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

Akira Takeuchi1,+, Takeshi Wada2 and Hidemi Kato2

1Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2Institute 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 formationof single, dual, and triple phases of bcc, fcc, and hcp structures. These structures were predicted with Thermo-Calc 2019a and the TCHEA3database on a cross-sectional phase diagram along a composition line: Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox (x: 0­50 at%). AtT = 2100K, 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 2100K revealed that Alloys C­E tended to exhibit better reproducibility and that Alloy E can be regarded as a new refractoryhigh-entropy alloy (HEA) with fcc structure. Alloy C annealed at T = 1273K for 200 h maintained a single-hcp structure. The non-appearanceof thermodynamically stable phases at low temperature in the Ir­Rh­Ru­W­Mo system was analogically explained as slow diffusion. The VECanalysis for HEAs with hcp structures was extended by including the range of 7.5 ¯ VEC ¯ 8.4 for alloys consisting of 4d and 5d transitionmetals annealed near their solidus temperature. The Ir­Rh­Ru­W­Mo system was significant in providing all possible simple solid solutions ofbcc, 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 materialssince their first reports in 2004.1,2) The developmentalprogress of HEAs has been accompanied by the expansionof their definitions in terms of alloy composition and relevantquantities. Initially, HEAs were defined1) as alloys with exactequiatomicity and with five or more constituent elements,which corresponds to the description with the configurationentropy normalized by the gas constant (Sconfig/R) satisfyingSconfig/R ² 1.61.3) Here, Sconfig is given by eq. (1) with afraction of the i-th elements ( pi) in the alloy with N elementsand is simply expressed as Sconfig = lnN in case of exactequiatomic alloy.

Sconfig=R ¼ �XN

i¼1

pi lnpi ð1Þ

Subsequently, the criteria for HEAs have been furtherextended with the recent progress in HEAs. For instance,HEAs in a narrow sense4,5) are alternatively defined bySconfig/R ² 1.5 and by the constituent element content inatomic percent (ci) in the range of 5 ¯ ci/at% ¯ 35.Furthermore, a recent definition for HEAs includes alloyswith Sconfig/R ³ 1.0­1.5 as medium-entropy alloys (MEAs)in a class of HEAs within their wide definition. Thus, HEAshave been loosely defined in a wide sense in multicomponentalloy systems.

As well as changes of the definition of HEAs in terms ofcompositions, the structural types of HEAs have also beenchanged gradually. Specifically, the definition had long beenlimited 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 pastseveral years. For instance, the constituent elements and/orproduction methods of HEAs with hcp structure reportedto date consist of heavy lanthanide elements with6) andwithout6,7) Y, light-weight elements by mechanical alloyingand subsequent transformation,8) 3d transition metals byapplying high pressure,9) and 4d and 5d transition metals bychemical reaction.10) Following these reports, the authorshave recently succeeded in fabricating HEAs with hcpstructure for alloys from 4d and 5d elements inIr26Mo20Rh22.5Ru20W11.5 and Ir25.5Mo20Rh20Ru25W9.5 al-loys11) by conventional arc melting and subsequentannealing. A unique feature of these Ir­Mo­Rh­Ru­WHEAs11) is that the hcp structure of the alloys is controlledby valence electron concentration (VEC)12) ³7.8. Specifi-cally, the alloy design is supported by a concept of structuralstability evaluated according to the enthalpy by Miedema’smodel13,14) as a function of VEC. Furthermore, the Ir­Mo­Rh­Ru­W HEAs with hcp structure11) are also unique in thatthe alloy compositions are optimized by thermodynamicpredictions11) using Thermo-Calc with the TCHEA3 databasefor HEAs. This implies that one can fabricate Ir­Mo­Rh­Ru­W HEAs with bcc or fcc structure by paying attentionto the appropriate VEC values for their structures andcomposition optimization. In other words, the authors cameto believe that the Ir­Mo­Rh­Ru­W system has the abilityto provide HEAs with bcc and fcc structures as well asunprecedented bcc+hcp and hcp+fcc structures as stabilizedphases when the VEC values and compositions areoptimized.

