Single-phase high-entropy alloys – A critical update

Journal Pre-proof Single-phase high-entropy alloys – A critical update

Walter Steurer PII:

S1044-5803(19)32913-4

DOI:

https://doi.org/10.1016/j.matchar.2020.110179

Reference:

MTL 110179

To appear in:

Materials Characterization

Received date:

23 October 2019

Revised date:

7 January 2020

Accepted date:

2 February 2020

Please cite this article as: W. Steurer, Single-phase high-entropy alloys – A critical update, Materials Characterization (2020), https://doi.org/10.1016/j.matchar.2020.110179

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Journal Pre-proof

Single-phase high-entropy alloys – a critical update Walter Steurer Prof. em. ETH Zurich Loorenstrasse 60, 8053 Zurich, Switzerland [email protected]

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Keywords: High-entropy alloys Single-phase Solid solutions Materials characterization Review

Abstract

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Maximization of the configurational entropy – this has been the magic formula promising thousands or even millions of intermetallic multiple-principal-element solid solutions with potentially novel physical and/or mechanical properties. What has been left of this dream fifteen years after the first publication on high-entropy alloys (HEAs)? So far, intermetallic single-phase HEAs have been identified in ≈80 quaternary, quinary and senary intermetallic systems, only. With a few exceptions their not so unexpected physical properties are mainly determined by the average of the properties of the constituents. The, in some cases, exceptional mechanical properties have been related to lattice distortions and/or local clustering. In the following, I will give an update of the development in this area over the past five years. The main focus will lie on the synthesis of HEAs, their phase stability and characterization from a crystallographic point of view.

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1 Introduction

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Since the first paper on high-entropy alloys (HEAs) in the year 2004 (Yeh et al. [1]), the number of publications on this topic has been exploding. More than 80% of the ≈3100 papers so far deal with multiphase HEAs, and their number is still growing exponentially in contrast to the just linear increase of publications on single-phase HEAs (see Fig. 1). Compositionally complex multi-phase alloys have to be based on at least one single-phase HEA to be called a „high-entropy alloy‟. Therefore, single-phase HEAs are the topic of the present critical update of our first review (Kozak et al.[2]), which was based on all the ≈400 papers on both single- as well as multi-phase HEAs that appeared in the decade after the seminal paper by Yeh et al. [1]. In contrast, our present review focuses just on the ≈500 papers on single-phase HEAs published since 2004. Caveat: not all HEAs denoted „single-phase‟ in literature may be true singlephase materials, because the methods employed for their synthesis and characterization did not always allow an unambiguous and reliable determination of their equilibrium phase state at a given temperature.

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Indeed, it was not an easy task identifying those papers that were dealing with materials that could be called „single-phase HEAs‟. The decision was straightforward only in the rare cases of studies on singlecrystalline HEAs. The main problem were the many papers reporting investigations on as-cast samples. Such specimens have an undefined thermal history and, as a consequence, an undefined structural state. Consequently, measurements of mechanical and physical properties on as-cast HEAs may not be accurately reproducible or comparable to those of other HEAs, and might be of limited value for potential applications. HEAs containing nonmetallic elements such as B, C, N, etc. were not considered in this review although they may have interesting mechanical properties (see, e.g. Seol et al. [3], Wang et al. [4], Moravcik et al. [5]). The preference of these non-metallic atoms for specific interstitial sites (tetrahedral voids, e.g.) as well as their directional chemical bonding can locally inhibit the formation of random solid solutions, i.e., of HEAs in the original meaning of the word.

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The physical properties of HEAs are controlled to a large extent by the average of the properties of the constituting elements. In some cases novel properties may emerge („cocktail effect‟). The transport properties such as electric or thermal conductivity or diffusion processes as well as the movement of dislocations can be strongly influenced by the missing actual lattice periodicity, in particular by significant lattice distortions caused by large atomic size differences. Caveat: due to specific chemical interactions, i.e., homo- and heteroatomic pair potentials differing from one another, local ordering phenomena will also have a significant or even decisive influence on the properties. Given 44 common non-radioactive metallic elements (29 TM + 14 RE + Al) and neglecting thermodynamics, the number of potential HEAs with five or six components, for instance, would be incredibly large, theoretically, i.e, (

)

or (

)

element combinations,

respectively. Therewith, the probability could be high of finding materials with novel and exciting properties, which could even be compositionally (electronically) fine-tuned if wanted. Unfortunately, the reality looks somewhat different with the just ≈80 quaternary, quinary and senary intermetallic systems, where HEAs could be observed so far (see Table 1). In our first review article, five years ago, we could review 10 quaternary and quinary systems with HEAs, only (Kozak et al.[2]). However, quite a few of the newly discovered HEAs are just derivatives of the previous ones. The present review focuses on the phase stability, materials synthesis and characterization of intermetallic single-phase HEAs. In contrast to the numerous other reviews, the problems resulting from non-state-ofthe-art sample preparation and characterization by X-ray diffraction are addressed from a crystallographic point of view. The mechanical properties of HEAs strongly depend on the actual structural ordering phenomena within the solid solutions as well as on their microstructure. Both of them strongly depend themselves on the thermal history of the specimen to be investigated. And that is undefined in many, if 2

Journal Pre-proof not the majority, of the papers on HEAs. Therefore, mechanical properties will not be discussed in this review.

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Finally, I want to point to a few other more recent reviews, complementary to the present review, which include multi-phase HEAs and some of their properties: for a general overview see Miracle & Senkov [6], on refractory HEAs Senkov et al. [7], and on high-pressure (HP) induced phase transitions in HEAs see Zhang et al. [8] and Dong et al. [9]. There are also recent reviews on the synthesis of HEAs by mechanical alloying (Vaidya et al. [10]), by powder metallurgy (Torralba et al. [11]), and by additive manufacturing (Li et al. [12]). Concepts regarding the thermodynamics of HEAs and modeling by firstprinciple calculations were reviewed by Widom [13], Gao et al. [14],[15], and Ge [16], for instance. Potential HT-applications for HEAs were reviewed by Praveen & King [17]. A review on mechanical properties, with the focus on CoCrNi-based HEAs, was published by Li et al. [18]. For an extensive overview on nano-mechanical studies on all kinds of HEAs see Zou [19]. For a general review just on bcc HEAs, see Couzinie & Dirras [20], and for a review on superconducting HEAs, see Sun & Cava [21].

2 Terminology

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The term high-entropy alloy (HEA) was coined in 2002 by the Taiwanese materials scientist Jien-Wei Yeh in his US patent application No US2002159914-A1 [22] : “The features of the alloys are that there are five to eleven major metallic elements and with or without minor elements, the minor elements are selected from the element group other than the major metallic elements, the mole fraction of each major metallic element in the alloy is between 5% and 30%, and the mole fraction of each minor element in the alloy is less than 3.5%.”

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From the very beginning, the definition of HEAs has not only been extended to multiphase materials, but also to solid solutions with just four approximately equiatomic components, also called „medium-entropy alloys‟, MEAs. LEAs, „low-entropy alloys‟ could then be solid solutions of just two or three elements. One should keep in mind that not only random solid solutions are entropy stabilized but also all hightemperature (HT) compounds. However, in most cases HT-intermetallics are so-called line-compounds without compositional flexibility, and are stabilized by the vibrational entropy, , rather than by the configurational mixing entropy, . The latter is only of importance for intermetallics with an extended compositional stability field at T > 0 K. Examples are the HT-phases -AlMn and -AlMn with wedge-shaped stability fields and simple bcc and hcp structures, respectively. They are separated by a small two-phase region. Should these binary phases be called LEAs or just disordered intermetallic compounds? The same question applies to compositionally flexible ternary or quaternary intermetallics as well. I think it is also not justified to classify concentrated solid solutions as „HEAs‟ if they crystallize in structure types such as B2 (cP2-CsCl), other superstructures of the simple bcc, fcc or hcp structures or even more complex structure types. As we will see below, their configurational entropy is too low to be called a „HEA‟. Zhou et al. [23] suggested to name randomly disordered phases with structures other than simple bcc, fcc or hcp solid solutions „high-entropy intermetallic compounds (HEICs)‟ HEAs can also be amorphous, and are then called high-entropy metallic glasses (HEMGs) (see, e.g., Bazlov et al. [24]). Perhaps a better, more general name for HEAs that has already been used in some papers, could be „multiple principal element alloys (MPEAs)‟ or „complex, concentrated solid solutions (CCSSs)‟. Both terms intrinsically assume lattice periodicity on average. Thus, in the original meaning of the term, a HEA corresponds to a statistically disordered single-phase material, a „multicomponent concentrated solid solution alloy‟ (MCSSA) with simple average crystal structure such as cI2-W (bcc), cF4-Cu (fcc) or hP2-Mg (hcp). Senkov et al. [7] distinguish between „refractory high entropy alloys‟ 3

