More than entropy in high-entropy alloys Forming solid solutions or amorphous phase

More than entropy in high-entropy alloys:Forming solid solutions or amorphous phase

Sheng Guo a,Qiang Hu b,Chun Ng c,C.T.Liu a,*

a Center of Advanced Structural Materials,College of Science and Engineering,City University of Hong Kong,Kowloon,Hong Kong,China

b School of Materials Science and Engineering,Northwestern Polytechnical University,Xi’an710072,PR China

c Department of Mechanical Engineering,The Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Kong,China

a r t i c l e i n f o

Article history:

Received14March2013 Accepted2May2013 Available online

Keywords:

E.Phase stability,prediction B.Alloy design

B.Glasses,metallic a b s t r a c t

Metastable solid solutions can form preferably over intermetallic compounds,in cast high-entropy alloys or multi-component alloys with equi-or nearly equi-atomic compositions,due to the entropy contri-bution at elevated temperatures.Meanwhile,the high mixing entropy also favors the amorphous phase formation.The phase selection between solid solutions and the amorphous phase upon alloying in high-entropy alloys is intriguing.A two-parameter physical scheme,utilizing the atomic size polydispersity and mixing enthalpy,is found to be capable of capturing this phase selection mechanism.

ó2013Elsevier Ltd.All rights reserved.

1.Introduction

High-entropy alloys(HEAs)emerge as a new type of advanced metallic materials[1e4],and have received increasing attentions from the materials community.HEAs possess some excellent me-chanical and physical properties[4],and they have great potential to be used as high temperature materials,coating materials requiring high hardness and high wear resistance,and corrosion resistant materials with high strength.Some unique applications include the diffusion barrier material between copper in-terconnects and the Si substrate[5].The scienti?c understanding toward HEAs,however,lags much behind the technical exploration to them.The probably most outstanding scienti?c questions are the mechanism and condition for the solid solution phases(and not intermetallic compounds)to form in these highly concentrated multi-component alloys.The high entropy contribution at elevated temperatures lowering the Gibbs free energy of the solid solution phase[6],and the confusion principle[7]are apparent mecha-nisms,but meanwhile one is aware that these two mechanisms simultaneously favor the formation of the amorphous phase.The amorphous alloys,also known as metallic glasses(MGs),are another type of novel metallic materials and are at present the hot spot in the materials and condensed matter physics?eld[8e11]. The recent discovery of high-entropy bulk metallic glasses(HE-BMGs)[12e16]made the question more prominent:why(qualita-tively)and when(quantitatively)do solid solutions or the amor-phous phase form in multi-component alloys with high mixing entropies?A scienti?c scheme capable of predicting the formation of solid solutions or the amorphous phase in HEAs thus becomes both scienti?cally and technically signi?cant,which constitutes the topic of this work.We will show that simply using two alloy composition dependent physical parameters,i.e.,a topology natured atomic size polydispersity,and a chemistry natured mixing enthalpy,the phase selection mechanism in HEAs is effectively captured.

2.The high-entropy effect

By de?nition,HEAs are multi-component alloys having at least5 principle elements,and all the principle elements are mixed in equiatomic or close-to-equiatomic ratios[2].HEAs differ with con-ventional multi-component alloys in that there are no dominant one or two principle elements in the former.This metallurgy concept is a breakthrough in the history of the alloy development,as in the past people thought such a high percentage of alloying elements would lead to the formation of many unwanted phases,particularly the hard intermetallic compounds,and hence embrittle the material.Sur-prisingly,in various cast HEAs only simple solid solutions with fcc and/or bcc structures are obtained,and no intermetallic compounds form at all.Intuitively,the preferred formation of solid solutions over intermetallic compounds can originate from the high mixing en-tropy,as thermodynamically a high entropy contributes signi?cantly to decrease the Gibbs energy of the solid solutions at elevated

*Corresponding author.Tel.:t852********;fax:t852********.

E-mail addresses:csuguosheng@https://www.360docs.net/doc/b914974502.html,(S.Guo),chainliu@https://www.360docs.net/doc/b914974502.html,.hk (C.T.

Liu).

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Intermetallics

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0966-9795/$e see front matteró2013Elsevier Ltd.All rights reserved.