The purpose of this study was to examine the presence ofsingle bcc, fcc, and hcp structures and plural phases in theIr­Mo­Rh­Ru­W alloy system in accordance of an alloydesign based on VEC analysis and thermodynamic calcu-lations and optimizations.+Corresponding author, E-mail: akira.takeuchi.a8@tohoku.ac.jp

Materials Transactions, Vol. 60, No. 11 (2019) pp. 2267 to 2276©2019 The Japan Institute of Metals and Materials

2. Methods

In the present study, the capital and lower-case letters wereintentionally distinguished for denoting the structures clearlybetween the predictions and experiments including conven-tional descriptions, respectively. For instance, “BCC_A2,”“FCC_A1,” and “HCP_A3” were used for the predictionswith Thermo-Calc, whereas lower-case letters, “bcc,” “fcc,”and “hcp” were given for the experiments and conventionaldescriptions.

2.1 Alloy designAn Ir­Rh­Ru­W­Mo alloy system was investigated

experimentally as well as computationally in accordancewith an alloy design. The significant point of the presentalloy design, from a computational aspect, was to try toidentify a compositional line on which all the possible threestructures of bcc, hcp, and fcc appear at a given temperature.In determining the composition line, the authors referred toa relationship between the VEC value of the structure12,14)

and computational calculations of the cross-sectional phasediagram by the CALPHAD scheme before starting theexperiments. An underlying concept of the sandwichstrategy11) for the Ir­Mo­Rh­Ru­W system was adopted inselecting the Ir­Rh­Ru­W­Mo system. That is, Ru with aVEC of 8 is put in Mo and W with VEC = 6 and Rh andIr with VEC = 9 in the periodic table. As a result of trialand error, as described in the Appendix, the alloy designeventually led to selecting Ir0.415254(100¹2x)Rh0.415254(100¹2x)-Ru0.169492(100¹2x)WxMox alloys, which involved five repre-sentative alloys (Alloys A­E). Specifically, the alloycompositions were determined by trial and error to meetthe requirement that the VEC values of the alloys varyapproximately in the range of 6.8­8.5 by referring toempirically and statistically obtained data12) relating theVEC and types of structures: VEC < 6.87 (bcc), 6.87 ¯VEC < 8.0 (bcc+fcc), and VEC ² 8 (fcc). Table 1 summa-rizes the compositions of Alloys A­E, their VEC values, andtheir configuration entropies normalized by the gas constant(Sconfig/R). The values of Sconfig/R of Alloys A, D, and E areslightly smaller than 1.5, such that these three alloys cannotbe HEAs by the strict definition. Furthermore, the contents ofIr 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 strictdefinition. However, the present study regards Alloys A­E asHEAs based on the definition of HEAs in a wide sense.

The cross-sectional phase diagram calculated withThermo-Calc 2019a with the TCHEA3 database is shownin Fig. 1, which includes Alloys A­E on a compositionline. In the computations, only the following phases fromsolutions (LIQUID, FCC_A1, BCC_A2, BCC_B2, andHCP_A3) and chemically ordered fcc- and bcc-family solidsolutions (FCC_L12 and BCC_B2) were considered in thecalculations because of the restriction on the number ofphases in the computations. Here, preliminary investigationrevealed that both FCC_L12 and BCC_B2 phases werecalculated in disordered states, and thus, they exactlycorresponded to FCC_A1 and BCC_A2, respectively.However, the absence of the other conventional intermediateor intermetallic compounds in the calculation results wasconfirmed 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_A3BCC_A2

HCP_A3+

FCC_A1

BCC_A2 + HCP_A3

L + BCC_A2

L + FCC_A1

Ir0.415254(100-2x)Rh0.415254(100-2x)Ru0.169492(100-2x)WxMox AlloysL + fcc_A1 + HCP_A3 L + HCP_A3 + BCC_A2

ECA DB

BCC_A2+ FCC_A1

8.558.387.987.47VEC = 6.85

C’

Tem

pera

ture

, 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

Fig. 1 Cross-sectional phase diagram calculated with Thermo-Calc 2019aand the TCHEA3 database along a composition line denoting theIr0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox alloys. The sym-bols A­E and CA indicated by circles denote the annealing temperature ofAlloys A­E. The horizontal axes represent the contents of W and Mo asbcc former, those of Ru as hcp former, and those of Ir and Rh as fccformer, together with the VEC of the alloys.