Journal Pre-proof (RHEAs) consisting of five or more principal elements with concentrations between 5% and 35%, and „refractory complex concentrated alloys‟ (RCCAs), containing three or more elements with concentrations > 35%. Generally, the term „high-entropy alloy‟is somewhat misleading, because the vibrational entropy of HTphases is much higher than the configurational entropy of HEAs. Strictly speaking, the solid solutions we are interested in should be called „high-mixing-entropy alloys (HMEAs)‟ or „high-configurational-entropy alloy (HCEAs).‟ In the following, however, we will stick to the term „HEA‟ because it is almost exclusively used in literature. Furthermore, if not other stated otherwise by the term „HEA‟ I always mean „intermetallic single-phase HEA‟.

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3 Phase stability 3.1 Thermodynamic parameters

∑

( )

. Since in a real solid solution the atoms are not

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By definition, single-phase HEAs are thermodynamically stabilized by their high mixing entropy, . The main contribution comes from the ideal ∑ configurational mixing entropy , with R the gas constant, 8.314 Jmol-1, and ci the mole fraction of the i-th of the N components (different chemical elements). , is always positive and maximum for an equiatomic chemical composition and random distribution of the N components on the lattice sites. For N = 5, for instance, and equiatomic composition we get

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non-interacting hard balls of equal size, Ye et al. [25] suggested to supplement the ideal by an always negative excess entropy term, , which takes into account the true atomic sizes and their packing fractions. Based on this additional term, they formulated a generalized thermodynamic rule for phase selection in multi-component alloys, which should allow separating single- from the multi-phase regimes of HEAs in the generalized thermodynamic phase diagram.

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One should keep in mind that the vibrational mixing entropy, , can be positive or negative. This depends on the difference between the atomic interaction potentials in the pure elements and in the HEA (see, e.g., Wu et al. [26],) as well as on the changes in the vibrational density of states. Its contribution to the total mixing entropy can be significant in contrast to that of the electronic mixing entropy, (see, e.g., Manzoor et al. [27]). The latter results from the change in the distribution of localized electrons and holes in the HEA as a result of mixing (see, e.g., Zhou et al. [28]). The magnetic mixing entropy, , can be significant for HEAs based on atoms with large magnetic moments such as some rareearth (RE) elements (Yuan et al. [29]). Ma et al [30] compared by ab initio thermodynamics the different entropy contributions of the quinary HEA CoCrFeMnNi. At 1000 K, for instance, they obtained in their calculations , , , and . It is obvious that the vibrational entropy contributes several times more to the total entropy than the configurational mixing entropy. Due to its entropy-stabilization, a HEA will be thermodynamically stable only above a given threshold temperature T for which the Gibbs free mixing energy is negative, ΔGmix = ΔHmix – TΔSmix < 0. This is always the case if the mixing enthalpy obeys |ΔHmix| < |TΔSmix| and ΔSmix > 0. Intermetallic compounds are formed if |ΔHmix| > |TΔSmix| and ΔHmix < 0. Phase separation will take place in the case of ΔHmix > 0 and ΔHmix > |TΔSmix|. If |ΔHmix| is not significantly larger than |TΔSmix| and ΔHmix < 0, then an ordered substructure may be formed accompanied by some disorder on one or more sublattice sites (Wyckoff positions). An example would be a HEA with B2 (cP2-CsCl) type structure, which is a superstructure of 4

Journal Pre-proof the simple bcc (cI2-W) structure type. In the case of a senary HEA ABCDEF, with atoms A, B and C smaller than the other ones, atoms (A,B,C) may randomly occupy one sublattice and (C,D,E) the other, for instance. Since a super-ordered solid solution with B2 (cP2-CsCl) type structure is on average longrange ordered it should be called a HEIC rather than a HEA.

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It has to be taken into account that the ideal case of a random distribution of different chemical elements on the lattice sites can never be realized. The different atomic radii, electronegativities and mutual interaction potentials will not only lead to local lattice distortions but also to local ordering (clustering, short-range order, sro). In single-crystal diffraction patterns, this is indicated by more or less pronounced and structured diffuse scattering phenomena (see, e.g., Maiti & Steurer [31]). The influence of local ordering on the mixing entropy was shown as a function of temperature on the example of Al1.33CoCrFeNi and other HEAs based on Monte Carlo/Molecular Dynamics and CALPHAD simulations by Widom [13]. He also demonstrated how short-range ordering can take place as precursor to the formation of intermetallic phases of the B2 (cP2-CsCl) or L12 (cP4-Cu3Au) structure type. The local ordering in CoCrFeNi, for instance, was studied by Schönfeld et al. [32] experimentally and theoretically. It was shown that this HEA behaves like a disordered quasibinary Me0.75Cr0.25 alloy with the L12 (cP4Cu3Au) structure type.

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Based on the knowledge of the respective binary phase diagrams, we can expect local atomic ordering if one or more of the binary subsystems of the HEA-forming N-ary system show either a large miscibility gap (e.g., Hf-Nb or Sm-V with repulsive hetero-atomic interactions) or many intermetallic compounds (e.g., Al-Ta or Ni-Sm with attractive hetero-atomic interactions). In the case of Ta-Zr, there is a very wide miscibility gap below 2056 K and full miscibility beyond up to the melting temperature of 2120 K. Consequently, we can expect for Ta and Zr containing HEAs some kind of local ordering depending on their thermal history. In the case of the full solid solution Ta-V, a C14 Laves phase (hP12-MgZn2 type) forms below 1702 K. This can be expected to happen in a HEA containing these elements as well. All local ordering phenomena will have a significant influence on the mechanical and transport properties, of course. Local clustering can be compared to nanoparticle precipitation in some way. Therefore, physical and mechanical properties should be measured on thermally equilibrated samples, only, to be reliable. And, if possible, as a function of temperature within the stability region of the HEA.

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In contrast to the predictions of the existence of thousands or even millions of HEAs (see, e.g., Widom [33], [13], Senkov et al. [34]), only a very limited number (≈80) of intermetallic systems have been identified so far with, in a given temperature/pressure range, thermodynamically or kinetically stable HEAs or MEAs. So far, adding more elements to, say, quinary or senary HEAs rarely leads to new HEAs, but rather to phase separation, although the mixing entropy of an ideal (N+1)-component equiatomic alloy would increase. In the case of an equimolecular mixture we would get . For example, going from a bcc quinary to a bcc senary equiatomic HEA would increase the mixing entropy by more than 11% from 1.61 R to 1.79 R. In the case of a senary HEA ABCDEF with B2-type (cP2CsCl) structure, however, there are two Wyckoff positions 1a (0,0,0) and 1b (1/2,1/2,1/2) to be occupied differently. Let us assume random occupancy of A, B, C and D, E, F on 1a (sublattice s = 1) and 1b (sublattice s = 2), respectively. Then we get, according to the sublattice model by Sundman and Ågren [35], with the number of sites (multiplicity of the Wyckoff position) on the s-th of the n sublattices (Wyckoff positions), and the fraction of element species i randomly distributed thereon, and ∑ everything normalized to one mol: (∑ )⁄∑ compared to

in the case of a bcc senary HEA. Since a quinary

MPEA with defines what should be called a HEA, the senary MPEA with B2 (cP2CsCl) structure type would just be a LEA ( ) or, better, a HEIC, consequently. Of

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Journal Pre-proof course, these are ideal values for hard balls of equal size and without any interaction, what is far from reality.