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Intermetallics41(2013)96e103

temperatures (D G mix ?D H mix àT D S mix ,where G mix is the Gibbs en-ergy,H mix is the enthalpy of mixing (alloying),S mix is the entropy of mixing and T is the absolute temperature;D indicates the change after mixing the pure elements [17])and hence to win the phase selection against intermetallic compounds [6,18].The mixing entropy of multi-component alloy systems,assuming a completely random

mixing,has the form of D S mix ?àR P

n i ?1c i ln ?c i ,where R is the gas constant,n is the number of alloying elements,c i is the atomic per-centage for the i th element [17].HEAs have much higher mixing entropies compared with conventional multi-component alloys and here comes their name.As a matter of fact,the solid solutions ob-tained in the cast HEAs were theoretically and experimentally veri-?ed by the current authors to be the ?rstly formed solid solution phases when cooling from the molten liquid [18].The slow diffusion kinetics of HEAs renders the metastable solid solutions (stable at high temperatures)to be frozen to the room temperature [4,18],in a way similar to how the amorphous phase is formed during the rapid solidi ?cation [19].This scenario lends support to the role that the high entropy plays in stabilizing the solid solutions.

The high entropy effect can also be related to the well-known confusion principle [7],which was originally proposed to account for the amorphous phase formation in metallic glasses.The confusion principle articulates that the more alloying elements are involved,the lower the chance that the alloy can form well de ?ned crystal structures.It was used with success to explain that the amorphous phase formation is easier (with a lower critical cooling rate to achieve the fully amorphous state from the molten liquid)in multi-component alloys with more than three alloying elements [20],where the mixing entropy is higher than in simpler alloy systems [21].In a similar way,the confusion principle can account for the formation of random solid solutions in HEAs,where the mixing en-tropy is even higher.The random solid solution differs with the amorphous phase in that the former is chemically disordered and topologically ordered,while the latter is both chemically and topo-logically disordered.Naturally,the confusion principle raises a question:on condition that the mixing entropy is high,is the for-mation of random solid solutions or the amorphous phase preferred?Indeed,one knows that in HEAs solid solutions tend to form,but the amorphous phase also forms,sometimes even in a bulk form [12e 16].From the alloy design point of view,it is thus interesting to frame out the scienti ?c principles capable of distinguishing the for-mation of solid solutions and the amorphous phase in HEAs.

In the mean time,the high mixing entropy does not always lead to the formation of random solid solutions or the amorphous phase,as intermetallic compounds also form in HEAs [21e 24].The available experimental evidences thus clearly suggest that apart from the entropy effect,there are other factors controlling the phase selection in HEAs.It is the target of this work to identify those factors playing the decisive roles,and we are particularly interested at those composition dependent factors out of physical metallurgy principles.3.Methodology

3.1.A parametric approach

In terms of the relevancy to the formation of solid solutions and the amorphous phase,two well-known physical metallurgy prin-ciples can provide clues to identify the key factors on the phase selection.First,the Hume-Rothery rules on the formation of binary solid solutions [25,26],which states that to have a large solubility of element A in element B,these two elements shall have a small difference in the electronegativity and atomic size.Second,Inoue ’s three empirical rules to form the bulk metallic glasses (BMGs)[20].According to Inoue,to form BMGs the alloy compositions shall have more than three elements,the atomic size difference among the

three main elements (A,B,C)needs to be large enough (>12%),and the mixing enthalpies between the main elements (A e B,A e C,B e C)have to be very negative.A similar principle was also proposed by Johnson [8].Summarizing Hume-Rothery rules and Inoue ’s rules,it seems that two types of factors are controlling the phase selection between solid solutions and the amorphous,on condition that the mixing entropies are comparable:1)topological,mainly the atomic size,and 2)chemical,the electronegativity,electron concentration or the mixing enthalpy.We then use these two types of parameters to search for the phase selection rules,based on a statistical analysis of the available experimental results in HEAs.For the multi-component alloys,the atomic size polydispersity [21e 24,27],d ,can be a good parameter to represent the atomic size differences among the constituent elements.d plays a critical role in the glass transition of hard sphere colloidal systems [27],and above a critical d no crystallization occurs for an arbitrary density.It is de ?ned as

d ????????????????????????????????????????P n i ?1c i e1àr i =r T2

q ,where r ?P n i ?1c i r i ,c i and r i are the atomic percentage and atomic radius of the i th element,and n is the number of alloying elements.We choose the mixing enthalpy to re ?ect the chemical factor,since on one hand this parameter has been proven effective in suggesting the easy glass formers [20],and on the other hand,compared to the electronegativity and electron concentration,the mixing enthalpy shows a better performance in distinguishing the formation of solid solutions and the amorphous phase [21].For simplicity,we use the weight averaged mixing en-thalpies of different pairs of alloying elements to represent the mixing enthalpy,D H mix ,of the alloys.D H mix is de ?ned as

D H mix ?P n i ?1;i s j c i c j U ij ,where U ij ?4D AB mix ,D AB

mix is the mixing enthalpy of binary liquid equiatomic AB alloys [28,29].D AB mix is calculated based on the Miedema ’s model [29]and only the chemical contribution is considered,assuming a random solid so-lution of atom A in B.It is noted that the electronegativity effect is actually included in the calculation of D AB mix [29].We then evaluate how d and D H mix can act as controlling factors for the phase se-lection in HEAs.

