Solid Solutions with bcc, hcp, and fcc Structures Formed in a Composition Line in Multicomponent Ir Rh Ru W Mo System

Solid Solutions with bcc, hcp, and fcc Structures Formed in a Composition Line in

Multicomponent Ir

­

Rh

­

Ru

­

W

­

Mo System

Akira Takeuchi

, Takeshi Wada

and Hidemi Kato

1_{Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan} 2_{Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan}

Five Ir­Rh­Ru­W­Mo alloys selected based on alloy design with valence electron concentration (VEC) were examined for their formation of single, dual, and triple phases of bcc, fcc, and hcp structures. These structures were predicted with Thermo-Calc 2019a and the TCHEA3 database on a cross-sectional phase diagram along a composition line: Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox(x: 0­50 at%). At

T=2100 K, four types of phases were predicted: (1) a single bcc, fcc, and hcp phase, respectively, at x=35 (Alloy A, VEC=6.849), 15 (Alloy C, VEC=7.981), and 5 (Alloy E, VEC=8.574); (2) a mixture of bcc+hcp and hcp+fcc at x=24 (Alloy B, VEC=7.472) and 8 (Alloy D, VEC=8.378), respectively; (3) a triple mixture of bcc+hcp+fcc; and (4) a mixture of bcc+fcc in Alloys A­E at low temperature. Experiments at 2100 K revealed that Alloys C­E tended to exhibit better reproducibility and that Alloy E can be regarded as a new refractory high-entropy alloy (HEA) with fcc structure. Alloy C annealed atT=1273 K for 200 h maintained a single-hcp structure. The non-appearance of thermodynamically stable phases at low temperature in the Ir­Rh­Ru­W­Mo system was analogically explained as slow diffusion. The VEC analysis for HEAs with hcp structures was extended by including the range of 7.5¯VEC¯8.4 for alloys consisting of 4d and 5d transition metals annealed near their solidus temperature. The Ir­Rh­Ru­W­Mo system was significant in providing all possible simple solid solutions of bcc, hcp, and fcc phases. [doi:10.2320/matertrans.MT-M2019212]

(Received August 1, 2019; Accepted August 27, 2019; Published October 4, 2019)

Keywords: high-entropy alloys, solid solutions, transition metals, valence electron concentration

1. Introduction

It goes without saying that high-entropy alloys (HEAs) have developed into the most attractive metallic materials

since their first reports in 2004.1,2) _{The developmental}

progress of HEAs has been accompanied by the expansion

of their definitions in terms of alloy composition and relevant

quantities. Initially, HEAs were defined1)_{as alloys with exact}

equiatomicity and with five or more constituent elements,

which corresponds to the description with the configuration

entropy normalized by the gas constant (Sconfig/R) satisfying

Sconfig/R²1.61.3) Here, Sconfig is given by eq. (1) with a

fraction of thei-th elements (pi) in the alloy withNelements

and is simply expressed as Sconfig=lnN in case of exact

equiatomic alloy.

Sconfig=R¼ XN

i¼1

pilnpi ð1Þ

Subsequently, the criteria for HEAs have been further extended with the recent progress in HEAs. For instance,

HEAs in a narrow sense4,5) _{are alternatively defined by}

Sconfig/R²1.5 and by the constituent element content in

atomic percent (ci) in the range of 5¯ci/at%¯35.

Furthermore, a recent definition for HEAs includes alloys

with Sconfig/R³1.0­1.5 as medium-entropy alloys (MEAs)

in a class of HEAs within their wide definition. Thus, HEAs

have been loosely defined in a wide sense in multicomponent

alloy systems.