3.2 Composition space

HEAs, i.e., 84,709, if we count

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solutions‟. This would still result in incredible 1.2% of (

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The distribution of N-component HEAs can be described in an N-component composition space, which itself resides within a d-dimensional simplex (generalization of the notion of a triangle or tetrahedron to arbitrary dimension), with d = N - 1. When increasing d, the volumes V of the simplices become smaller ⁄ √ for unit edge lengths), and at the same time the surface area increases. and smaller ( √ Therefore, it is more probable that a phase resides on the surface of such a simplex than therein (Widom [33]). Per definition, equiatomic HEAs are located at the center of their respective N-dimensional phase space, in contrast to the majority of intermetallics: of the 20,829 intermetallics known in 2015, there were mere 888 binary compounds of composition AB and 1074 of the type ABC (see, e.g., Steurer & Dshemuchadse [36]). Thus, the composition space for HEAs is much smaller than that for intermetallics. This is also reflected, for instance, in the number of N-component intermetallics per number of Ncomponent systems in Pearson‟s Crystal Data (PCD), which decreases from ≈4.6 for binary to ≈2.6 for ternary systems (Steurer & Dshemuchadse [36]). According to Widom [33] (and references therein), „the logarithmic increase of entropy with N is insufficient to counter the extreme enthalpies of small N compounds, so that only about 1.2% of N = 6 compounds are expected to form single phase solid

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The number of binaries in the case of a single N-component system amounts to ( ), i.e., to 3 for a ternary, to 6 for a quaternary, to 10 for quinary, and to 15 for a senary system. This means, that a single quinary equiatomic HEA will have to compete in energy with on average 46 binary and 26 ternary intermetallics. This can be one cause for the frequent deviation of the chemical composition of a HEA away from an equiatomic one (see Table 2), which would have the highest configurational entropy but may be too close in composition to particular intermetallics. However, the number of N-ary IMCs is strongly decreasing with N: for ternary systems, there are 13,026 intermetallics known, for quaternary 973, for quinary 65, for senary 24, for septenary 13, for octonary 8, and for nonary 2. But this are still large numbers compared to that of the known N-component HEAs (Steurer & Dshemuchadse [36]).

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According to Steurer & Dshemuchadse [36], out of the 3240 theoretically possible binary intermetallic systems, there are 1401 (43.2%) known forming at least one intermetallic compound. Ternary intermetallics have been found so far in only 5109 (6%) out of the 85 320 possible ones. For 4041 of these ternary systems, binary phases have been reported in all three binary subsystems, for 1053 only in two subsystems, and for the remaining 15 only in one subsystem. In the following 15 systems ternary compounds have been observed although two of the three binary subsystems do not form any intermetallic phase: Al–Cs–Tl, Bi–Fe–Zn, Bi–Li–V, Ca–Co–Pb, Ca–Cr–Pb, Ca–Pb–Ru, Cr–La–Pb, Cu– Ta–V, Ge–Np–Tc, Ge–Tc–U, Hf–V–Y, K–Tc–Tl, La–Mn–Pb, Mn–Rh–Tl, and Mn–Sn–W. This means that the N-ary systems bounded by binary systems without any intermetallic compound (and not a full miscibility gap) could be good starting points for the search for new HEAs. Almost ideal solid solutions can be expected and do exist for the system Mo-Nb-Ta-W because all its binary subsystems show almost ideal solid solutions without any intermetallic compound. For instance, the binary system bcc Mo-Nb shows a solid-solution stability range from 0 to 100% (rMo=1.36 Å, rNb=1.43 Å). The almost linear solidus curve indicates that homo- and hetero-atomic interaction potentials are very similar. However, below a given threshold temperature any solid solution would become metastable/instable, and phase segregation would take place if diffusion would be kinetically possible. In contrast, the bcc solid solution in the system Al-Cu is all but ideal (rCu=1.28 Å, rAl=1.43 Å). The wedge-shaped stability field ranges from 69.5% to 82% Cu at temperatures between 840 6

Journal Pre-proof K and 1322 K, respectively. The solidus curve has a maximum at 1322 K and 75% Cu where the alloy melts congruently. The wedge-shaped stability range is a sign of entropy stabilization (it gets wider with increasing temperature), the congruent melting point and the non-equiatomic composition indicate electronic stabilization. Indeed, this alloy is a Hume-Rothery phase, a compositionally flexible, disordered intermetallic compound (HEIC) rather than a typical solid solution. Its structure is bcc in contrast to that of Al and Cu, respectively, which is fcc. Another example is the hcp solid solution in the system Mo-Pd (rMo=1.36 Å, rPd=1.38 Å), which has a very small stability range from 48% to 51% Pd, only, despite the negligible size difference between bcc Mo and fcc Pd. It could better be denoted a disordered intermetallic compound ( -phase).

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The system Cr-Ni may serve as an example for asymmetric solubility, which is found in an analogous way in some HEAs: although they have the same radii (rCu,Ni = 1.25 Å), more electronegative ( ) fcc Ni can dissolve up to 50% less electronegative ( ) bcc Cr without much decreasing the melting temperature of Ni, while bcc Cr can only accommodate up to 32% fcc Ni by strongly lowering the melting temperature of Cr. Between 32% and 50% Ni there is a miscibility gap. Its asymmetry may result from the existence of a complex intermetallic phase in the Ni-rich part of the phase diagram below 863 K. Almost all Cr-containing HEAs known so far have fcc structures.

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Attractive and repulsive interactions can lead to local chemical ordering in a melt of an intermetallic phase close to the solidification temperature (see, e.g., Schenk et al. [37] or Holland-Moritz et al. [38]). In some HEA forming systems even phase separation takes place in the liquid state. This can influence local ordering in as-cast HEAs as well as the formation of the microstructure (Derimov & Abbaschian [39]). To minimize such difficult to control effects, HEAs should always be thermally equilibrated.

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A successful approach for identifying single-phase HEAs has been presented by Qi et al. [40]. Based on binary-phase-diagram parameters and machine learning they predicted ≈80% of the so-far reported HEAs correctly, and identified in 42 randomly selected new systems 81% of HEAs correctly, as experimentally validated. 19 out of them are single phase.

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3.3 Structure types and lattice distortions The loss of strict long-range order by a statistical distribution of the atoms on the lattice sites will have significant influence on the electronic, magnetic and vibrational excitations as well as on the transport properties. Tan et al. [41] suggest an approach based on the „dimensionless enthalpy of mixing‟ that is claimed to be able to predict stability fields of single-phase HEAs. Chauhan et al. [42] reviewed the different parameters introduced for explaining the stability fields of HEAs compared to crystalline and amorphous intermetallics. They identified interdependencies, and state that the parameters ⁄ , with the melting temperature calculated by the rule of mixtures, and √∑

⁄ ̅

(atomic size mismatch) are sufficient for predicting the stability of HEAs.

Accordingly, and is claimed to be sufficient for predicting the stability of a HEA in a given alloy system. However, the values of for the HEAs AlCoFeNiSm0.1V0.9 and AlCoFeNiSm0.1TiV0.9, for instance, are with 9.2% and 8.5%, respectively, significantly larger than the limit of [43]. Since can be far off the ideal value, these empirical parameters are not always very helpful for the a priori prediction of new HEAs. A posteriori, new HEAs may obey these empirical rules, which may not even be necessary but are certainly not sufficient. For a list of atomic radii and electronegativities see Fig. 2.

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Journal Pre-proof The coordination polyhedron (CP) of any atom in a bcc (cI2-W) or a B2 (cP2-CsCl) type structure corresponds to a rhomb-dodecahedron. There are 8 atoms at the corners of a cube (edge length a) at distances of √ ⁄ from the central atom, and 6 more at distances a. The coordination number equal CN = 8 + 6 = 14, and the packing density for equal spheres amounts to 0.680. In the case of a fcc (cF4-Cu) and hcp (hP2-Mg) structure, respectively, CN = 12, the central atom has a distance of √ ⁄ to each coordinating atom, and the packing density amounts to 0.740. The CP of a fcc structure is a cuboctahedron, that of a hcp structure a disheptahedron (anticuboctahedron). Consequently, a simple bcc structure has more space for thermal lattice vibrations leading to larger vibrational entropies than in the case of close packed structures. Therefore, bcc structures are more favorable for HT phases than close packed ones. Bcc lattices can also accommodate larger atoms with less distortions than close-packed lattices.