3.2.Experimental procedure

To experimentally prove the validity of the phase selection rules that are proposed here,some new alloys (1:AlCoCrCuFeNi;2:AlCoCrFeNiZr;3:CoCrCuFeNiZr;4:AlCoCrFeNiZr 0.6;5:CoCrCuFe-NiZr 0.8;6:CoCrCuFeNiZr 0.6)were prepared via the melt-spinning route.The master alloys were ?rst prepared by arc melting the pure element mixture in a Ti-gettered high-purity argon atmo-sphere.Ribbon-form alloys were then prepared via single roller melt spinning at a wheel surface velocity of 50m/s in the high-purity argon atmosphere.The width and thickness of the ribbons are about 0.6e 1mm and 15m m,respectively.An AlCoCrCuFeNi alloy was splat quenched to achieve higher cooling rates.The splats were produced in vacuum in an electromagnetic levitation cham-ber,and the produced splats are w 25mm in diameter and have an average thickness of w 40m m.The phase constitution was identi ?ed using a Bruker AXS D8Discover X-ray diffractometer (XRD)with the Co K a radiation.The glass transition and crystallization be-haviors of amorphous ribbons were evaluated using the differential scanning calorimetry (DSC,Setaram SETSYS Evolution 1750)under ?owing puri ?ed argon,with a heating rate of 0.33K/s.4.Results

4.1.Statistics analysis

Fig.1shows a statistical analysis of representative experimental results on the phase selection in HEAs,using d and D H mix (source

S.Guo et al./Intermetallics 41(2013)96e 10397

data given in Table 1).Almost all analyzed alloys were prepared by arc or induction melting,some followed by suction or injection casting,and only a few amorphous alloys were prepared by the melt spinning method.It is truly surprising to see that the phase selection between solid solutions and the amorphous phase can be so reasonably delineated by d and D H mix .Basically,solid solutions can form when d is small (d 0.064),and D H mix is noticeably negative (D H mix <à12.2kJ/mol).Interestingly,intermetallic com-pounds can form in the intermediate conditions in terms of d and D H mix ,as indicated by the olive ellipse in Fig.1.The intermetallic compound forming region does not indicate that intermetallic compounds are the sole alloyed products,but rather refer to the condition where the amount of intermetallic compounds is suf ?-cient to be detected by the X-ray diffraction (XRD).

d apparently plays a critical rol

e in distinguishing the formation o

f solid solutions and the amorphous phase.It is also surprisin

g to observe that the critical d to form the amorphous phase in high-entropy alloys is very close to that in hard sphere colloids,about 0.06w 0.07[27].This agreement possibly indicates that the requirement on the critical size polydispersity to form the amor-phous phase is universal among different systems.Solid solutions forming at a small d in the multi-component alloys can be seen as an extension of the Hume-Rothery rules on the solid solubility of binary solid solutions.The necessity of a large d to form the amorphous phase shall originate from the requirement on the suf ?cient atomic-level stress to destabilize the solid solution phase [30,31].According to Egami [30],the amorphous phase is stabilized partly because the solid solution phase of the corresponding composition is topologically unstable.This can account for the almost sharp transition between the solid solution phase and the amorphous phase in terms of d .

D H mix is also playing a key role in the phase selection between solid solutions and the amorphous phase.A small D H mix favoring the solid solution is still in line with the Hume-Rothery rules in that elements with similar chemistries have larger solid solubility.However,a large D H mix favoring the amorphous phase rather than the intermetallic compound,is surprising at the ?rst sight.On one hand,this could be due to the de ?nition of D H mix in this work.It is de ?ned as the composition weight averaged mixing enthalpies of different pairs of alloying elements.This averaged D H mix actually can not sensitively re ?ect the large mixing enthalpy of an

individual pair,which promotes the intermetallic compound for-mation anyway.This explains the competition between the amor-phous phase and intermetallic compounds in intermediate conditions in terms of D H mix .On the other hand,this scenario could possibly have a signi ?cant physical indication.The formation of intermetallic compounds or the amorphous phase is determined by the competition between D S mix (actually T $D S mix )and D H mix .In the case of forming intermetallic compounds,the more negative D H mix dominates as D S mix is negligible (note that D S mix here apparently cannot assume a fully random state of the atomic distribution);D S mix plays an important role when forming the amorphous phase and solid solutions.In cases when D S mix is high and at the same time D H mix is very negative,the statistical analyses here suggest that it is the amorphous phase that is preferred.The amorphous phase could be stabilized by the formation of short-range ordered atomic clusters (and at the same time not forming the long-range ordered intermetallic compounds),which is favored by the very negative D H mix [32,33].