As well as changes of the definition of HEAs in terms of

compositions, the structural types of HEAs have also been

changed gradually. Specifically, the definition had long been

limited to simple crystallographic structures, in particular,

solid solutions of bcc, fcc, and their mixtures.1)_{Subsequently,}

HEAs with hcp structures have been found in the past

several years. For instance, the constituent elements and/or

production methods of HEAs with hcp structure reported

to date consist of heavy lanthanide elements with6) _and

without6,7) _{Y, light-weight elements by mechanical alloying}

and subsequent transformation,8) _{3d transition metals by}

applying high pressure,9)_{and 4d and 5d transition metals by}

chemical reaction.10) _{Following these reports, the authors}

have recently succeeded in fabricating HEAs with hcp

structure for alloys from 4d and 5d elements in

Ir26Mo20Rh22.5Ru20W11.5 and Ir25.5Mo20Rh20Ru25W9.5

al-loys11) by conventional arc melting and subsequent

annealing. A unique feature of these Ir­Mo­Rh­Ru­W

HEAs11) is that the hcp structure of the alloys is controlled

by valence electron concentration (VEC)12) ³7.8. Specifi

-cally, the alloy design is supported by a concept of structural

stability evaluated according to the enthalpy by Miedema’s

model13,14) _{as a function of VEC. Furthermore, the Ir­Mo­}

Rh­Ru­W HEAs with hcp structure11)_{are also unique in that}

the alloy compositions are optimized by thermodynamic

predictions11)_{using Thermo-Calc with the TCHEA3 database}

for HEAs. This implies that one can fabricate Ir­Mo­Rh­

Ru­W HEAs with bcc or fcc structure by paying attention

to the appropriate VEC values for their structures and composition optimization. In other words, the authors came

to believe that the Ir­Mo­Rh­Ru­W system has the ability

to provide HEAs with bcc and fcc structures as well as

unprecedented bcc+hcp and hcp+fcc structures as stabilized

phases when the VEC values and compositions are optimized.

The purpose of this study was to examine the presence of single bcc, fcc, and hcp structures and plural phases in the

Ir­Mo­Rh­Ru­W alloy system in accordance of an alloy

design based on VEC analysis and thermodynamic calcu-lations and optimizations.

+_{Corresponding author, E-mail: akira.takeuchi.a8@tohoku.ac.jp}

2. Methods

In the present study, the capital and lower-case letters were intentionally distinguished for denoting the structures clearly between the predictions and experiments including

conven-tional descriptions, respectively. For instance, “BCC_A2,”

“FCC_A1,” and “HCP_A3” were used for the predictions

with Thermo-Calc, whereas lower-case letters,“bcc,” “fcc,”

and “hcp”were given for the experiments and conventional descriptions.

2.1 Alloy design

An Ir­Rh­Ru­W­Mo alloy system was investigated

experimentally as well as computationally in accordance

with an alloy design. The significant point of the present

alloy design, from a computational aspect, was to try to identify a compositional line on which all the possible three structures of bcc, hcp, and fcc appear at a given temperature. In determining the composition line, the authors referred to

a relationship between the VEC value of the structure12,14)

and computational calculations of the cross-sectional phase diagram by the CALPHAD scheme before starting the experiments. An underlying concept of the sandwich

strategy11)for the Ir­Mo­Rh­Ru­W system was adopted in

selecting the Ir­Rh­Ru­W­Mo system. That is, Ru with a

VEC of 8 is put in Mo and W with VEC=6 and Rh and

Ir with VEC=9 in the periodic table. As a result of trial

and error, as described in the Appendix, the alloy design

eventually led to selecting Ir_{0.415254(100¹2x)}Rh_{0.415254(100¹2x)}

-Ru_{0.169492(100¹2x)}WxMox alloys, which involved five

repre-sentative alloys (Alloys A­E). Specifically, the alloy

compositions were determined by trial and error to meet the requirement that the VEC values of the alloys vary

approximately in the range of 6.8­8.5 by referring to

empirically and statistically obtained data12) relating the

VEC and types of structures: VEC<6.87 (bcc), 6.87¯

VEC<8.0 (bcc+fcc), and VEC²8 (fcc). Table 1

summa-rizes the compositions of Alloys A­E, their VEC values, and

their configuration entropies normalized by the gas constant

(Sconfig/R). The values ofSconfig/Rof Alloys A, D, and E are

slightly smaller than 1.5, such that these three alloys cannot

be HEAs by the strict definition. Furthermore, the contents of

Ir and Rh in Alloy E are not in the range of 5¯ci/at%¯35,

and thus, this alloy cannot be a HEA according to the strict

definition. However, the present study regards Alloys A­E as

HEAs based on the definition of HEAs in a wide sense.

The cross-sectional phase diagram calculated with

Thermo-Calc 2019a with the TCHEA3 database is shown

in Fig. 1, which includes Alloys A­E on a composition

line. In the computations, only the following phases from

solutions (LIQUID, FCC_A1, BCC_A2, BCC_B2, and

HCP_A3) and chemically ordered fcc- and bcc-family solid

solutions (FCC_L12 and BCC_B2) were considered in the

calculations because of the restriction on the number of phases in the computations. Here, preliminary investigation

revealed that both FCC_L12 and BCC_B2 phases were

calculated in disordered states, and thus, they exactly

corresponded to FCC_A1 and BCC_A2, respectively.