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Fredrickson [44] developed the concept of chemical pressure for the understanding of the preference of one crystal structure type over others. Depending on the size ratios and orbital interactions of neighboring atoms in the coordination sphere positive or negative chemical pressure results. This means that in a simple bcc, fcc or hcp multielement structure such as a HEA, with CNs of 8+6 or 12, not only atomic size frustration but also conflicting electronic packing frustration will take place. Local ordering phenomena and/or a deviation from an equiatomic chemical composition can release a part of this chemical pressure counteracting the maximization of the configurational entropy.

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According to a study on the Cantor alloy fcc CoCrFeMnNi, Divinski et al. [45] found that atomic diffusion in HEAs cannot a priori be considered as sluggish due to lattice distortions, they call it a „myth‟. Responsible for the sometimes observed sluggish diffusion in this HEA are both atomic interactions as well as cross-correlation effects (Beke et al. [46]) between different atomic species rather than higher activation energies. Indeed, the radii of the elements forming the Cantor alloy, , do not differ much from one another leading to rather small lattice distortions, only. The 20% fraction of larger Mn atoms will not have a significant influence on the fcc lattice, it may just increase the local chemical pressure (lattice stress). A thorough study combining both EXAFS and electronic structure calculations identified the mean lattice distortions to 0.1% (Oh et al. [47]). However, the element-resolved mean bond distortions can be one order of magnitude larger, in particular for Cr-Cr (0.66%), Cr-Mn (0.54%) and Mn-Mn (0.71%) bonds.

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The atomic size effect on lattice distortions in HEAs can be drastically overestimated if the charge transfer is not considered. The size mismatch parameter for bcc HfNbTaTiZr, for instance, amounts to 7.4 without and to 1.2 with charge transfer (Tong & Zhang [48]). The smaller size mismatch has influence on the stacking fault energy and hence mechanical properties. Substituting Pd for Mn in the Cantor alloy fcc CoCrFeMnNi changes the local ordering considerably as shown by atomic resolution HAADF and EDS maps (Ding et al. [49]). In contrast to the rather small local groupings of specific atoms in the Cantor alloy, the atomic aggregation in fcc CoCrFeNiPd is much larger. This is ascribed the higher electronegativity of Pd compared to Mn leading to a kind of local structure formation (concentration waves). The influence of Mn on the local structure and vacancy formation enthalpy in the Cantor alloy was studied by Huang et al. [50]. They found structural rearrangements accompanying the lattice formation at elevated temperatures, which was larger in the Cantor alloy than in fcc CoCrFeNi. In the case of bcc HfNbTaZr, for instance, with (Maiti & Steurer [31]), the atomic displacement parameters (ADPs) of all four atomic species were found to be approximately two times larger than in the pure elements indicating local lattice distortions. Another example is NbTaTiV, where lattice distortions were derived from first-principles calculations and 8

Journal Pre-proof experimentally confirmed (Lee et al. [51]). The largest lattice distortions result from Nb-V and Ti-V pairs with 6.1% and 8.1%, respectively. The significant impact of lattice distortions on solid solution strengthening in AlCrMoNbTi was studied experimentally by Chen et al. [52].

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Wang et al. [53] emphasize that due to atoms that are much larger or smaller than the others in a solid solution the topological packing instability must be taken into account. For that purpose, they define a ⁄ parameter ( √ ̅ ̅ ⁄ ̅ )⁄( √ ̅ ̅ ⁄ ̅ ), with and the radii of the smallest and the largest atom, respectively, and and the solid angles around the smallest and the largest atoms in respect to the surrounding atoms, respectively. The Hume– Rothery rule of 15% of the atomic size difference in binary alloys then corresponds to a critical value of packing misfit of . According to the authors, is a much better criterion for distinguishing between the stability regions of HEAs ( ) and those of intermetallics and metallic glasses ( ). Of course, beside the atomic size factor also electron negativity differences, valence electron concentration, mixing entropy and mixing enthalpy play a decisive role whether a HEA or an intermetallic phase will form.

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4 Sample preparation and materials characterization

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In this section I will mainly discuss problems related to the use of as-cast specimens for the study of mechanical properties and to their characterization by standard powder X-ray diffraction.

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4.1 Sample preparation

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Most studies of intermetallic single-phase HEAs so far are based on metastable as-cast materials, which have an undefined thermal history, and, therewith, a kind of uncontrolled and undefined local ordering in the structure. Depending on the cooling rate (see, e.g., Ma et al. [54]) as well as size and shape of a specimen, thermal gradients can significantly influence the evolving structure. As a consequence, the quenched-in structural state is more or less accidental and will be metastable at any temperature. The microstructure of an as-cast material is also developing in an uncontrolled way. The properties of any kind determined on such a specimen may not be accurately reproducible and representative for a thermally equilibrated HEA of this chemical composition. For examples of the effect of annealing on composition, microstructure and mechanical properties see Sun et al. [55], Kim et al. [56] or Kong et al. [57], for instance. To get a well-defined sample, one needs a well-defined annealing protocol. Thermal equilibration is based on diffusion processes, which will be fastest close to the melting temperature. The empirical Tamman rule suggests for binary alloys a minimum annealing temperature of at least two third of the melting temperature of the lower melting component. For N-ary HEAs, it is suggested to anneal at 2/3 of the estimated melting temperature (the mean value of the melting temperatures of the constituents). In the case of the HEA MoNbTaW, this would mean an annealing temperature of at least 2239 K. As a rule of thumb, the annealing time should be in this case at least 24 h. However, the lower the temperature is the longer the annealing time has to be. Annealing this HEA in a quartz ampoule at 1400 K, an annealing time of at least one weak would be recommended for thermal equilibration. One has to keep in mind that the quenched-in structural state of a HEA, thermally equilibrated at a give temperature, is metastable at ambient temperature. Aging will change this structure sooner or later depending on temperature. The purity of the metallic elements and of the protective gas as well as the existence of an oxygen getter during arc melting can be decisive for the formation of the kind of end-product(s). Oxides may form, for instance, acting as nucleation centers for secondary phases. So, it would be important to specify the 9

Journal Pre-proof experimental details in a paper: purity of elements, sample weight and shape, kind of furnace, annealing temperature and time, protective environment (argon, nitrogen, oxygen getter, …), ampoule and/or crucible material, sample wrapped in Ta foil or in contact with quartz ampoule, sample quenching or slow furnace cooling, etc. Similar details should be given for other ways of sample preparation besides the classical synthesis by arc melting of compacted metal powders. For instance, laser additive manufacturing has been used for HEA preparation, which yields relatively dense samples (Tong et al. [58]); another method employed was powder metallurgy based on sintering (Guo et al. [59]). In any case, a well-defined thermal processing protocol should be the prerequisite of further investigations.

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Diffusion multiples are a powerful means for studying phase diagrams. They may be successfully employed for the study of the phase composition of HEAs, as well. This was shown on the example of the quinary system Co-Cr-Fe-Mn-Ni (Wilson et al. [60]). The large areas of solid solution formed were used for testing the hardness by nanoindentation and producing contour maps as function of composition. The results did not confirm the predictions by the usual parameters and .

4.2 Materials characterization

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Diffraction methods can give global (of the whole sample) structural information where the local ordering phenomena are globally averaged. Imaging techniques show local structural features which are averaged over the sample thickness. Spectroscopic methods give local structural information that is globally averaged. It should be common practice to determine the chemical composition of a thermally processed specimen, which may significantly deviate from the nominal starting composition, in particular in the presence of volatile elements such as Cr, Mn, Zn or Cd.