A. Takeuchi, T. Wada and H. Kato2268

range shown in Fig. 1. The non-appearance of compounds isa nature of the Ir­Rh­Ru­W­Mo alloy system, as presentedin a previous report.11) Figure 1 predicts that Alloys A, C,and E, respectively, will form a single bcc, hcp, and fcc phaseat high temperatures, such as T = 2100K, whereas Alloys Band D will be obtained as dual phases of bcc+hcp andhcp+fcc, respectively. Furthermore, Alloys A­E have theability to be formed into triple phases of bcc+hcp+fcc andbcc+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 Ir­Rh­Ru­W­Mo System. These computationally predicted phaseswere examined experimentally.

Additionally, a property diagram that displays the amountsof all phases as a function of temperature was computed forAlloys A­E to compensate for the sparsity of Fig. 1 in termsof the phases considered under the restriction. In calculatingthe property diagrams, all the possible phases, includingintermetallic/intermediate compounds, were consideredwhere these phases were derived from a default conditionafter selecting the constituent elements of Ir, Rh, Ru, Mo andW. The property diagrams shown in Fig. 2 indicate the non-appearance of other phases, except for bcc, fcc, hcp, andliquid over a wide temperature range from 500 to 2500Kin Alloys A­E, supporting results in Fig. 1 calculated underlimited conditions by considering LIQUID FCC_A1,FCC_L12, BCC_A2, BCC_B2, and HCP_A3 only.

2.2 ExperimentsAlloy ingots of ³5 g with nominal compositions of

the Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMoxalloys (Alloys A­E: x = 35, 24, 15, 8, 5) were prepared byarc melting from raw metals with industrial purity. The alloycompositions are summarized in Table 1. The raw metalswere commercially obtained and had a purity of 99.9mass%.The Ir, Rh, and Ru elements, which had an initial form ofpowders, were separately consolidated in a bulk form prior to

alloying. The 5-g samples were formed into button-shapedingots of ³10mm diameter and ³5mm height. The sampleswere annealed at a high temperature to confirm theequilibrium phases. The as-prepared ingots were annealedwith a magnesium oxide crucible as a contacting material in ahigh-temperature furnace with a graphite heater. The chamberof the furnace was vacuumed (³10¹2 Pa) in advance andthen filled with high-purity Ar gas of ambient pressure. Thesamples were homogenized by annealing, followed bycooling 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 theirmorphology by scanning electron microscopy (SEM), and thechemical composition was analyzed by energy-dispersiveX-ray spectroscopy (EDX) equipped on the SEM.

3. Results

Alloys A­E annealed at 2100K for 2 h and Alloy Cannealed at 1273K for 200 h were analyzed with XRD fortheir crystallographic structures. The XRD profiles shown inFigs. 3(c), (e) indicate that Alloys C and E annealed at2100K exhibit reflections consistent with a single hcp phaseand a single fcc phase, respectively. These identified phasesare denoted with Miller indices. Figures 3(c), (e) for Alloys Cand E indicate the reproducibility of the predictions shownin Fig. 1. However, Alloy D does not provide the mixture ofhcp+fcc structures, but forms into a single hcp phase asshown in Fig. 3(d). This disagreement between the predictionand experiment for Alloy D was presumably due to anarrower composition region of hcp+fcc predicted in Fig. 1.

Fig. 2 Property diagrams calculated with Thermo-Calc 2019a and theTCHEA3 database for Alloys A­E by considering all the possible phases,including the intermetallic/intermediate compounds from a defaultcondition, which were determined by selecting the constituent elementsof Ir, Rh, Ru, Mo, and W. The vertical broken lines correspond to theannealing temperatures for comparison.

Fig. 3 XRD patterns measured with Co-K¡ radiation for (a)­(e) AlloysA­E annealed at 2100K for 2 h and (cA) Alloy C annealed 1273K for200 h.