However, the absence of the other conventional intermediate or intermetallic compounds in the calculation results was

confirmed separately for Alloys A­E over the temperature

Table 1 Fractions of components in Alloys A­E, their values of VEC, and configuration entropy normalized by gas constant (Sconfig/R), where Alloys A­E are on the composition line of Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox.

Contents, x/ at%

50 45 40 35 30 25 20 15 10 5 0

L

FCC_A1 HCP_A3 BCC_A2

HCP_A3 + FCC_A1 BCC_A2 + HCP_A3

L + BCC_A2

L + FCC_A1

Ir_{0.415254(100-2x)}Rh_{0.415254(100-2x)}Ru_{0.169492(100-2x)}W_xMo_xAlloys

L + fcc_A1 + HCP_A3 L + HCP_A3 + BCC_A2

E C

A B D

BCC_A2+ FCC_A1

8.55 8.38 7.98 7.47 VEC = 6.85

C’

Te

mperature,

T

/ K

3000

2500

2000

1500

1000

500

Ir, Rh 0 5 10 15 20 25 30 35 40

0 5 10 15 Ru

6 6.5 7 7.5 8 8.5

VEC

W, Mo

range shown in Fig. 1. The non-appearance of compounds is

a nature of the Ir­Rh­Ru­W­Mo alloy system, as presented

in a previous report.11) Figure 1 predicts that Alloys A, C,

and E, respectively, will form a single bcc, hcp, and fcc phase

at high temperatures, such asT=2100 K, whereas Alloys B

and D will be obtained as dual phases of bcc+hcp and

hcp+fcc, respectively. Furthermore, Alloys A­E have the

ability to be formed into triple phases of bcc+hcp+fcc and

bcc+fcc phases with decreasing annealing at low

temper-atures. This variety of phases that may appear on a

cross-sectional phase diagram is a significant feature of the Ir­Rh­

Ru­W­Mo System. These computationally predicted phases

were examined experimentally.

Additionally, a property diagram that displays the amounts of all phases as a function of temperature was computed for

Alloys A­E to compensate for the sparsity of Fig. 1 in terms

of the phases considered under the restriction. In calculating the property diagrams, all the possible phases, including

intermetallic/intermediate compounds, were considered

where these phases were derived from a default condition after selecting the constituent elements of Ir, Rh, Ru, Mo and W. The property diagrams shown in Fig. 2 indicate the non-appearance of other phases, except for bcc, fcc, hcp, and liquid over a wide temperature range from 500 to 2500 K

in Alloys A­E, supporting results in Fig. 1 calculated under

limited conditions by considering LIQUID FCC_A1,

FCC_L12, BCC_A2, BCC_B2, and HCP_A3 only.

2.2 Experiments

Alloy ingots of ³5 g with nominal compositions of

the Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox

alloys (Alloys A­E: x=35, 24, 15, 8, 5) were prepared by

arc melting from raw metals with industrial purity. The alloy compositions are summarized in Table 1. The raw metals

were commercially obtained and had a purity of 99.9 mass%.

The Ir, Rh, and Ru elements, which had an initial form of powders, were separately consolidated in a bulk form prior to

alloying. The 5-g samples were formed into button-shaped

ingots of³10 mm diameter and³5 mm height. The samples

were annealed at a high temperature to confirm the

equilibrium phases. The as-prepared ingots were annealed with a magnesium oxide crucible as a contacting material in a high-temperature furnace with a graphite heater. The chamber

of the furnace was vacuumed (³10¹2Pa) in advance and

thenfilled with high-purity Ar gas of ambient pressure. The

samples were homogenized by annealing, followed by cooling in the furnace. The cross-sections of these alloys, which were cut into two pieces perpendicular to the base,

were examined for their structure by X-ray diffraction

(XRD). In addition, the samples were observed for their morphology by scanning electron microscopy (SEM), and the chemical composition was analyzed by energy-dispersive X-ray spectroscopy (EDX) equipped on the SEM.

3. Results

Alloys A­E annealed at 2100 K for 2 h and Alloy C

annealed at 1273 K for 200 h were analyzed with XRD for

their crystallographic structures. The XRD profiles shown in

Figs. 3(c), (e) indicate that Alloys C and E annealed at

2100 K exhibit reflections consistent with a single hcp phase

and a single fcc phase, respectively. These identified phases

are denoted with Miller indices. Figures 3(c), (e) for Alloys C and E indicate the reproducibility of the predictions shown in Fig. 1. However, Alloy D does not provide the mixture of

hcp+fcc structures, but forms into a single hcp phase as

shown in Fig. 3(d). This disagreement between the prediction and experiment for Alloy D was presumably due to a

narrower composition region of hcp+fcc predicted in Fig. 1.