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4.2.1 Diffraction Standard in-house powder X-ray diffraction (PXRD) is not sufficient to prove the single-phase character of a HEA. One has to be aware that the commonly used CuK radiation has only a very limited penetration depth in the strongly absorbing 4d or 5d transition elements (a few m in Ta or W, for instance). In a multi-phase sample, the primary X-ray beam will be partially absorbed by the majority phase before it hits a minority phase as well as the diffracted beam on its way out of the sample. Consequently, a secondary phase may be easily overlooked, in particular, if the counting statistics is not so good anyway. For a high-quality sample, the detection limit is ≈1% in the home lab, at a synchrotron source ≈0.0001%. HEAs, however, have a rather short correlation length of their periodic average structure (10-20 nm in most cases) and broad Bragg peaks, consequently. This increases the detection limit significantly. Furthermore, if two or more phases have similar lattice parameters, the material could also be characterized as single-phase due to overlapping peaks (see, e.g., Zhang et al. [61]). A problem may also be orientation effects, in particular, if the samples are only coarse grained (see, e.g., Vaidya et al. [62]). A thorough theoretical and experimental study demonstrated that a HEA just characterized by a standard PXRD as single-phase may not be single phase at all as shown by scanning electron microscopy (SEM) and atom-probe tomography (APT) (Ye et al. [63]). There, a criterion is presented which should help identifying single-phase HEAs. For an accurate characterization of polycrystalline R-HEAs high-resolution PXRD (synchrotron radiation) or PNS (powder neutron scattering) would be best suited. The evaluation should always include a quantitative Rietveld refinement for verifying the structure model (see, e.g., Maiti & Steurer [31] or Marik et al. [64]). The analysis of the peak width (full-width at half-maximum, FWHM) can give further information on the degree of lattice strain/stress and the correlation length of the average structure. Highresolution PXRD or PNS allows the calculation of the atomic pair-distribution (autocorrelation) function (PDF) of a HEA. If the PDF is determined as a function of temperature, then the variation of the lattice 10

Journal Pre-proof distortions and the local ordering can be derived (see, e.g., Zhang et al. [65], Schaub et al. [66]). 3D-PDF calculations based on single-crystal data (Bragg plus diffuse scattering) can give detailed information on local-ordering phenomena (Simonov et al. [67]). A thorough analysis of the influence of the number of components in LEAs, MEAs, and HEAs on lattice distortions and the related peak shifts, peak distortions and peak intensities in PXRD was given by Cheng et al. [68]. Owen et al. [69] found in their total-neutron-scattering experiments on the Cantor alloy, fcc CoCrFeMnNi, and on five other fcc phases with varying complexity that the local lattice strain was comparable and not anomalously large. In contrast, Oh et al. [47] identified in their combined densityfunctional theory (DFT) and EXAFS study on the Cantor alloy that the individual mean distortions are small on average, but their local fluctuations are an order of magnitude larger, in particular for Cr and Mn.

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It may also be difficult distinguishing between HEAs with partially disordered B2 (cP2-CsCl) type structure and those with fully disordered bcc (cI2-W) structure. An example is the MEA AlNbTiV (Yurchenko et al. [70]). In the case of a bcc phase, reflections with h+k+l = 2n+1 are systematically absent. If the scattering contrast between the atoms occupying the different Wyckoff positions is small then it will be difficult to identify the superstructure peaks with standard methods. For instance, if the difference in the average atomic scattering factors between the two occupied Wyckoff positions 1a (0,0,0) and 1b (1/2,1/2,1/2) equals one electron as it is the case for (Hf,Zr) and (Nb,Ta), for example, then the strongest superstructure peak would be the 1 0 0 with an intensity ratio to the strongest peak 0 1 1 of ≈1.3x10-4 (for CuK ). Consequently, this peak could only be observed with synchrotron PXRD on a high quality HEA with narrow peaks. Employing neutron scattering with the same wave length, the ratio of the 1 0 0 peak to the in this case strongest reflection 1 2 3 would be with ≈4.4x10-4 not much larger. However, depending on the constituting elements neutron diffraction can give much better scattering contrast for elements with similar X-ray scattering contrast; for instance, in the case of V and Ti, Cr, or for Mn and Fe, or Cu and Ni.

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If ordering phenomena are to be studied in greater detail, single-crystal X-ray diffraction would be the method of choice. In combination with a pixel detector, intensity ratios of up to nine orders of magnitude would be accessible (see, e.g., Weber et al. [71], [72]). This intensity resolution allows also to quantitatively investigate disorder-diffuse scattering for identifying local ordering phenomena. Of course, if single crystals of HEAs can be grown, the characterization of structure and properties can be done in the best possible way, generally (see, e.g., Mishra et al. [73], Ma et al. [74] or Yasuda et al. [75]). For studying local clustering or nano-particle precipitation, small-angle scattering (SAXS or SANS) may be helpful. 4.2.2 Imaging and spectroscopy Electron microscopic methods show the projected local structure of a thin specimen on the micrometer scale (TEM) or with atomic resolution (HRTEM or HAADF-STEM). TEM is mainly used for the investigation of the microstructure or of defects in the volume of the specimen. SEM, in combination with EDX or WDX, is the standard method for the study of the microstructure of a specimen as imaged from the surface. The resolution is usually on the micrometer scale. For a more precise determination of the chemical composition on a similar scale, electron-probe micro-analysis (EPMA) is the method of choice. With atom-probe tomography (APT), a tens-of-nanometer-sized needle can be analyzed atom by atom with atomic resolution in 3D space (see, e.g. Maiti et al. [76]). The elemental distribution can also be mapped in 2D projection with atomic resolution by HAADF-STEM in combination with EDS (energydispersive X-ray spectroscopy). See, e.g., Ding et al. [49]. It has to be kept in mind that the specimen thickness is in the range of tens of nanometers at best. This means the the image corresponds to a projection over 50 to 100 atomic layers averaging over lattice distortions and different atomic species.

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Unfortunately, it is quite common in literature that as-cast HEAs are described as single-phase although their PXRD patterns exhibit weak, unidentified, additional peaks and/or the SEM images show dendrites and interdendrite regions with significantly different compositions (see, e.g., Yao et al. [77], Lin et al. [78], Mu et al. [79]). It has been shown on the example of the „single-phase-like‟ septenary bcc alloy CrMoNbReTaVW, that an accurate in-house PXRD measurement with good counting statistics is not suffient to prove a single-phase state (Zhang et al. [61]). In contrast, BSE and SE images clearly show the two-phase character of the investigated specimens. Selected area electron diffraction (SAED) allows the identification of the crystal structure on the micrometer scale. By spectroscopic methods such as EXAFS the local environment of target atoms can be accurately explored.

5 Main systems studied

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In spite of the thousands or even millions of new HEAs predicted by different approaches, the handful of intermetallic systems with single-phase HEAs observed so far is somewhat disappointing (see Table 1). Most of these HEAs can be assigned to one of the three groups: (i) Transition-metal-based HEAs (TMHEAs), (ii) Refractory-element-based HEAs (R-HEAs), (iii) Rare-earth-element-based HEAs (RE-HEAs) (Fig. 2). HEAs of the first two groups may also have Al as constituent. In the case of group (iii), the HEAs consist of RE-elements, only. It is remarkable, that most of the TM-HEAs contain the chemically very similar elements Fe, Co, Ni, and other elements of the 3d series only. Most R-HEAS have Zr, Hf, Ti and Nb as their constituents. In contrast to the TM-HEAs they mainly consist of homologous elements, i.e., electrochemically similar elemenst of the same column of the periodic table of elements. Approximately half of all HEAs are aluminides. All RE-HEAs share Tb and Gd, and most of them Ho, Dy and Y as well. So far, no RE-HEAs with Ce, Pr, Nd, Pm, Yb have been synthesized.

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The modification of HEAs can take place horizontally or vertically in the Periodic Table of Elements. In contrast to vertical modification, horizontal modification changes the valence electron concentration (VEC) as well as the electronegativities to a much higher amount in the case of transition metals. In the case of rare earth elements, electronegativities and radii all are similar except for Eu. Eu-containing HEAs have not been synthesized so far, anyway.