Solid Solutions with bcc, hcp, and fcc Structures Formed in a Composition Line in Multicomponent Ir­Rh­Ru­W­Mo System 2269

The authors did not investigate further to identify theintermediate alloy composition between Alloys D and E thatexhibits hcp+fcc at 2100K. This is because the accurateassessment of the cross-sectional phase diagram is not thepurpose of the present study. On the contrary, the authorsstrongly believe that Alloy D with the hcp structure andAlloy E with the fcc structure indirectly prove the presenceof a composition region of hcp+fcc between the composi-tions of Alloys D and E. Thus, it appears that the experimentstended to reproduce the predictions shown in Fig. 1 forAlloys C­E.

In strong contrast, experiments for Alloys A and Bexhibited considerably different results compared with thepredictions. Specifically, the XRD profiles of Alloys A andB annealed at 2100K 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 compositionregion of bcc+hcp and bcc predicted in Fig. 1 shouldconsiderably 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 todetermine the exact alloy compositions that exhibit a single-bcc structure. This is because the present study wasperformed in a framework of HEAs with the approximatecomposition of 5 ¯ ci/at% ¯ 35. The above experimentalresults shown in Fig. 3(a)­(e) reveal that the CALPHADpredictions at 2100K gave better agreement with experi-ments for Alloys C­E with greater VEC than ³8 than forAlloys A and B. Moreover, Alloy C annealed at T = 1273Kfor 200 h, as shown in Fig. 3(cA), was not formed into amixture of structure bcc+fcc as predicted computationallyin Fig. 1, but into a single hcp structure. The reason for thenon-appearance of the thermodynamically stable bcc+fccstructure in Alloy C annealed at 1273K will be discussed in

the next section. Additionally, Alloys B­D in the as-preparedstates were identified as having an hcp structure; their resultsare not shown in Fig. 3.

An analysis to determine the lattice constants of the bccand fcc phase (a) and the hcp phase (a, c), as well as theirratio (c/a) was performed for Alloys A­E annealed at 2100Kfor 2 h and Alloy C annealed at 1273K for 200 h (Alloy CA).The results summarized in Table 2 indicate that Alloy Awith a partial hcp structure and Alloys B­D with an hcpstructure exhibit c/a ranging 1.611­1.593. The values of c, a,and c/a in Alloy C with VEC = 7.981 are almost the sameas those of the previous data:11) Ir26Mo20Rh22.5Ru20W11.5

and Ir25.5Mo20Rh20Ru25W9.5 HEAs with hcp structure withVEC ³ 7.86, and those of pure Ru.15) Moreover, no apparentdifferences in a, c, and c/a are seen between Alloys C and CA.

The results of further examinations of Alloys C and Eannealed at 2100K, performed by observing their morphol-ogy with SEM and by analyzing chemical compositions withEDX, are shown below. Figure 4 presents SEM and EDXimages of Alloy C annealed at 2100K for 2 h, whereas Fig. 5depicts 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 ofgrain boundaries indicated by areas with slightly darkcontrast. The EDX analysis revealed that these grainboundaries were slightly poor in Ir in Fig. 4(b) and rich inRh in Fig. 4(c). However, Ru, W, and Mo are homoge-neously distributed over the grain boundaries, as shown inFig. 4(d)­(f ). Thus, Figs. 3 and 4 revealed that Alloy Cannealed at 2100K for 2 h were formed into a single hcpstructure. Moreover, an analysis of the SEM image andelement-mapping images of Alloy E annealed at 2100K for2 h, shown in Figs. 5(a) and 5(b)­(f ), respectively, demon-strates the formation of a single fcc phase.

Table 2 Lattice constants of the bcc and fcc phase (a) and hcp phase (a, c), and their ratio (c/a) of Alloys A­E annealed at 2100K for 2 hand Alloys C annealed at 1273K for 200 h (Alloy CA). The data of Ir26Mo20Rh22.5Ru20W11.5 and Ir25.5Mo20Rh20Ru25W9.5 alloys11) andpure Ru15) are also shown for comparison, where the alloy compositions are described in the order of Ir, Rh, Ru, W, and Mo to adjustAlloys A­E.

A. Takeuchi, T. Wada and H. Kato2270

The possible reasons for the formation of single solidsolutions in Alloys B­E, as experimentally observed in theIr­Rh­Ru­W­Mo system, are rationalized in terms of thegeometrical features of the liquidus and solidus lines/temperatures in the cross-sectional phase diagram shown inFig. 1. Furthermore, a feature of Alloy E as a HEA with hcpstructure was highlighted by the analysis of the Gibbs freeenergy (G).