4.2.Avoiding the formation of intermetallic compounds

From Fig.1,we know that d and D H mix are necessary conditions,but not suf ?cient conditions for the phase selection in HEAs.The d àD H mix scheme becomes suf ?cient only if the formation of intermetallic compounds can be avoided.To con ?rm the validity of the d àD H mix scheme in predicting the phase selection in HEAs,and more importantly,to reveal how the formation of intermetallic compounds is interrupting this phase selection rule,we prepared some new alloys using the melt spinning method to support the argument.We initially made three alloys,AlCoCrCuFeNi,AlCoCr-FeNiZr and CoCrCuFeNiZr (indicated by alloys 1,2and 3,respec-tively,in Fig.2).The alloy compositions were chosen based on their calculated d and D H mix (see Table 2),and their relative positions in the d -D H mix plot are shown in Fig.2.Fig.3(a)shows the XRD pat-terns for the three alloys.The identi ?ed phases in the AlCoCrCuFeNi (alloy 1)ribbon are mixed fcc and bcc solid solution phases,the same as those in the cast bulk alloys [34].This result is in agreement with the d -D H mix prediction.In AlCoCrFeNiZr (alloy 2)and CoCr-CuFeNiZr (alloy 3),where the amorphous phase formation is pre-dicted from the d -D H mix plot,experimentally the main phase is indeed amorphous,but crystalline phases apparently form.After careful analyses of the XRD patterns,the crystalline phase in AlCoCrFeNiZr (alloy 2)is mainly ZrX 2(X ?Co or Ni),with the space group (no.227).An uncertain phase exists in this alloy,which is labeled by the question mark in Fig.3(a),and it could correspond to AlNiZr with the space group P62m (no.189).The crystalline phases in CoCrCuFeNiZr (alloy 3)are ZrCu 5and ZrX 5(X ?Co or Ni).ZrCu 5and ZrX 5(X ?Co or Ni)have the same crystalline structure with the space group F43m (no.216),but the lattice constants are different.Clearly,in both AlCoCrFeNiZr (alloy 2)and CoCrCuFeNiZr (alloy 3),it is the formation of Zr-containing compounds that pre-vents the achieving of a fully amorphous structure.The preferred formation of Zr-containing compound phases is due to the more negative mixing enthalpy between Zr and other elements:à41kJ/mol for Zr e Co,à49kJ/mol for Zr e Ni and à23kJ/mol for Zr e Cu [28].For reference,the mixing enthalpies between the related alloying elements in these alloys are given in Fig.4.

We continued to prove that the phase selection rules can work for the amorphous phase formation,if the formation of interme-tallic compounds is avoided.As the formed intermetallic com-pounds in alloys 2and 3all contain Zr,they can possibly be avoided by simply reducing the Zr content,while keeping d and D H mix in the amorphous phase forming range.Along this line of thinking,we reduced the Zr content in AlCoCrFeNiZr (alloy 2)and prepared a new alloy with the composition of AlCoCrFeNiZr 0.6(alloy 4).Its

XRD

Fig.1.A d -D H mix plot delineating the phase selection in high entropy alloys.The dash-dotted regions highlight the individual region to form solid solutions,intermetallic compounds and the amorphous phase.(For interpretation of the references to colour in this ?gure legend,the reader is referred to the web version of this article.)

S.Guo et al./Intermetallics 41(2013)96e 103

98

S.Guo et al./Intermetallics41(2013)96e10399

Table1

Calculated parameters d,D H mix and D S mix for alloys used in Figs1and2.AM stands for amorphous phases,SS for solid solution phases and IM for intermetallic compound phases.The number in the subscript for alloys indicates the atomic portion of each element and is1if not labeled.