Fig. 2 Property diagrams calculated with Thermo-Calc 2019a and the TCHEA3 database for Alloys A­E by considering all the possible phases, including the intermetallic/intermediate compounds from a default condition, which were determined by selecting the constituent elements of Ir, Rh, Ru, Mo, and W. The vertical broken lines correspond to the annealing temperatures for comparison.

The authors did not investigate further to identify the intermediate alloy composition between Alloys D and E that

exhibits hcp+fcc at 2100 K. This is because the accurate

assessment of the cross-sectional phase diagram is not the purpose of the present study. On the contrary, the authors strongly believe that Alloy D with the hcp structure and Alloy E with the fcc structure indirectly prove the presence

of a composition region of hcp+fcc between the

composi-tions of Alloys D and E. Thus, it appears that the experiments tended to reproduce the predictions shown in Fig. 1 for

Alloys C­E.

In strong contrast, experiments for Alloys A and B

exhibited considerably different results compared with the

predictions. Specifically, the XRD profiles of Alloys A and

B annealed at 2100 K indicated, as shown in Figs. 3(a), (b),

a mixture of bcc+hcp phase and a single hcp phase,

respectively. These results suggest that the composition

region of bcc+hcp and bcc predicted in Fig. 1 should

considerably shift to the left, corresponding to the high-fraction direction of the bcc-forming elements of W and Mo. Again, the authors did not perform further experiments to determine the exact alloy compositions that exhibit a single-bcc structure. This is because the present study was performed in a framework of HEAs with the approximate

composition of 5¯ci/at%¯35. The above experimental

results shown in Fig. 3(a)­(e) reveal that the CALPHAD

predictions at 2100 K gave better agreement with

experi-ments for Alloys C­E with greater VEC than ³8 than for

Alloys A and B. Moreover, Alloy C annealed atT=1273 K

for 200 h, as shown in Fig. 3(cA), was not formed into a

mixture of structure bcc+fcc as predicted computationally

in Fig. 1, but into a single hcp structure. The reason for the

non-appearance of the thermodynamically stable bcc+fcc

structure in Alloy C annealed at 1273 K will be discussed in

the next section. Additionally, Alloys B­D in the as-prepared

states were identified as having an hcp structure; their results

are not shown in Fig. 3.

An analysis to determine the lattice constants of the bcc

and fcc phase (a) and the hcp phase (a,c), as well as their

ratio (c/a) was performed for Alloys A­E annealed at 2100 K

for 2 h and Alloy C annealed at 1273 K for 200 h (Alloy CA).

The results summarized in Table 2 indicate that Alloy A

with a partial hcp structure and Alloys B­D with an hcp

structure exhibitc/aranging 1.611­1.593. The values ofc,a,

and c/ain Alloy C with VEC=7.981 are almost the same

as those of the previous data:11) Ir26Mo20Rh22.5Ru20W11.5

and Ir25.5Mo20Rh20Ru25W9.5 HEAs with hcp structure with

VEC³7.86, and those of pure Ru.15)Moreover, no apparent

differences ina,c, andc/aare seen between Alloys C and CA.

The results of further examinations of Alloys C and E annealed at 2100 K, performed by observing their morphol-ogy with SEM and by analyzing chemical compositions with EDX, are shown below. Figure 4 presents SEM and EDX images of Alloy C annealed at 2100 K for 2 h, whereas Fig. 5 depicts those of Alloy E. The SEM image in Fig. 4(a) demonstrates that Alloy C appears to be almost homoge-neous at a submillimeter scale, except for the presence of grain boundaries indicated by areas with slightly dark contrast. The EDX analysis revealed that these grain boundaries were slightly poor in Ir in Fig. 4(b) and rich in Rh in Fig. 4(c). However, Ru, W, and Mo are homoge-neously distributed over the grain boundaries, as shown in

Fig. 4(d)­(f ). Thus, Figs. 3 and 4 revealed that Alloy C

annealed at 2100 K for 2 h were formed into a single hcp structure. Moreover, an analysis of the SEM image and element-mapping images of Alloy E annealed at 2100 K for

2 h, shown in Figs. 5(a) and 5(b)­(f ), respectively,

demon-strates the formation of a single fcc phase.

The possible reasons for the formation of single solid

solutions in Alloys B­E, as experimentally observed in the

Ir­Rh­Ru­W­Mo system, are rationalized in terms of the

geometrical features of the liquidus and solidus lines/

temperatures in the cross-sectional phase diagram shown in Fig. 1. Furthermore, a feature of Alloy E as a HEA with hcp structure was highlighted by the analysis of the Gibbs free

energy (G).

