiometry summarized in Table 2 revealed that the CoCuPdTiZrHf and CoCuFeTiZrHf HEAs (Nos. 1 and 2) ex-hibit a frequent appearance of symbol “w4”, suggesting a high possibility of the alloys to form CsCl structure. In strong contrast, the AgAuCuNiPdPt (No. 5) HEA with dual fcc structures exhibits “w4” only at BD (Cu50Pd50). Thus, the crystallographic structures of the CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt HEAs are affected by those of binary constituent compounds to a certain extent. The Al4CoNiPdPt alloy (No. 6) also give frequent appearance of symbol “w4”, but “w4” is seen at speci�c atomic pairs where “D” element (Al) is involved, such as AD (NiAl), BD (PdAl), CD (PtAl) and DE (AlCo). On the other hand, ScYLaTiZrHf (No. 3, dual hcp)12) and NbTaTiZrHf (No. 4, bcc)5) HEAs exhibit absence of the constituent binary com-pounds at 1:1 where crystallographic structures of these al-loys tend to be affected by those of the constituent elements, as reported previously16).

The relationships between the values of ΔHmix and topo-logical types of phase diagrams15) are summarized in Tables 3 and 4 with paying attention to complete solid solutions. It was reported23) that complete solid solutions are achieved by sat-isfying the conditions of the interaction parameters of solid

Table 1　Alloys, phases, values of delta parameter (δ), mixing enthalpy (ΔHmix) and valence electron concentration (VEC) the CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt HEAs and the Al4CoNiPdPt alloy where the data for YGdTbDyLu, GdTbDyTmLu, NbTaTiZrHf and CoCrFeMnNi HEAs, ScYLaTiZrHf alloy and CuNiTiZrHf, BeCuTiZrHf HE-BMGs are also shown for comparison.

Alloy Phase δΔHmix / kJmol−1 VEC Ref.

YGdTbDyLu hcp 1.6 0 3 7)

GdTbDyTmLu hcp 1.4 0 3 7)

ScYLaTiZrHf dual hcp 8.3 11.4 3.5 12)

NbTaTiZrHf bcc 4.0 2.7 4.4 5)

CuNiTiZrHf HE-BMG 10.3 −27.4 5.8 9)

Al4CoNiPdPt CsCl 5.4 −33.4 6.375 This work

BeCuTiZrHf HE-BMG 12.9 −25.4 6.6 10)

CoCuFeTiZrHf CsCl 10.5 −22.0 6.67 This work

CoCuPdTiZrHf bcc 9.7 −44.2 7 This work

CoCrFeMnNi fcc 4.8 −4.2 8 4,6)

AgAuCuNiPdPt dual fcc 5.4 −2.2 10.5 This work

Table 2　Crystallographic information of the binary constituent equi-atomic compositions from Pettifor map with 1:1 stoichiometry for the CoCuPdTiZrHf (No. 1, bcc), CoCuFeTiZrHf (No. 2, CsCl), and AgAuCuNiPdPt (No. 5, dual fcc) HEAs and Al4CoNiPdPt alloy (No. 6, CsCl) as a reference, with the ScYLaTiZrHf (No. 3, dual hcp) alloy, NbTaTiZrHf (No. 4, bcc) and CoCrFeMnNi (No. 7, fcc) HEAs for comparison where the order of elements that appear in alloys are changed and structures were denoted by *symbols.

No A B C D E F AB AC AD AE AF BC BD BE BF CD CE CF DE DF EF Ref

1 Ti Zr Hf Cu Co Pdp3

w4w4

w4 w4 w4 w4 –w2 q1

2 Ti Zr Hf Cu Co Fep3

w4 w4 w4 w4 w4 w4 –w2

3 Ti Zr Hf Sc Y La 12)

4 Ti Zr Hf Nb Ta 5)

5 Ni Pd Pt Cu Ag Au p3 w4 p3 –

6 Ni Pd Pt Al Co p3 w4P

w4P

w4p3 w4 –

7 Co Cr Fe Mn Ni w4 rv p3 p3 4,6)

*symbols13). p3: AuCu (tP4), w2: CuTi (tP4), w4: CsCl (cP2), P: FeSi (cP8), q1: AuCu (oP4), rv: CrFe (cP30), X: absence of corresponding compound in the phase diagram, \: no-existence of a compound from enthalpy estimations by Miedema and co-workers, /: no-existence of a compound from predic-tions by Villars, LT\HT: High- and low-temperature compounds, m1

m2: Information is lacking or where both temperature and pressure are involved

1199High-Entropy Alloys Including 3d, 4d and 5d Transition Metals from the Same Group in the Periodic Table

and liquid as Ωsol ≤  0 kJmol−1 and Ωliq ≤  40 kJmol−1, respec-tively. Here, it should be noted that ΔHmix’ are for liquid phase18,24) and that a relationship Ωliq ~  4 ΔHmix holds. The information of Ωsol and resultant Ωsol ~  4 ΔHmix(sol) lacks in the present study, but it can be roughly estimated that Ωsol and

Ωliq would have the same sign. Permitting this estimation en-ables to consider the formation mechanism of the AgAuCu-NiPdPt HEA as follows. The positive values of ΔHmix and resultant immiscible nature of solids in binary phase diagrams for Ag-Cu and Ag-Ni systems enhance the dual phases, but

Table 4　The values of ΔHmix18,24) in the units of kJmol−1 of a liquid at A50B50 (at%), and A-B binary phase diagrams15) for the CoCuPdTiZrHf and

CoCuFeTiZrHf HEAs, where the phase are drawn as A- and B-element on the left and right side, respectively. Hatched areas in binary phase diagrams exhibit liquid and solid solution phases.