The present results are significant from a viewpoint of thegeometrical features of liquidus and solidus lines, in thatAlloy E is a new class of refractory HEA with fcc structure.In particular, it is worth emphasizing that the liquidustemperature (Tl) of Alloy E reaches ³2600K, which isapproximately 1000K higher than that of the CrMnFeCoNiHEA.16) According to Fig. 1, the composition of Alloy Eshows a narrow range of the L+hcp_A3 region, nearly asnarrow 100K, followed by a relatively small temperaturerange of the hcp_A3+fcc_L12 phase region above 2200K.These narrow composition regions made it possible to forma single fcc structure during its solidification from a melt. Asimilar situation could be observed in Alloys C and D whenthey solidified from their melts. The narrow temperaturerange between Tl and Ts (¦Tl¹s) over the compositions ofAlloys 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 disagreementof Alloys A and B with relatively wide ¦Tl¹s of 200Kor more. The large ¦Tl¹s of Alloys A and B led to themforming other phases in the experiments with respect to thepredictions.

The formation of a HEA with fcc structure in Alloy E inthe Ir­Rh­Ru­W­Mo system was analyzed in detail with aG-composition diagram, as shown in Fig. 6. Alloy E isunique as a HEAwith fcc structure, in that the difference in Gbetween the FCC_A1 and HCP_A3 phase (¦GHCP_A3­FCC_A1)is smaller than 1 kJ/mol, as depicted in Fig. 6. Furthercalculations were performed to examine the temperaturedependence of G of LIQUID, BCC_A2, FCC_A1, andHCP_A3 structures for Alloy E. Figure 7(a) exhibits theconventional tendency that G increases with decreasing T.Also, Fig. 7(b) indicates that ¦GHCP_A3­FCC_A1 increases withdecreasing T. The extrapolated value of ¦GHCP_A3­FCC_A1 wasevaluated to be 4.5 kJ/mol, which roughly corresponds to¦Ghcp­fcc values of SGTE of pure elements of fcc formers:17)

3.00 kJ/mol (Rh) and 4.00 kJ/mol (Ir). Alloy E exhibitedsomewhat high value of ¦GHCP_A3­FCC_A1 at low temperature,such as ¦GHCP_A3­FCC_A1 = 3.9 kJ/mol at T = 300K. 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 2100K for 2 h.

Fig. 5 (a) SEM image and (b)­(f ) element-mapping images of Alloy E annealed at 2100K for 2 h.

Solid Solutions with bcc, hcp, and fcc Structures Formed in a Composition Line in Multicomponent Ir­Rh­Ru­W­Mo System 2271

¦GHCP_A3­FCC_A1 < 1 kJ/mol at high temperature rangearound 2000K. This small value of ¦GHCP_A3­FCC_A1 at hightemperature range suggests that Alloy E would possess anextremely low stacking fault energy and that it would tendto exhibit a mixed structure of hcp+fcc when it wasmechanically tested at elevated temperatures. In otherwords, such a small difference in ¦GHCP_A3­FCC_A1 ofAlloy E will lead to transformation-induced plasticity(TRIP),18) which includes a lamellar hcp phase in the fccmatrix containing high-density stacking faults. Similarly,Alloy E will contain twins introduced during deformationand will possess low stacking fault energy (SFE). Thus, theIr0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox sys-tem has great advantage over the CrMnFeCoNi HEA, inthat the hcp phase is in a thermodynamically stable statewithout compulsory loading of high pressure, and that ¦Gbetween the hcp and fcc structures can simply be analyzedwith the CALPHAD scheme.

4. Discussion

First, the agreement and disagreement between theexperimental and computational data on the structure ofAlloys B­D are discussed by focusing on the formation ofHEAs from thermodynamic viewpoints and the applicabilityof TCHEA3 database. Then, the effect of the VEC on theformation of HEAs without and with hcp structure isdiscussed with respect to conventional HEAs comprising3d transition metals and the present alloys in the Ir­Rh­Ru­W­Mo system.