Material d?100D H mix(KJ/mol)D S mix(J/K$mol)Phase Preparation method References

Cu0.5NiAlCoCrFeSi 6.35à22.5816.01AM Mold-clamp casting[36] PdPtCuNiP9.29à23.6813.38AM Fluxed water quenching[13] SrCaYbMgZn15.25à13.1213.38AM Copper mould casting[14] SrCaYbMgZnCu18.14à13.1114.90AM Copper mould casting[14] SrCaYb(Li0.55Mg0.45)Zn15.63à12.1514.53AM Copper mould casting[14] ErTbDyNiAl13.74à37.6013.38AM Copper mould casting[14] CuNbNiTiZr9.24à21.2813.38AM Melt spinning[37] ZrHfTiCuNi10.32à27.3613.38AM Copper mould casting[15] ZrHfTiCuFe10.42à15.8413.38AM Melt spinning[15] ZrHfTiCuCo10.23à23.5213.38AM Melt spinning[15] ZrTiNiCuBe12.51à30.2413.38AM Injection casting[16] WNbMoTa 2.31à6.5011.53SS Arc Melting[38] WNbMoTaV 3.15à4.6413.38SS Arc Melting[38] FeCoNiCrCu 1.03 3.2013.38SS Copper mould casting[34] FeCoNiCrCuAl0.3 3.420.1614.43SS Copper mould casting[34] FeCoNiCrCuAl0.5 4.17à1.5214.70SS Copper mould casting[34] FeCoNiCrCuAl0.8 4.92à3.6114.87SS Copper mould casting[34] FeCoNiCrCuAl1.0 5.28à4.7814.90SS Copper mould casting[34] FeCoNiCrCuAl1.5 5.89à7.0514.78SS Copper mould casting[34] FeCoNiCrCuAl2.0 6.26à8.6514.53SS Copper mould casting[34] FeCoNiCrCuAl2.3 6.40à9.3814.35SS Copper mould casting[34] FeCoNiCrCuAl2.8 6.57à10.2814.01SS Copper mould casting[34] FeCoNiCrCuAl3 6.61à10.5613.86SS Copper mould casting[34]

FeNi2CrCuAl0.2 2.940.1212.01SS Copper mould casting[39]

FeNi2CrCuAl0.4 3.86à1.7012.45SS Copper mould casting[39]

FeNi2CrCuAl0.6 4.49à3.2712.72SS Copper mould casting[39]

FeNi2CrCuAl0.8 4.96à4.6112.88SS Copper mould casting[39]

FeNi2CrCuAl1.0 5.32à5.7812.98SS Copper mould casting[39]

FeNi2CrCuAl1.2 5.60à6.7813.02SS Copper mould casting[39]

AlCo0.5CrCuFeNi 5.45à4.5014.70SS Copper mould casting[40]

AlCoCr0.5CuFeNi 5.44à5.0214.70SS Copper mould casting[40] AlCoCrCu0.5FeNi 5.51à7.9314.70SS Copper mould casting[40] AlCoCrCuFe0.5Ni 5.40à5.5514.70SS Copper mould casting[40] AlCoCrCuFeNi0.5 5.43à3.9014.70SS Copper mould casting[40] CoCrCu0.5FeNi0.840.4913.15SS Copper mould casting[40]

Al0.5CoCrCu0.5FeNi 4.37à4.6014.53SS Arc melting[41] AlCoCrCu0.5FeNi 5.51à7.9314.70SS Arc melting[41]

Al1.5CoCrCu0.5FeNi 6.12à10.1414.53SS Arc melting[41]

Al2CoCrCu0.5FeNi 6.46à11.6014.23SS Arc melting[41]

AlCrCu0.5FeNi 5.92à7.7013.15SS Arc melting[41]

AlCo0.5CrCu0.5FeNi 5.71à7.9214.53SS Arc melting[41] AlCoCrCu0.5FeNi 5.51à7.9314.70SS Arc melting[41]

AlCo1.5CrCu0.5FeNi 5.33à7.8314.53SS Arc melting[41]

AlCo2CrCu0.5FeNi 5.17à7.6714.23SS Arc melting[41]

AlCo3CrCu0.5FeNi 4.88à7.2513.48SS Arc melting[41]

AlCo3.5CrCu0.5FeNi 4.75à7.0313.09SS Arc melting[41] AlCoCu0.5FeNi 5.90à8.6913.15SS Arc melting[41]

AlCoCr0.5Cu0.5FeNi 5.70à8.3214.53SS Arc melting[41] AlCoCrCu0.5FeNi 5.51à7.9314.70SS Arc melting[41]

AlCoCr1.5Cu0.5FeNi 5.34à7.5614.53SS Arc melting[41]