The present results are significant from a viewpoint of the

geometrical features of liquidus and solidus lines, in that Alloy E is a new class of refractory HEA with fcc structure. In particular, it is worth emphasizing that the liquidus

temperature (Tl) of Alloy E reaches ³2600 K, which is

approximately 1000 K higher than that of the CrMnFeCoNi

HEA.16) According to Fig. 1, the composition of Alloy E

shows a narrow range of the L+hcp_A3 region, nearly as

narrow 100 K, followed by a relatively small temperature

range of the hcp_A3+fcc_L12 phase region above 2200 K.

These narrow composition regions made it possible to form

a single fcc structure during its solidification from a melt. A

similar situation could be observed in Alloys C and D when

they solidified from their melts. The narrow temperature

range between Tl and Ts (¦Tl¹s) over the compositions of

Alloys C­E is considerably important to obtain a single solid

solution. This importance was pointed out in the authors’

previous work.6)This alternatively supports the disagreement

of Alloys A and B with relatively wide ¦Tl¹s of 200 K

or more. The large ¦Tl¹s of Alloys A and B led to them

forming other phases in the experiments with respect to the predictions.

The formation of a HEA with fcc structure in Alloy E in

the Ir­Rh­Ru­W­Mo system was analyzed in detail with a

G-composition diagram, as shown in Fig. 6. Alloy E is

unique as a HEA with fcc structure, in that the difference inG

between the FCC_A1 and HCP_A3 phase (¦GHCP_A3­FCC_A1)

is smaller than 1 kJ/mol, as depicted in Fig. 6. Further

calculations were performed to examine the temperature

dependence of G of LIQUID, BCC_A2, FCC_A1, and

HCP_A3 structures for Alloy E. Figure 7(a) exhibits the

conventional tendency that G increases with decreasing T.

Also, Fig. 7(b) indicates that¦GHCP_A3­FCC_A1increases with

decreasingT. The extrapolated value of¦GHCP_A3­FCC_A1was

evaluated to be 4.5 kJ/mol, which roughly corresponds to

¦G_hcp­fccvalues of SGTE of pure elements of fcc formers:17)

3.00 kJ/mol (Rh) and 4.00 kJ/mol (Ir). Alloy E exhibited

somewhat high value of¦GHCP_A3­FCC_A1at low temperature,

such as ¦GHCP_A3­FCC_A1=3.9 kJ/mol atT=300 K. Thus,

it was found that Alloy E exhibits small value of Fig. 4 (a) SEM image and (b)­(f ) element-mapping images of Alloy C annealed at 2100 K for 2 h.

¦GHCP_A3­FCC_A1<1 kJ/mol at high temperature range

around 2000 K. This small value of¦GHCP_A3­FCC_A1at high

temperature range suggests that Alloy E would possess an extremely low stacking fault energy and that it would tend

to exhibit a mixed structure of hcp+fcc when it was

mechanically tested at elevated temperatures. In other

words, such a small difference in ¦GHCP_A3­FCC_A1 of

Alloy E will lead to transformation-induced plasticity

(TRIP),18) which includes a lamellar hcp phase in the fcc

matrix containing high-density stacking faults. Similarly, Alloy E will contain twins introduced during deformation and will possess low stacking fault energy (SFE). Thus, the Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox

sys-tem has great advantage over the CrMnFeCoNi HEA, in that the hcp phase is in a thermodynamically stable state

without compulsory loading of high pressure, and that ¦G

between the hcp and fcc structures can simply be analyzed with the CALPHAD scheme.

4. Discussion

First, the agreement and disagreement between the experimental and computational data on the structure of

Alloys B­D are discussed by focusing on the formation of

HEAs from thermodynamic viewpoints and the applicability

of TCHEA3 database. Then, the effect of the VEC on the

formation of HEAs without and with hcp structure is discussed with respect to conventional HEAs comprising

3d transition metals and the present alloys in the Ir­Rh­

Ru­W­Mo system.