4.1 Thermodynamic viewpoints and applicability ofTCHEA3 database

The present experiments revealed that HEAs with a singlehcp structure were formed in Alloys B­D annealed at 2100Kfor 2 h and Alloy C annealed at 1273K for 200 h. Theseresults indicate that the hcp structure in the Ir­Rh­Ru­W­Mosystem might exist more widely than thermodynamicallyexpected. Such disagreements between the experimental andcomputational results at low temperature range are alsoreported in the Ir26Mo20Rh22.5Ru20W11.5 and Ir25.5Mo20Rh20-Ru25W9.5 alloys11) in the authors’ previous study. Specifically,these two alloys,11) both annealed at 2373K and as-preparedby arc-melting, formed into a single hcp structure, althoughthe calculations with Thermo-Calc suggested the co-existenceof bcc and fcc with hcp structures at temperatures lower than1300K. The presence of the stable phase in the hightemperature 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 theGibbs free energy, as expressed by G = H ¹ TS, leading to areduction in G and stabilized solid solutions.

However, the experimental data of Alloys B­D as well, asthe previously reported Ir­Rh­Ru­W­Mo HEAs, with hcpstructure11) in the low temperature range, present an ironicproblem. That is, the strong tendency to form an hcp structuremight not be controlled intentionally to produce bcc and fccstructures, although they were predicted in the thermody-namic calculations. From thermodynamic viewpoints, itappears that the formation of the structure of Alloys B­Dmay be affected by imperfections of TCHEA3 database19)

when applying it to the multicomponent Ir­Rh­Ru­W­Mosystem for the following sub-ternary and sub-binary systems.Specifically, only the Mo­Ru­W ternary system is tentativelyassessed19) among sub-ternary systems and Mo­Ir, W­Ir,Mo­Rh, and W­Rh binary systems are not19) assessed in thefull range of composition and temperature. Thus, these binarysystems were computed with a template of Property Diagramby selecting Phase Diagram in Calculation Type as shown inFig. 8. Features of Fig. 8 showed the absence of the HCP_A3phase and the overestimation of maximum solid solubility(maximum amount of primary solid solubility). Specifically,Fig. 8 indicates that the calculated binary phase diagramsdid not contain HCP_A3, but just contained BCC_A2 andFCC_A1 and their mixture. However, the maximum solidsolubilities shown in Fig. 8 were overestimated, particularlyin the BCC_A2 sides. In details, the maximum solidsolubility of the BCC_A2 structure was calculated to be as

Fig. 6 Gibbs free energy (G) calculated with Thermo-Calc 2019a and theTCHEA3 database at T = 2100K along the cross-sectional compositionline of Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)WxMox, whichincludes 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 withThermo-Calc 2019a and the TCHEA3 database and (b) difference in Gbetween FCC_A1 and HCP_A3 structures (¦GHCP-A3-FCC_A1).

A. Takeuchi, T. Wada and H. Kato2272

large as approximately 30 at% of solute or more. Themaximum solid solubility of the FCC_A1 structure wasalso large, and in the range of approximately 15­30 at% ofsolute. According to phase diagrams,20) the maximum solidsolubility of the Ir­Mo, Ir­W, Mo­Rh, and Rh­W binarysystems should be approximately 5­20 at% and 15­22 at% ofsolute for bcc_A2 and fcc_A1, respectively.

As described above, absence of the hcp structure andoverestimation of solid solubility ® in particular, at bccformer side ® should affect the assessment of the Ir­Rh­Ru­W­Mo system. The former directly affected the smaller areaof HCP_A3 in Fig. 1 than that in the experiments. However,the latter also affected the shift in the area of BCC_A2 inFig. 1. In reality, the latter showed that the prediction ofAlloy A at 2100K as BCC_A2 instead of bcc_A2+hcp_A3was experimentally denied and that better reproducibility ofexperiments at 2100K was observed for Alloys C­E thanfor Alloys A and B. Furthermore, the former and latteraffected the disagreement between the prediction andexperiments for Alloy CA at low temperature. Specifically,the prediction shown in Figs. 1 and 2 revealed that AlloyCA (Ir29.0678Rh29.0678Ru11.8644W15Mo15) decomposed intoBCC_A2 (Ir3.835Rh15.368Ru0.802W45.119Mo34.876) and FCC_A1(Ir35.341Rh32.474Ru14.615W7.512Mo10.058) as summarized inTable 3. The tie line at its equilibrium is not present on thecomposition line of the cross-sectional phase diagram shownin Fig. 1 because of the nature of Alloy CA from themulticomponent system. The compositions of the equili-brated phases of Alloy CA at 1273K shown in Table 3indicate that the BCC_A2 was poor in Ir and Ru and rich inW and Mo by composition differences of 14 at% or more.However, the FCC_A1 was slightly poor in W and Mo andrich in Ir and Mo but the differences were nearly 5 at% orsmaller. Consequently, it was considered that the largerdifference in compositions between the BCC_A2 and