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5.1 HEAs based on transition elements, groups 3 – 12 without refractory elements (TM-HEAs) Cantor investigated alloys with up to 20 multiprincipal components, and identified just one single-phase HEA, quinary fcc CoCrFeMnNi, later on called Cantor alloy (Cantor et al. [80]). Many papers in the following years have been focusing on this HEA, or trying to derive novel HEAs by replacing, removing or adding other elements to it. These horizontally or vertically (with regard to the Periodic Table) modified single-phase Cantor alloys are listed in Table 2, and will also be discussed to some extent in the following to get an overview of what has been done and achieved. The solidus and liquidus temperatures of the Cantor alloy were measured to be 1563 K and 1613 K, respectively (Laurent-Brocq et al. [81]). What does such a narrow compositional and thermal stability range of a HEA mean? On one hand, it indicates a strong competition between the stability of the HEA and that of intermetallic phases. On the other hand, it may indicate strong local ordering phenomena, precursors of the formation of intermetallics that can exist at slightly different compositions. This can already be expected looking at the respective binary phase diagrams: the binary system Mn-Ni shows an equiatomic solid solution only above 1183 K, below this temperature -MnNi with B2 (cP2-CsCl) structure type is formed. The system Cr-Ni shows an asymmetric miscibility gap from 32 to 50% Ni below 1618 K. That in Co-Cr ranges from 38.3% to 53.6% Cr, in Cr-Cu from ≈1% to 100% Cr, in Cu-Fe 12

Journal Pre-proof from ≈5% to 88% Fe. At equiatomic compositions, CoCr and CoMn form -phase (tP30-Cr46Fe54). In contrast, the binary subsystems Co-Ni, Cr-Ni, Cu-Mn, Cu-Ni, Fe-Mn, Fe-Ni, Mn-Ni show fcc solid solutions at equiatomic compositions in a larger temperature range. The VEC = 8 of the Cantor alloy is equal to that of Fe, and it is, like Fe, an anti-Invar system, i.e., it shows an enhanced thermal expansion coefficient (for details see Acet [82]).

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5.1.1 Variation of the stoichiometry of the Cantor alloy As-cast single-phase samples of fcc Cox(CrFeMnNi)1-x (x = 0.05, 0.10, 0.20) were annealed at 1123 K for up to 48 h. Remarkably, only the HEA with composition Co0.20(CrFeMnNi)0.80, i.e., the composition of the original Cantor phase, remained stable (Zhu et al. [83]), even after annealing for 500 days at 1173 K (Otto et al. [84]); the other ones, as well as a sample of CoCrFeMnNi annealed at 973 K for 1000 h, showed precipitation of -phase (tP30-Cr46Fe54) [85]. The phase stability of CoCrFeMnNi was investigated by CALPHAD as well as experimentally by Bracq et al. [86]). They identified a very large compositional stability region at 1273 K. Co and Ni favor the formation of the solid solution, not surprisingly, because they are fully miscible in the binary system. Fe behaves rather neutral. Too much Cr and Mn (>30%) destabilize the solid solution (Christofidou et al. [87]). Around 1600 K, the -phase (tP30-Cr46Fe54) is formed in the systems Co-Cr and Cr-Mn, below 1100 K in the system Cr-Fe, and below 818 K in the system Co-Mn as well.

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All possible subsystems (quaternary, ternary, binary) of the Cantor alloy fcc CoCrFeMnNi, as cast as well annealed, were studied whether they form solid solutions (Wu et al. [88]). It was found that three out of five quaternaries, CoCrFeNi, CoFeMnNi, and CoCrMnNi, five out of 10 ternaries, CoFeNi, CrFeNi, FeMnNi, CoCrNi, and CoMnNi, and two out of 10 binaries, FeNi and CoNi, are single-phase fcc solid solutions in the as-cast and at 1373 K or 1473 K, respectively, homogenized state.

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An experimental and theoretical study on a Bridgman-grown quaternary fcc CoCrFeNi single-crystal annealed at 723 K clearly revealed the existence of short-range-order (sro) due to strong Cr-Ni and Cr-Co pair correlations (Schonfeld et al. [32]). Around 500 K an order-disorder phase transformation to (Co,Fe,Ni)3Cr, with the L12 (cP4-Cu3Au) structure type, was predicted. Due to local ordering, the main contribution to the mixing entropy stems from the random distribution of Co, Fe and Ni, only. Thus, this „HEA‟ should be rather called a „LEA‟, or, better, a HEIC. By a variation of the iron content in as-cast Fex(CoCrNi)1-x samples, fcc phases were reported for x = 0.25, 0.45 and 0.55, and bcc phases for x = 0.65 and 0.75 (Zhou et al. [89]). According to CALPHAD calculations and experimental investigations on annealed samples, the concentrations of Co, Fe and Ni can be separately varied from 20% to 40% (He et al. [90]). Co0.40-xCr0.20Fe0.20Mn0.20Nix with x = 0.05 and 0.10 are single-phase shape-memory materials, which show a Martensitic transformation (HT) fcc hcp (LT) (Lee et al. [91]). 5.1.2 Element addition or substitution to the Cantor alloy Adding some Pd (rPd = 1.34 Å) to CoCrFeNi, (CoCrFeNi)1-xPdx, (x = 0.01, 0.03, 0.05, 0.20) maintains the fcc single-phase in the as-cast state but leads to a strong lattice distortion even for small amounts of Pd. Pd-doping also shifts the HP phase transformation to higher pressures, from 13 GPa to 20 GPA, while it is as high as 74 GPa for equiatomic fcc CoCrFeNiPd (Zhang et al. [65]). Replacing Co in fcc CoCrFeNi by (Mo,Ru,W) yields fcc Cr0.21Fe0.20Ni0.38Mo0.06Ru0.13W0.02 in annealed samples (24 h at 1273 K), confirming the prediction by CALPHAD calculations (Lu et al. [92]). However, this is certainly not a senary HEA but a Mo and W doped quaternary MEA. Indeed, the mixing

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Journal Pre-proof entropy amounts to , only, which is somewhere in between that of a quaternary HEA, , and that of a quinary HEA, . A calculation of Gibbs-energy-composition plots was combined with experimental investigations on annealed (24 h at 1273 K) samples of fcc CoCrMnNi, AlCoCrMnNi, and CoCrCuMnNi (Guruvidyathri et al. [93]). Only fcc CoCrMnNi remained single-phase, the others segregated into duplex structures consisting either of two fcc phases for the Cu-containing HEA or to a B2 and a bcc phase for the aluminide. Replacing Co and Cr by Ga and Si leads to the quinary HEA Fe0.267Ga0.156Mn0.20Ni0.267Si0.11, which shows an interesting magnetocaloric effect (Sarlar et al. [94]).

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5.1.3 New chemical compositions Noble-metals containing HEAs were studied by Sohn et al. [95] and the results confirmed by DFT calculations (Yin et al. [96]). The only single-phase HEA found in the dendritic regions is the senary fcc HEA CuIrNiPdPtRh, which shows a high ductility (≈30%) and a high maximum yield strength (1839 MPa). On a first glance, CuIrNiPdPtRh looks very different from the Cantor alloy, it does not seem to be related to it at all. However, you get it by replacing in CoCrFeMnNi Co by homologues Rh and Ir, adding to Ni its homologues Pd and Pt, and, finishing up with Cu. The first Zn and Sn containing brasses, fcc Cu2MnNiZn and fcc Cu2MnNiSn0.2Zn, respectively, were prepared by Nagase et al. [97]. The phase states of these HEAs strongly depend on their Cu content. The atomic radii of Sn (rSn=1.41 Å) and Zn (rZn=1.34 Å) are not so much larger than those of Mn (rMn=1.37 Å), Cu (rCu=1.28 Å) and Ni (rNi=1.25 Å), respectively.

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There are not only „HEAs‟ known with simple structures but also with more complex ones. For instance, a senary disordered Laves phase (hP12-MgZn2) in the system Cr-Fe-Ni-Ti-V-Zr (Mishra et al. [98]). This Laves phase has three occupied Wyckoff positions, with the larger Mg (r = 1.60 Å) in 4f (1/3,2/3,0), and smaller Zn (r = 1.34 Å) in 2a (0,0,0) and 6h (0.83, 0.66,1/4). It is obvious that the large Ti (r = 1.45 Å) and Zr (r = 1.59 Å) atoms will occupy the Mg sites and the other elements (1.24 ≤ r ≤ 1.31 Å) the Zn sites. Consequently, the configurational entropy corresponds to that of a random (4+2)-component phase, if at all, rather than to a 6-component one.