BA

Co Cu Fe Pd Ti Zr Hf

Co ̶

Cu 6 ̶

Fe −1 13 ̶ ̶

Pd −1 −14 ̶ ̶

Ti −23 −9 −17 −65 ̶

Zr −41 −23 −25 −91 0 ̶

Hf −35 −17 −21 −80 0 0 ̶

Table 3　The values of ΔHmix18,24) in the units of kJmol−1 of a liquid at A50B50 (at%), and A-B binary phase diagrams15) for the AgAuCuNiPdPt HEA and

Al4CoNiPdPt alloy, where the phase diagrams are drawn as A- and B-element on the left and right side, respectively. Hatched areas in binary phase dia-grams exhibit liquid and solid solution phases.

AB

Ag Au Cu Al Co Ni Pd Pt

Ag ̶

Au −6 ̶

Cu 2 −9 ̶

Al ̶

Co −19 ̶

Ni 15 7 4 −22 0 ̶

Pd −7 0 −14 −46 −1 0 ̶

Pt −1 4 −12 −44 −7 −5 2 ̶

1200 A. Takeuchi, K. Amiya, T. Wada and K. Yubuta

the presence of solid solutions in Ag-Au and Ag-Pd and those in other constituent binary systems allows Ag dissolving into both phases to form the dual fcc phases, as Sc in the ScY-LaTiZrHf alloy with dual hcp structures12).

Tables 3 and 4 contain complete solid solutions frequently in constituent binary phase diagrams. For instance, the com-plete solid solutions are seen in Table 3 for binary systems among the TMs in the same group for Ag-Au, Au-Cu, Ni-Pd, Ni-Pt and Pd-Pt as well as the others for Ni-Au, Ni-Cu, Ni-Co, Pd-Ag, Pd-Au, Pd-Cu, Pd-Co, Pt-Au, Pt-Cu and Pt-Co systems. On the other hand, Table 4 exhibits that Ti-Zr, Ti-Hf and Zr-Hf from TMs in the same group as well as the others for Co-Fe, Co-Pd and Cu-Pd systems form complete solid solutions. In part, the frequent appearance of complete solid solution is due to the selections of three elements from TMs in the same group. Presumably, the presence of complete sol-id solutions in constituent binary systems partially contrib-utes to form a solid solution in solidifying from a liquid, such as an ideal case represented by Ti-Zr binary system with con-gruent liquid/solid solidi�cation and bcc/hcp allotropic transformations. On the other hand, the CoCuPdTiZrHf and CoCuFeTiZrHf HEAs in Table 4 are much more complicated than the AgAuCuNiPdPt HEA in Table 3. In particular, the constituent binary phase diagrams for Late-TM (LTM: Co, Cu, Fe, Pd) and Early-TM (ETM: Ti, Zr, Hf) tend to form a lot of compounds at 1:1 and other stoichiometries, which is represented by the constituent binary phase diagrams at the upper-right section of Table 4. This tendency between ETM-LTM is regarded as a disadvantageous aspect to form HEA, but this can be avoided by keeping the ratio of LTM:ETM =  1:1 in terms of chemical species. In reality, senary exact equi-atomic alloys examined in the present study can keep the LTM:ETM  =  1:1, since the senary alloys are composed of three elements from ETMs and those from LTMs. This rela-tionship can help to avoid the intermediate compounds with different stoichiometry excepting for 1:1 with complex struc-ture (Laves phase etc.) but for simple solid solution (fcc, bcc and hcp) to appear in the alloys for the formation of HEAs. Thus, the present alloy design based on binary crystallo-graphic data and binary phase diagrams is worth utilizing in terms of its ability to compensate for the lacks of data in mul-ticomponent system for HEAs under a current situation that the data in multicomponent alloy systems have not estab-lished completely.

4.　 Conclusions

An alloy design utilizing Pettifor map for binary com-pounds and binary phase diagrams led to success in forming the CoCuPdTiZrHf, CoCuFeTiZrHf and AgAuCuNiPdPt high-entropy alloys (HEAs) with bcc, CsCl and dual fcc structures, respectively, together with the Al4CoNiPdPt alloy in CsCl structure. The valence electron concentration values of these alloys explain the difference in their crystallographic structures between bcc (CsCl) and fcc. The presence of com-plete solid solutions in constituent binary systems makes it

possible to form HEAs in a multicomponent system in case of selecting constituent elements from the same group. It has been shown that the alloy design based on binary crystallo-graphic data of compounds and constituent binary phase dia-grams compensates for the lacks of data in multicomponent systems, leading to �nding out new HEAs.

Acknowledgments

This work was supported by Grant-in-Aid for Scienti�c Research from Japan Society for the Promotion of Science (JSPS): grant number 24360284.

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1201High-Entropy Alloys Including 3d, 4d and 5d Transition Metals from the Same Group in the Periodic Table