Alloy CA made it difficult to equilibrate, because of the largecomposition modulation. Hence, it is tentatively concludedthat the disagreements between the experiments andcalculations in Fig. 1 are principally affected by theshortcomings of the TCHEA3 database. A supplementary,slow diffusion effect in the Ir­Rh­Ru­W­Mo system at alower temperature range would affect the disagreement ofAlloy CA, which required large composition modulation toachieve equilibrium (BCC_A2+FCC_A1).

4.2 The effect of the VECThe conventional VEC analysis reported by Guo et al.12)

indicates that bcc, bcc+fcc, and fcc are stable in HEAswhen VEC < 6.87 (bcc), 6.87 ¯ VEC < 8.0 (bcc+fcc), andVEC ² 8 (fcc). This analysis reported in 2011 does notcontain the hcp structure, as the first HEAs with the hcpstructure6) were presented in 2014. It has recently beenreported that the hcp structure is stable at VEC = 36) forlanthanide alloys, VEC = 2.821) for light-weight elements,8)

and VEC ³ 7.86 for Ir26Mo20Rh22.5Ru20W11.5 andIr25.5Mo20Rh20Ru25W9.5 alloys;11) moreover, VEC = 7.472­8.378 for Alloys B­D in the present study. These VEC valuesof HEAs with hcp structure of ³3 and ³7­8 act as a guidingprinciple derived by Miedema’s model13,14) for structuralstability 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 theparamagnetic elements. Accordingly, the VEC analysis basedon these models provides rational results for refractory HEAswith bcc structure23,24) with VEC ³ 5. In general, the VECanalysis given by Guo et al. is correct, as a result of thestatistical analysis that combined the structures of HEAs withthe VEC values. However, the VEC analysis given by Guoet 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

Fig. 8 Calculate binary phase diagrams of (a) Ir­Mo, (b) Ir­W, (c) Mo­Rh, and (d) Rh­W systems with TCHEA3 database whereCalculation Type was set to be Property Diagram: these binary systems are not19) assessed by TCHEA3 database in the full range ofcomposition and temperature, and thus, they were not computable with Binary Calculator as Graphical Mode Activity.

Solid Solutions with bcc, hcp, and fcc Structures Formed in a Composition Line in Multicomponent Ir­Rh­Ru­W­Mo System 2273

ferromagnetic constituents of Fe, Ni, and Co. For instance, ifFe with VEC = 8 were a paramagnetic element such as Ruand Os with VEC = 8, the VEC analysis given by Guo et al.would provide slightly different threshold values of VEC forthe boundary between bcc+fcc and fcc structures. Con-sequently, the VEC analysis given by Guo et al. should bemodified by including the experimentally confirmed VECranges for HEAs with hcp structure under special supple-mentary conditions. The present results showed that thesupplemental conditions are that HEAs with hcp structure arecomposed of 4d and 5d transition metals and these alloys aresubjected to high-temperature annealing near the solidustemperature or solidified from a melt. Thus, the supplementalVEC analysis should include 7.5 ¯ VEC ¯ 8.4 as well asVEC ³ 3 for HEAs with hcp structure. In particular, theformer 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), andVEC ² 8 (fcc). This is because Alloy C annealed at 1273Kfor an extremely long time leaves scope for the formation ofthe bcc+fcc structure, as shown in Fig. 2, when the slowdiffusion is overcome to yield a thermodynamic equilibriumstate.