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CoNiSbSnTi2, a quinary HEA with the structure type of a Heusler phase shows potential for interesting thermoelectric applications (Krati et al. [99]). Since the structure of the Heusler phase, L21 (cF16Cu2MnAl) is a 2x2x2 superstructure of the cI2-W type, CoNiSbSnTi2 cannot be fully disordered. Likely, Ti occupies the Cu sites, (Co,Ni) the Mn sites, and the large (Sb,Sn) the Al sites. Consequently, this would be a LEA or HEIC rather than a HEA. 5.1.4 Cantor alloy aluminides Aluminum plays an important role in most light-weight alloys. With transition metals, which are more electronegative than aluminum, it forms many compositionally flexible intermetallic compounds and it also can dissolve significant amounts of TM elements and vice versa. For instance, the ternary phase Al(Co,Ni) shows full miscibility of Co and Ni on one sublattice of the B2 (cP2-CsCl) structure type. Consequently, it is promising to derive new HEAs by adding Al to the Cantor alloy or to one of its subsystems. The influence of the size difference between Al (rAl=1.43 Å) and the other smaller elements (see Fig. 1) in annealed samples of fcc Al0.2CoCrFeMnNi and fcc Al0.2CoCrCu0.3FeNi, respectively, on the mechanical properties was investigated by Wu et al. [100]. The addition of Al to CoCrFeMnNi leads to significantly larger lattice distortions and therewith to superior mechanical properties. Theoretical 14

Journal Pre-proof calculations confirm the experimental findings (Widom [13]). However, they show that the atomic distribution around Al and Cr atoms, for instance, is far from a random distribution. The substitution of Cu for Mn changes the atomic environment that was around Mn. In contrast to Mn, Cu is immiscible with Co, Cr and Fe. However, it is fully miscible with Ni like Mn, and dissolves up to 20% Al like Mn. This example shows that local ordering must exist in these HEAs due to repulsive and attractive interactions, in this way reducing its entropy. Only the non-equiatomic composition can stabilize this HEA against the formation of Al-TM intermetallics.

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What happens if Ni is removed from the Cantor alloy and Al added? This was studied theoretically and experimentally on the structure of as-cast AlxCoCrFeMn (x = 0, 0.05, 0.2) by Singh et al. [101]. Firstprinciples calculations indicate that Al drives the transformation from fcc (x = 0) to bcc (x ≥ 0.1) at 0 K. Thereby, the hybridization of the sp orbitals with the TM d orbitals and the resulting short-range order (sro) plays an important role. It is obvious that there has to be local ordering due to the quite different pair potentials of Al-Al, Al-Co, Al-Ni, Co-Co and Ni-Ni (Widom et al. [102]).

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It is also enlightening for the understanding of the phase stability of Cantor alloy derivatives to have a look on the respective binary phase diagrams, where around equiatomic composition wide stability fields exist for B2 type AlCo, AlFe and AlNi. AlCo and AlNi have even higher melting temperatures than the constituting elements. AlCu shows a complex structure and a narrow compositional stability range while AlMn is simple bcc. Al-Cr exhibits a miscibility gap at 50% Al, while bcc Cr can dissolve up to 46% Al at high temperature.

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Removing Mn (rMn=1.37 Å) from the Cantor alloy and adding some fraction of the only slightly larger Al (rAl = 1.43 Å) leads to AlxCoCrFeNi. It was studied with varying x as a function of pressure up to ≈50 GPa by Wang et al. [103]. Only for the as-cast samples with x = 0, 0.1, 0.3, a sluggish transformation from a fcc to a hcp phase was observed (≈14 GPa for x = 0), with a critical pressure related to the Al content. For bcc Al1.5CoCrFeNi, no transformation took place up to the highest pressure, probably due to the higher stacking fault energy caused by the high Al content of this phase. In contrast, bcc Al0.5CoCrFeNi0.5 and fcc Al0.25CoCrFeNi0.75 transformed both to hcp HEAs under pressures between 40 and 50 GPa (Liu et al. [104]).

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In an in-situ TEM study of AlxCoCrFeNi (x = 0.3, 0.5, 0.7) as a function of temperature, only fcc Al0.3CoCrFeNi remained single-phase after heating up to 1523 K (Rao et al. [105]). Cooling down to 1123 K resulted in the precipitation of a B2 (cP2-CsCl) phase. CALPHAD calculations confirmed the stability of the fcc phase between 1299 K and 1675 K, and the formation of the B2 (cP2-CsCl) phase between 1299 K and 823 K. Due to its HT stability, it was possible to grow a single crystal of fcc Al0.3CoCrFeNi by the Bridgman method and to study its mechanical properties (Ma et al. [74]). The ultimate tensile elongation of the single-crystal along the [001] direction approaches 80%. The deformation behavior was studied by Yasuda et al. [75], showing serrated flow under compression between 873 K and 1073 K. The different types of serrated flows under mechanical deformation of polycrystalline fcc Al0.5CoCrCuFeNi were studied experimentally and theoretically in great detail at temperatures beween 473 K and 873 K by Niu et al. [106], Chen et al. [107] and Brechtl et al. [108]. The special role of Al in the interaction between solute atoms and dislocation was discussed as well. Adding V to AlCoCrFeNi leads to a phase with the B2 (cP2-CsCl) structure type. An in situ PXRD study of as-cast AlCoCrFeNiV at temperatures between 293 K and 1273 K revealed the stability of the B2 (cP2-CsCl) type structure up to 873 K (Karpets et al. [109]). At higher temperatures, -phase (tP30Cr46Fe54) starts to form consuming the B2 (cP2-CsCl) phase. 15

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Al(Co0.2Cu0.2Fe0.2 Mn0.2Ni0.2), Al(Co0.25Cu0.25Fe0.25Ni0.25) and Al(Co0.25Fe0.25Mn0.25Ni0.25) were shown to form a single-phase B2 (cP2-CsCl) structure after annealing at 1373 and 1573 K, respectively. Below ≈1273 K phase decomposition starts (Zhou et al. [23]). In this case, one B2 (cI2-CsCl) sublattice is occupied by Al, only, and the other by the other elements. The Sm-doped HEAs fcc AlCoFeNiSm0.1V0.9 and fcc AlCoFeNiSm0.1TiV0.9 have been reported to be single-phase after being manufactured using the selective laser melting technique (Sarswat et al. [43]). However, the stability of these Sm-doped quinary and senary HEAs was not checked by annealing.

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To summarize this subchapter, based on the Cantor alloy several single-phase HEAs could be derived. Their stability under annealing was studied in a few cases, only. The off-equiatomic compositions of most of the derivatives indicate a narrow compositional stability range due to competing intermetallics. A consequence can be that significant local ordering takes place not only at lower temperatures. Addition of Al to the Cantor alloy derivatives frequently leads to larger lattice distortions or even to superordering of the type bcc => B2 (cP2-CsCl).

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5.2 Refractory-element-based HEAs (R-HEAs)

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The studies of R-HEAs have mainly been motivated by the search for novel HT materials. Refractory elements are the 4d and 5d bcc transition metals Nb, Ta, Mo, W, as well as hcp Re, which have melting points far beyond 2500 K. In the wider definition of the International Journal of Refractory Metals and Hard Materials, also high-melting hcp Ti, Zr, Hf, bcc V, Cr, Mn, and hcp Tc, Ru, Os, as well as fcc Rh and Ir are assigned to this group. In addition, Al can be alloyed to some of the R-HEAs. For a recent review on refractory-element-based HEAs see Senkov et al. [7], and for a compilation of mechanical properties see Couziniè et al. [110].