4.1 Thermodynamic viewpoints and applicability of

TCHEA3 database

The present experiments revealed that HEAs with a single

hcp structure were formed in Alloys B­D annealed at 2100 K

for 2 h and Alloy C annealed at 1273 K for 200 h. These

results indicate that the hcp structure in the Ir­Rh­Ru­W­Mo

system might exist more widely than thermodynamically expected. Such disagreements between the experimental and computational results at low temperature range are also

reported in the Ir26Mo20Rh22.5Ru20W11.5and Ir25.5Mo20Rh20

-Ru25W9.5alloys11)in the authors’previous study. Specifically,

these two alloys,11)both annealed at 2373 K and as-prepared

by arc-melting, formed into a single hcp structure, although the calculations with Thermo-Calc suggested the co-existence of bcc and fcc with hcp structures at temperatures lower than 1300 K. The presence of the stable phase in the high temperature range is rational in HEAs, because of the

high-entropy effect. That is, the high entropy (S) term due to

high-entropy effect accompanied by a high absolute temperature

(T) environment overcomes the enthalpy term (H) in the

Gibbs free energy, as expressed byG=H¹TS, leading to a

reduction in Gand stabilized solid solutions.

However, the experimental data of Alloys B­D as well, as

the previously reported Ir­Rh­Ru­W­Mo HEAs, with hcp

structure11) in the low temperature range, present an ironic

problem. That is, the strong tendency to form an hcp structure might not be controlled intentionally to produce bcc and fcc structures, although they were predicted in the thermody-namic calculations. From thermodythermody-namic viewpoints, it

appears that the formation of the structure of Alloys B­D

may be affected by imperfections of TCHEA3 database19)

when applying it to the multicomponent Ir­Rh­Ru­W­Mo

system for the following sub-ternary and sub-binary systems.

Specifically, only the Mo­Ru­W ternary system is tentatively

assessed19) _{among sub-ternary systems and Mo­Ir, W­Ir,}

Mo­Rh, and W­Rh binary systems are not19)_{assessed in the}

full range of composition and temperature. Thus, these binary systems were computed with a template of Property Diagram by selecting Phase Diagram in Calculation Type as shown in

Fig. 8. Features of Fig. 8 showed the absence of the HCP_A3

phase and the overestimation of maximum solid solubility

(maximum amount of primary solid solubility). Specifically,

Fig. 8 indicates that the calculated binary phase diagrams

did not contain HCP_A3, but just contained BCC_A2 and

FCC_A1 and their mixture. However, the maximum solid

solubilities shown in Fig. 8 were overestimated, particularly

in the BCC_A2 sides. In details, the maximum solid

solubility of the BCC_A2 structure was calculated to be as

Fig. 6 Gibbs free energy (G) calculated with Thermo-Calc 2019a and the TCHEA3 database atT=2100 K along the cross-sectional composition line of Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox, which includes Alloys A­E.

Fig. 7 (a) Temperature dependence of Gibbs free energy (G) of LIQUID, BCC_A2, FCC_A1, and HCP_A3 structures calculated for Alloy E with Thermo-Calc 2019a and the TCHEA3 database and (b) difference inG

large as approximately 30 at% of solute or more. The

maximum solid solubility of the FCC_A1 structure was

also large, and in the range of approximately 15­30 at% of

solute. According to phase diagrams,20) _{the maximum solid}

solubility of the Ir­Mo, Ir­W, Mo­Rh, and Rh­W binary

systems should be approximately 5­20 at%and 15­22 at%of

solute for bcc_A2 and fcc_A1, respectively.

As described above, absence of the hcp structure and

overestimation of solid solubility® in particular, at bcc

former side®should affect the assessment of the Ir­Rh­Ru­

W­Mo system. The former directly affected the smaller area

of HCP_A3 in Fig. 1 than that in the experiments. However,

the latter also affected the shift in the area of BCC_A2 in

Fig. 1. In reality, the latter showed that the prediction of

Alloy A at 2100 K as BCC_A2 instead of bcc_A2+hcp_A3

was experimentally denied and that better reproducibility of

experiments at 2100 K was observed for Alloys C­E than

for Alloys A and B. Furthermore, the former and latter

affected the disagreement between the prediction and

experiments for Alloy CA at low temperature. Specifically,

the prediction shown in Figs. 1 and 2 revealed that Alloy CA (Ir29.0678Rh29.0678Ru11.8644W15Mo15) decomposed into

BCC_A2 (Ir3.835Rh15.368Ru0.802W45.119Mo34.876) and FCC_A1

(Ir35.341Rh32.474Ru14.615W7.512Mo10.058) as summarized in

Table 3. The tie line at its equilibrium is not present on the composition line of the cross-sectional phase diagram shown

in Fig. 1 because of the nature of Alloy CA from the

multicomponent system. The compositions of the

equili-brated phases of Alloy CA at 1273 K shown in Table 3

indicate that the BCC_A2 was poor in Ir and Ru and rich in

W and Mo by composition differences of 14 at% or more.