5. Conclusions

Five multicomponent alloys (Alloys A­E) on a composi-tion line, Ir0.415254(100¹2x)Rh0.415254(100¹2x)Ru0.169492(100¹2x)-WxMox (x = 35, 24, 15, 8, and 5 at%) were investigatedexperimentally for their phase stability according to computa-tional predictions with Thermo-Calc and the TCHEA3database. The experiments revealed that the samples annealedat 2100K for 2 h had a mixed dual-phase bcc+hcp structurein Alloy A, single hcp structure in Alloys B­D, and singlefcc structure in Alloy E. CALPHAD predictions gave betteragreement with the experiments for Alloys C­E, with greaterVECs of ³8, than for Alloys A and B. A refractory HEAwithfcc structure was newly found in Alloy E. Alloy C annealedat T = 1273K for 200 h retained its hcp structure instead ofthe predicted bcc+fcc phases. The formation of an hcpstructure in the Ir­Rh­Ru­W­Mo system could be affectedthermodynamically by the necessity of large compositionmodulation to achieve bcc+fcc phases and kinetically byslow diffusion particularly in the relatively low temperaturerange. The disagreements between the predictions and

experiments were principally because the Ir­W, Ir­Mo, Rh­W, and Rh­Mo binary systems were not assessed in the fullrange of composition and temperature by the TCHEA3database, leading to smaller HCP_A3 and a shift in BCC_A2to the HCP_A3 side in the predictions. A VEC analysis hasbeen modified to compensate for the lack of data on HEAswith hcp structure by adding 7.5 ¯ VEC ¯ 8.4, as well asVEC ³ 3. The former modification of the VEC analysis isvalid for HEAs comprising 4d and 5d transition metals andthe higher temperature range near the limit of the solid phase.

Acknowledgment

This work was supported by JSPS KAKENHI GrantNumber JP17H03375.

Appendix

The composition line has been determined under thefollowing five 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 which five alloys that correspond to theabove five phases can be present at an approximatelythe same composition interval in a cross-sectional phasediagram.

(3) The W and Mo are regarded as bcc formers, Ir and Rhas fcc formers, and Ru as an hcp former, and theresultant Ir­Rh­Ru­W­Mo quinary system is regardedas a pseudoternary system consisting of bcc­hcp­fccformers as illustrated in Fig. A1(a).

(4) The contents of bcc and fcc formers exhibit oppositeincreasing/decreasing behavior in the composition line,because the composition line contains bcc formers andfcc formers at both ends because of condition 1.

(5) The content of Ru either varies or keeps constantagainst the changes of the contents of the otherconstituent elements, which can be classified into thefollowing three cases (Cases 1­3). Within a composi-tion line under condition 4, the content of Ru increaseswith (Case 1) increasing that of fcc formers or (Case 2)decreasing that of fcc formers. Otherwise the content ofRu remains unchanged (Case 3).

Table 3 Composition of Alloy CA and composition of its equilibrium bcc and fcc phases at 1273K calculated with Thermo-Calc and theTCHEA3 database, and composition differences between equilibrium phases and Alloy CA.

A. Takeuchi, T. Wada and H. Kato2274

The specific procedure to determine the composition linewas 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 calculatingcross-sectional phase diagrams. As a result, it was revealedthat 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 atthe ends in the pseudoternary system.

Third, the composition line was modified slightly bygiving a modified composition that deviated by approx-imately 2­3 at% from the Ir20Rh20Ru20W20Mo20. Specifically,the modified composition was determined by changing theratios of the contents of bcc, hcp, and fcc formers from theinitial ratio of 2:1:2 for Ir20Rh20Ru20W20Mo20. This processwas swiping the compositions (Swipe-1), as shown inFig. A1(b). Then, the cross-sectional phase diagram wascomputed along the modified composition line.

Fourth, the calculated phase diagrams containing the initialand modified composition were compared in terms of thefollowing two parameters: (i) the composition gap betweenthe 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, furtherchanges of the ratios of the contents of bcc, hcp, and fccformers were carried out to consider the further modifiedcomposition line. This is because of the favorite tendency interms of condition 2. However, opposite ratios of bcc, hcpand fcc formers were tested when the composition gap (i)becomes larger. The authors also paid attention to (ii) to makethe experiments easier. The above trial was repeated insequence by replacing the relationship between the initial andmodified 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) weredifferentiated to find out the best composition line byreferring to condition 2. This process was termed “Swipe-2” in Fig. A1(b).

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