AlCoCr2Cu0.5FeNi 5.18à7.2014.23SS Arc melting[41] AlCoCrCu0.5Ni 5.81à10.1713.15SS Arc melting[41] AlCoCrCu0.5Fe0.5Ni 5.66à8.9214.53SS Arc melting[41] AlCoCrCu0.5FeNi 5.51à7.9314.70SS Arc melting[41] AlCoCrCu0.5Fe1.5Ni 5.37à7.1414.53SS Arc melting[41] AlCoCrCu0.5Fe2Ni 5.23à6.4914.23SS Arc melting[41] AlCoCrCu0.5Fe 5.87à6.1213.15SS Arc melting[41] AlCoCrCu0.5FeNi0.5 5.68à7.2814.53SS Arc melting[41] AlCoCrCu0.5FeNi 5.51à7.9314.70SS Arc melting[41] AlCoCrCu0.5FeNi1.5 5.35à8.2814.53SS Arc melting[41] AlCoCrCu0.5FeNi2 5.20à8.4314.23SS Arc melting[41] AlCoCrCu0.5FeNi2.5 5.06à8.4513.87SS Arc melting[41] AlCoCrCu0.5FeNi3 4.93à8.3913.48SS Arc melting[41] CrCuFeMnNi 3.20 2.7213.38SS Arc melting[42] CoCrFeMnNi 3.27à4.1613.38SS Induction melting[3]

Al0.3CrCuFeMnNi 4.21à0.2714.43SS Arc melting[42]

Al0.5CrCuFeMnNi 4.66à1.9214.70SS Arc melting[42]

Al0.8CrCuFeMnNi 5.15à3.9714.87SS Arc melting[42] AlCrCuFeMnNi 5.39à5.1114.90SS Arc melting[42]

Al0.8CrCu1.5FeMnNi 4.96à1.7414.74SS Arc melting[42]

Al0.8CrCuFe1.5MnNi 5.08à3.3114.74SS Arc melting[42]

Al0.8CrCuFeMn1.5Ni 5.05à4.2314.74SS Arc melting[42]

(continued on next page)

pattern shows a typical broad hump that is characteristic of the fully amorphous phase(Fig.3(b)).Similarly,we reduced the Zr content in CoCrCuFeNiZr(alloy3)and prepared two new alloys, CoCrCuFeNiZr0.8(alloy5)and CoCrCuFeNiZr0.6(alloy6).Zr-containing compound phases still existed in CoCrCuFeNiZr0.8 (alloy5),whose d is roughly the same as that of AlCoCrFeNiZr0.6 (alloy4),but disappeared in CoCrCuFeNiZr0.6(alloy6),with d and D H mix being w0.084andà9kJ/mol,respectively(Table2).The amorphous phase forming requirement on D H mix is noted to

expand slightly relative to the previous boundary(à12kJ/mol) shown in Fig.1,which possibly suggests that compared to d,D H mix is a relatively more relaxed controlling factor.The amorphous na-ture of the AlCoCrFeNiZr0.6(alloy4)and CoCrCuFeNiZr0.6(alloy6) was further con?rmed from the differential scanning calorimetric characterizations(Fig.5).The experimental results thus verify the physical scenario we revealed above:the formation of solid solu-tions and the amorphous phase can be effectively predicted by the d-D H mix scheme,on condition that the formation of intermetallic compounds can be avoided.5.Discussion

5.1.Amorphous phase vs.intermetallic compounds

The interruption of the phase selection rule by the formation of intermetallic compounds is discussed further,mainly on the physical meaning of a more negative D H mix.One knows that,a large negative D H mix promotes the formation of both short-range-ordered atomic clusters and long-range-ordered intermetallic compounds,the former favoring the amorphous phase formation [32,33].There seems to exist a competition between the formation of in?nite short-range-ordered atomic clusters and(?nite)long-range ordered intermetallic compounds,both driven by the more negative D H mix.Our work possibly indicates that on condition that solid solutions are topologically un-favored,this competition is essentially determined by the amount of strongly chemically attracted atomic pairs(SCAAPs).For example,in the cases we showed here,when the amounts of SCAAPs,i.e.,Zr e Co,Zr e Ni,or Zr e Cu,are beyond a critical value,intermetallic compounds(ZrX5 or ZrX2)form;once the amounts of these SCAAPs decrease to below the threshold,intermetallic compounds can not form and the fully amorphous phase forms.Unfortunately,D H mix,that we used here, is an essentially averaged chemical factor.It can reasonably re?ect the overall chemical attraction within an alloy system,but can not sensitively re?ect the contribution from those SCAAPs.A parameter that can simultaneously re?ect the overall chemical af?nities among an alloy system,and the individual contribution from the SCAAPs,is non-existent at the moment and certainly a target for future studies.On the other hand,based on this understanding,the undesired intermetallic compounds can be easily eliminated by reducing the amount of those SCAAPs forming elements,for example,by reducing the Zr content in this work.The identi?cation