However, the FCC_A1 was slightly poor in W and Mo and

rich in Ir and Mo but the differences were nearly 5 at% or

smaller. Consequently, it was considered that the larger

difference in compositions between the BCC_A2 and

Alloy CAmade it difficult to equilibrate, because of the large

composition modulation. Hence, it is tentatively concluded that the disagreements between the experiments and

calculations in Fig. 1 are principally affected by the

shortcomings of the TCHEA3 database. A supplementary,

slow diffusion effect in the Ir­Rh­Ru­W­Mo system at a

lower temperature range would affect the disagreement of

Alloy CA, which required large composition modulation to

achieve equilibrium (BCC_A2+FCC_A1).

4.2 The effect of the VEC

The conventional VEC analysis reported by Guo et al.12)

indicates that bcc, bcc+fcc, and fcc are stable in HEAs

when VEC<6.87 (bcc), 6.87¯VEC<8.0 (bcc+fcc), and

VEC²8 (fcc). This analysis reported in 2011 does not

contain the hcp structure, as the first HEAs with the hcp

structure6) _{were presented in 2014. It has recently been}

reported that the hcp structure is stable at VEC=36) _for

lanthanide alloys, VEC=2.821) _{for light-weight elements,}8)

and VEC³7.86 for Ir26Mo20Rh22.5Ru20W11.5 and

Ir25.5Mo20Rh20Ru25W9.5 alloys;11) moreover, VEC=7.472­

8.378 for Alloys B­D in the present study. These VEC values

of HEAs with hcp structure of³3 and³7­8 act as a guiding

principle derived by Miedema’s model13,14) _{for structural}

stability and the Friedel model for the number of d-electrons (nd)22)in the ranges 2.6<nd<3.5 and 6.5<nd<7.4. Here,

it should be noted that these models are valid for the paramagnetic elements. Accordingly, the VEC analysis based on these models provides rational results for refractory HEAs

with bcc structure23,24) with VEC³5. In general, the VEC

analysis given by Guo et al. is correct, as a result of the

statistical analysis that combined the structures of HEAs with the VEC values. However, the VEC analysis given by Guo

et al. for the Cantor alloy,2,25)_{as a HEA with fcc structure,}

should be treated with care because of the inclusion of the

BCC_A2 FCC_A1

BCC_A2 FCC_A1

BCC_A2 FCC_A1

BCC_A2 FCC_A1

BCC_A2+FCC_A1

BCC_A2+FCC_A1

BCC_A2+FCC_A1

BCC_A2+FCC_A1 (a) Mo-Ir

(b) W-Ir

(c) Mo-Rh

(d) W-Rh

L

L

L

L

ferromagnetic constituents of Fe, Ni, and Co. For instance, if

Fe with VEC=8 were a paramagnetic element such as Ru

and Os with VEC=8, the VEC analysis given by Guoet al.

would provide slightly different threshold values of VEC for

the boundary between bcc+fcc and fcc structures.

Con-sequently, the VEC analysis given by Guo et al.should be

modified by including the experimentally confirmed VEC

ranges for HEAs with hcp structure under special supple-mentary conditions. The present results showed that the supplemental conditions are that HEAs with hcp structure are composed of 4d and 5d transition metals and these alloys are subjected to high-temperature annealing near the solidus

temperature or solidified from a melt. Thus, the supplemental

VEC analysis should include 7.5¯VEC¯8.4 as well as

VEC³3 for HEAs with hcp structure. In particular, the

former supplemental VEC analysis, 7.5¯VEC (hcp)¯8.4,

does not contradict the VEC analysis given by Guo et al.

as VEC<6.87 (bcc), 6.87¯VEC<8.0 (bcc+fcc), and

VEC²8 (fcc). This is because Alloy C annealed at 1273 K

for an extremely long time leaves scope for the formation of

the bcc+fcc structure, as shown in Fig. 2, when the slow

diffusion is overcome to yield a thermodynamic equilibrium

state.

5. Conclusions

Five multicomponent alloys (Alloys A­E) on a

composi-tion line, Ir_{0.415254(100¹2x)}Rh_{0.415254(100¹2x)}Ru_{0.169492(100¹2x)}