Table1(continued)

Material d?100D H mix(KJ/mol)D S mix(J/K$mol)Phase Preparation method References

CoCrFeNiTi 6.68à16.3213.38IM Melt spinning[37] NbCrFeMnCoNi 5.49à12.0014.90IM Induction melting[3] TiCrFeMnCoNi 6.29à13.4414.90IM Induction melting[3] TiVCrCuFeMnCoNi 5.50à8.1317.29IM Injection casting[43]

Ti2.5CrCuFeCoNi7.24à14.0414.53IM Injection casting[22] AlTiVYZr10.95à14.8813.38IM Injection casting[22] ZrTiVCuNiBe11.48à24.8914.90IM Injection casting[22] CoCrCuFeNiTi0.8 5.70à6.7514.87IM Copper mould casting[44] CoCrCuFeNiTi1.0 6.12à8.4414.90IM Copper mould casting[44]

Al0.5CoCrCuFeNiTi0.8 6.26à10.1116.00IM Arc melting[45]

Al0.5CoCrCuFeNiTi1.0 6.54à11.6016.01IM Arc melting[45]

Al0.5CoCrCuFeNiTi1.2 6.76à12.8915.97IM Arc melting[45]

Al0.5CoCrCuFeNiTi1.4 6.94à14.0215.91IM Arc melting[45]

Al0.5CoCrCuFeNiTi1.67.09à15.0115.82IM Arc melting[45]

Al0.5CoCrCuFeNiTi1.87.21à15.8615.72IM Arc melting[45]

Al0.5CoCrCuFeNiTi2.07.31à16.6015.60IM Arc melting[45]

Al0.5CoCrCuFeNiV0.6 4.09à4.0715.92IM Arc melting[46]

Al0.5CoCrCuFeNiV0.8 4.07à4.7116.00IM Arc melting[46]

Al0.5CoCrCuFeNiV1.0 4.04à5.2516.01IM Arc melting[46] ZrHfTiAlCuNi9.42à34.1114.90IM Injection casting[47]

AlCoCrFeNiTi1.57.50à23.9114.78IM Injection casting

[48]

Fig.2.Updated Fig.1by adding new data from the newly prepared alloys in this work. The pink symbols annotated by numbers(1:AlCoCrCuFeNi;2:AlCoCrFeNiZr;3: CoCrCuFeNiZr;4:AlCoCrFeNiZr0.6;5:CoCrCuFeNiZr0.8;6:CoCrCuFeNiZr0.6)indicate the d-D H mix coordinates for the six newly prepared alloys.Note that the phase boundary for forming the amorphous phase is slightly expanded in terms of D H mix,and the original boundary in Fig.1is retained for comparison.(For interpretation of the references to colour in this?gure legend,the reader is referred to the web version of this article.)Table2

Calculated parameters d and D H mix for the prepared alloys in this work. Material d?100D H mix(KJ/mol)

AlCoCrCuFeNi(alloy1) 5.28à4.78 AlCoCrFeNiZr(alloy2)10.22à27.56 CoCrCuFeNiZr(alloy3)9.96à14.44 AlCoCrFeNiZr0.6(alloy4)9.17à22.91 CoCrCuFeNiZr0.8(alloy5)9.3à11.89 CoCrCuFeNiZr0.6(alloy6)8.42à8.93

S.Guo et al./Intermetallics41(2013)96e103 100

of necessary conditions for the amorphous phases to form,and also the proposing of convenient solutions to avoid the formation of intermetallic compounds when they compete with the amorphous phase,are thus of signi ?cant importance and provide new alloy design perspectives for amorphous alloys.The competition of intermetallic compounds with solid solutions is not discussed in detail in this work,but it is reasonable to assume that the competing intermetallic compounds with solid solutions can also be avoided by the compositional adjustment,in a way similar to that in cases where intermetallic compounds compete with the amorphous phase.5.2.Kinetics consideration