-WxMox (x=35, 24, 15, 8, and 5 at%) were investigated

experimentally for their phase stability according to computa-tional predictions with Thermo-Calc and the TCHEA3 database. The experiments revealed that the samples annealed

at 2100 K for 2 h had a mixed dual-phase bcc+hcp structure

in Alloy A, single hcp structure in Alloys B­D, and single

fcc structure in Alloy E. CALPHAD predictions gave better

agreement with the experiments for Alloys C­E, with greater

VECs of³8, than for Alloys A and B. A refractory HEA with

fcc structure was newly found in Alloy E. Alloy C annealed

atT=1273 K for 200 h retained its hcp structure instead of

the predicted bcc+fcc phases. The formation of an hcp

structure in the Ir­Rh­Ru­W­Mo system could be affected

thermodynamically by the necessity of large composition

modulation to achieve bcc+fcc phases and kinetically by

slow diffusion particularly in the relatively low temperature

range. The disagreements between the predictions and

experiments were principally because the Ir­W, Ir­Mo, Rh­

W, and Rh­Mo binary systems were not assessed in the full

range of composition and temperature by the TCHEA3

database, leading to smaller HCP_A3 and a shift in BCC_A2

to the HCP_A3 side in the predictions. A VEC analysis has

been modified to compensate for the lack of data on HEAs

with hcp structure by adding 7.5¯VEC¯8.4, as well as

VEC³3. The former modification of the VEC analysis is

valid for HEAs comprising 4d and 5d transition metals and the higher temperature range near the limit of the solid phase.

Acknowledgment

This work was supported by JSPS KAKENHI Grant Number JP17H03375.

Appendix

The composition line has been determined under the

followingfive conditions.

(1) The bcc, bcc+hcp, hcp, hcp+fcc and fcc phases appear

simultaneously in the composition line of a cross-sectional phase diagram.

(2) The contents of the constituents (ci) roughly satisfy 5¯

ci/at%¯35, in whichfive alloys that correspond to the

above five phases can be present at an approximately

the same composition interval in a cross-sectional phase diagram.

(3) The W and Mo are regarded as bcc formers, Ir and Rh as fcc formers, and Ru as an hcp former, and the

resultant Ir­Rh­Ru­W­Mo quinary system is regarded

as a pseudoternary system consisting of bcc­hcp­fcc

formers as illustrated in Fig. A1(a).

(4) The contents of bcc and fcc formers exhibit opposite

increasing/decreasing behavior in the composition line,

because the composition line contains bcc formers and fcc formers at both ends because of condition 1. (5) The content of Ru either varies or keeps constant

against the changes of the contents of the other

constituent elements, which can be classified into the

following three cases (Cases 1­3). Within a

composi-tion line under condicomposi-tion 4, the content of Ru increases with (Case 1) increasing that of fcc formers or (Case 2) decreasing that of fcc formers. Otherwise the content of Ru remains unchanged (Case 3).

The specific procedure to determine the composition line was as follows.

First, the exact equiatomic composition (Ir20Rh20Ru20

-W20Mo20, at%) was set up to be the initial composition,

which was included in the initial composition line.

Second, Cases 1­3 were tested preliminarily by calculating

cross-sectional phase diagrams. As a result, it was revealed that Case 1 met the demand in terms of conditions 1 and 2.

The initial composition line for Case 1 included Ir20Rh20

-Ru20W20Mo20, and W50Mo50, and Ir33.333Rh33.333Ru33.333 at

the ends in the pseudoternary system.

Third, the composition line was modified slightly by

giving a modified composition that deviated by

approx-imately 2­3 at%from the Ir20Rh20Ru20W20Mo20. Specifically,

the modified composition was determined by changing the

ratios of the contents of bcc, hcp, and fcc formers from the

initial ratio of 2:1:2 for Ir20Rh20Ru20W20Mo20. This process

was swiping the compositions (Swipe-1), as shown in Fig. A1(b). Then, the cross-sectional phase diagram was

computed along the modified composition line.

Fourth, the calculated phase diagrams containing the initial

and modified composition were compared in terms of the

following two parameters: (i) the composition gap between

the phase boundaries of bcc/bcc+hcp and hcp+fcc/fcc and

(ii) the size of the areas of the bcc, hcp, and fcc phases in the

cross-sectional phase diagram. When the composition gap (i) becomes smaller by modifying the composition, further changes of the ratios of the contents of bcc, hcp, and fcc

formers were carried out to consider the further modified

composition line. This is because of the favorite tendency in terms of condition 2. However, opposite ratios of bcc, hcp and fcc formers were tested when the composition gap (i) becomes larger. The authors also paid attention to (ii) to make the experiments easier. The above trial was repeated in sequence by replacing the relationship between the initial and

modified compositions with the modified and

second-modified compositions and so forth.

Finally, the contents between the bcc formers (W and Mo) and those between the fcc formers (Ir and Rh) were

differentiated to find out the best composition line by

referring to condition 2. This process was termed

“Swipe-2”in Fig. A1(b).

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