In the previous discussion,the kinetic issues were not empha-sized.The kinetics certainly plays an important role in the phase selection when cooling the molten liquids.Particularly,the for-mation of the amorphous phase is greatly in ?uenced by the ki-netics,and in principle any material can become amorphous given a suf ?cient rapid cooling rate from the molten liquid [35].One might raise such a question:then to what extent is the kinetics affecting the phase selection in HEAs?This question can possibly be answered from the following considerations.First,the formed phases in cast HEAs are mostly in a metastable state.The solid solution phases directly formed in cast alloys are actually the ?rst formed solid phases upon cooling,and they are frozen to the room temperature due to the slow diffusion kinetics of HEAs [18],in a way similar to the amorphous phase formation.Therefore,there certainly exists a phase selection between the formation of solid solutions or the amorphous phase upon cooling from the molten

liquid,when the cooling rates for various alloys are comparable,and it is at this state that we believe the composition dependent d and D H mix play the decisive role.Alternatively,it can be said that the d àD H mix phase selection rule we proposed here is helping to predict the trend of the formed phase in HEAs.For example,the alloys with small d and mildly negative D H mix have the trend to form solid solutions upon cooling,while those alloys with large d and more negative D H mix have the trend to form the amorphous phase.To further prove this point,the alloy 1(AlCoCrCuFeNi)was splat quenched with a high cooling rate compared to that from the melt spinning route,and the formed phases are still solid solutions (Fig.6).Recalling that alloy 4(AlCoCrFeNiZr 0.6)and 6(CoCrCuFe-NiZr 0.6)could achieve the fully amorphous state from the melt spinning route,it is fair to claim that the d àD H mix phase selection rule is effective,even bearing the kinetic effects in mind.Second,the predicted amorphous phase forming composition from the d àD H mix rule does not guarantee forming the amorphous phase,and the impact of this phase selection rule shall not be exaggerated.On one hand,as was discussed above,the competing intermetallic compounds have to be avoided.In the melt-spun alloys,the small amount and fewer types of intermetallic compounds make it easier to remove them based on the physical metallurgy considerations,as we did here in this work.On the other hand,the kinetics will play a role when the equilibrium phases or other metastable phase

are

Fig.3.(a)XRD patterns for alloys 1:AlCoCrCuFeNi,2:AlCoCrFeNiZr and 3:CoCrCuFeNiZr;(b)XRD patterns for alloys 2:AlCoCrFeNiZr and 4:AlCoCrFeNiZr 0.6,and alloys 3:CoCrCuFeNiZr,5:CoCrCuFeNiZr 0.8and 6:CoCrCuFeNiZr 0.6.(For interpretation of the references to colour in this ?gure legend,the reader is referred to the web version of this article.)

Fig.4.Mixing enthalpies (kJ/mol)of binary alloys in an equiatomic ratio.(For inter-pretation of the references to colour in this ?gure legend,the reader is referred to the web version of this article.)400

500

600

700800900

1000

AlCoCrFeNiZr 0.6

H e a t F l o w (a .u .)

T (K)

CoCrCuFeNiZr 0.6

0.33 K/s 0.04 W /g

Ex

T x

T x

T g

T g

Fig.5.DSC curves for amorphous AlCoCrFeNiZr 0.6(alloy 4)and CoCrCuFeNiZr 0.6(alloy 6)ribbons.(For interpretation of the references to colour in this ?gure legend,the reader is referred to the web version of this article.)

S.Guo et al./Intermetallics 41(2013)96e 103101

given suf ?cient time to form.How to improve the glass forming ability of HEAs,on the ground that the amorphous phase forming compositions can be reasonably predicted,is the next challenge.6.Conclusions

To conclude,a two-parameter physical scheme is revealed capturing the mechanism behind the phase selection upon alloying in high-entropy alloys.The topology natured atomic size poly-dispersity,d ,is the most critical parameter that distinguishes the formation of solid solutions and the amorphous phase.Solid solu-tions and the amorphous phase form below and above a critical d of w 0.065,respectively.The chemistry natured mixing enthalpy,D H mix ,is another important decisive factor and a more negative D H mix (<à12kJ/mol)favors the amorphous phase formation.The d àD H mix phase selection rule articulates the necessary conditions to form solid solutions or the amorphous phase in HEAs,but be-comes suf ?cient only after the possibility of forming intermetallic compounds is ruled out.In cases where undesired intermetallic compounds compete with the amorphous phase or solid solutions,they can be eliminated through simple compositional adjustments based on physical metallurgy considerations.The physical scheme unfolded here provides the comprehensive alloying strategy for HEAs,and shall have far-reaching in ?uence on the alloy develop-ment of conventional multi-component alloys.Acknowledgments

This research is ?nancially supported by the Research Grant Council (RGC),the Hong Kong Government,through the General Research Fund (GRF)under the project number CityU/521411.The splat-quenched AlCoCrCuFeNi sample was kindly provided by Dr.N.Wanderka from Helmhozz Centre Berlin for Materials and En-ergy,Germany.SG thanks Dr.XJ Liu for very helpful discussions.References

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