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5.2.1 MoNbTaW-based R-HEAs The first R-HEAs investigated were as-cast bcc MoNbTaW and MoNbTaVW (Senkov et al. [111]). Later on, the thermal stability of these HEAs and of HfMoNbZr and HfMoNbTiZr was explored by annealing at temperatures T >2000 K (Maiti [112]). No significant deviations from random solid solutions could be observed. Similar as the Cantor phase for TM-based HEAs, these R-HEAs have been used later on as basic model systems for a better understanding of this kind of alloys. The local chemical ordering in bcc MoNbTaW was studied by mean-field theory, applied to a firstprinciples-based effective Hamiltonian (Huhn & Widom [113]). Accordingly, B2 (cP2-CsCl) type ordering should take place below 1654 K, with (Ta,Nb) on one Wyckoff position and (Mo,W) on the other. Hybrid Monte Carlo/molecular dynamics simulations revealed that long-range ordered B2 (cP2CsCl) already disappears somewhere in the temperature range 600 K to 1200 K (Widom et al. [114]). More recent calculations identified as stable quaternary ground state compound hR7- Mo2NbTa2W2, formed by the Nb-driven decomposition of bcc MoNbTaW (Widom [13]). Raturi et al. [115] studied the stability of 126 equiatomic R-HEAs by CALPHAD, and identified just two stable single-phase ones: already known bcc MoNbTaVW and new bcc CrMoReVW, both of which were experimentally confirmed by annealing them for 24 h at 1273 K. 5.2.2 HfTiZr-based R-HEAs The binary systems Hf-Ti, Hf-Zr, Ti-Zr, all show full miscibility, where the solid solutions are bcc at HT and hcp at LT. Therefore, it was quite natural to use these binary alloys as starting point for the design of new HEAs whose thermal stability has been studied by several groups. At 1473 K homogenized bcc (HfTiZr)(NbTa), for instance, decomposes after annealing at 973 K into three phases, the bcc matrix, bcc 16

Journal Pre-proof (Ta,Nb)-rich, and hcp (Hf,Zr)-rich precipitates (Chen et al.[116]). The temperature dependence of the elastic moduli was measured between ambient temperature and 1100 K on a sample of bcc (HfTiZr)(NbTa) that was annealed for 5 h at 1373 K (Laplanche et al. [117]). The phase stability of the non-equiatomic ductile single-phase (Hf0.125Ti0.375Zr0.25)(NbTa)0.25 was studied by (Yao et al. [118]). It is still a single-phase solid solution after recrystallization for 3 h at 1273 K and remains in this state even after subsequent annealing at 1173 K for two weeks. However, it is unstable and forms second-phase precipitates below 1073 K. The bcc HEA in the (HfTiZr)(NbV) system proves stable under annealing at 1773 K (Feuerbacher et al. [119]). By hydrogen absorption of up to 1.2 wt.%, it undergoes a reversible phase transformation to a body-centered tetragonal (bct) hydride phase (Karlsson et al. [120]). Hydrogen cycling at 773 K was shown to be possible without destroying the HEA. Hydrogen occupies both tetrahedral as well octahedral sites, which is favored by the large lattice strain.

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Several superconducting R-HEAs have been identified so far: annealed bcc (Hf0.08Ti0.11Zr0.14)(Nb0.33Ta0.34) (Tc=7.3 K) [121] (see also Vrtnik et al. [122]), as-cast bcc (Hf23Ti20Zr20)(Nb21Re16) (Tc=5.3 K) (Marik et al. [123]), hcp (Hf0.11Ti0.11Zr0.11)(Nb0.11Re0.56) (Tc=4.4 K) [64], annealed bcc (Hf0.21Ti0.15 Zr0.24)(Nb0.25V0.15) (Tc=5.3 K) (Ishizu et al. [124]), as-cast bcc (Ti0.15Zr0.15)(Nb0.35Ta0.35) (Tc≈8 K) (Yuan et al. [125]). The critical temperature of as-cast (Hf,TiZr)0.33(Nb,Ta) 0.67 increases to 10 K at a pressure of 60 GPa, and then slowly decreases again to 9 K at 190.6 GPa (Guo et al. [126]). The influence of isoelectronic substitution of (NbTa) by (Sc,Cr), (Y,Mo), and (Sc,Mo) on the superconducting properties of bcc (ZrHfTi)x(NbTa)1−x was studied by Von Rohr & Cava [127]. The critical temperature is lowered by up to 60% by the substitutions. The alloying of Al to the pristine superconductor was also investigated for different compositions. None of these substitutions changed the single-phase state of the HEAs. (NbScZr)1-x(PdRh)x (0.35 ≤ x ≤ 0.42), (NbScTaZr)1-x(PdRh)x (0.31 ≤ x ≤ 0.38) and (ScZr)0.50(PdRh)0.50 with B2 (cP2-CsCl) type structures are superconducting as well (Stolze et al. [128]). The critical temperature (maximum Tc = 9.2 K) strongly depends on the composition and VEC. (MoReRu)-based superconductors have critical temperatures between 9.1 K (for MoReRu) and 2.1 K for (Mo0.1Re0.1Ru0.55)Rh0.1Ti0.15 [129].

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All superconducting HEAs studied so far are type-II superconductors based on refractory elements (Sun & Cava [21]). As we have seen above, they crystallize either in the simple bcc or hcp structure type or in the B2 (cP2-CsCl) one. Furthermore, superconducting „HEAs‟ have also been found with the complex Mn (cI58-Mn) structure type. These are (NbZr)0.1[MoReRu]0.9 (Tc=5.3 K), (HfIrTaW)0.4[Re]0.6 (Tc=4.0 K), and (HfPtTaW)0.4[Re]0.6 (Tc=4.4 K) (Stolze et al. [130]). However, alloys with the -Mn (cI58-Mn) structure type can hardly be called HEAs since the five different atomic species are distributed partially ordered on four different Wyckoff positions: 2a (0,0,0), 8c (x,x,x), and two in 24g (x,x,z) with different x and z. They should be called partially disordered intermetallic phases (HEICs) rather than HEAs. To summarize, superconducting bcc HEAs have been observed in several subsystems of Hf-Nb-Ta-Ti-VZr (4.0 ≤ Tc ≤ 9.2 K), Nb-Ta-Zr-Me (Me = Fe, Ge; 6.9 ≤ Tc ≤ 8.4 K) or of Nb-Ta-Zr-Si-Me (Me = Ge, V; 4.3 ≤ Tc ≤ 7.4 K)(Sun et al. [21]). The HEAs with B2 (cP2-CsCl) structure type are based on Nb-Pd-RhSc-Ta-Zr (3.9 ≤ Tc ≤ 9.3 K). The hcp HEA was observed in the system Hf-Nb-Re-Ti-Zr (Tc = 4.4 K). An important parameter for the optimum chemical composition is the VEC, similar as in the classical metallic superconductors of the A15 (cP-8 Cr3Si) structure type. Increasing the configurational entropy by adding more elements has, beside the averaging effect, no significant influence on Tc. A wide-temperature-range superelastic and a giant supercaloric effect in CuHf0.6NiTiZr0.4 was reported by Li et al. [131]. Thereby a reversible difusionless phase transformation austenite (B2 cP2-CsCl) martensite (B19‟ mP4-NiTi) takes place. In the martensite there are the two Wyckoff positions 2e (x, y, 1/4) occupied, with three (Hf, Ti, Zr) and two atoms (Cu, Ni), respectively. Both phases are MEAs rather 17

Journal Pre-proof than HEAs, consequently. The as-cast single-phase HEA HfMo0.2V0.5Ti2Zr was found quite irradiation tolerant (Qiao et al. [132]). 5.2.3 Other R-HEAs Bcc NbTaTiV proves stable after homogenization at 1473 K for 3 days. The effects of the high mixing entropy on the mechanical properties are discussed and quantified in terms of lattice distortions and interatomic interactions via first-principles calculations (Lee et al. [51]). The largest lattice distortions are caused by the pairs V-V (4.7%), Ti-Ti (5.1%), Nb-V (6.1%) and Ti-V (8.1%). Bcc Nb0.325Ti0.275V0.125 Zr0.125 can reversibly absorb up to 2 wt% hydrogen forming a bct hydride phase (Montero et al. [133]).

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Single phase hcp Ir0.26Mo0.20Rh0.225Ru0.20W0.115 and Ir0.255Mo0.20Rh0.20Ru0.25W0.095 alloys remained stable after annealing at 2373K for 1 h (Takeuchi et al. [134]). The authors explain the formation of the hcp structure by the role of Ru and the valence electron concentration VEC ≈ 8. The thermal stability range is given between 1300 – 1400 K and 2500 K. By calculations with Thermo-Calc 2019a, a cross section through the 5D phase diagram was obtained showing areas of fcc, hcp and bcc single-phase HEAs at different valence concentrations (Takeuchi et al. [135]). The fcc and hcp HEAs could be experimentally confirmed after annealing at 2100 K for 2 h.

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The as-cast quinary HEAs (NbScZr)1−x(PdRh)x (x = 0.45, 0.42, 0.40, and 0.39−0.35) and senary HEAs (NbScTaZr)1−x(PdRh)x (x = 0.43, 0.38,0.35, 0.33, 0.328, 0.32, 0.315, 0.31), as well as (ScZr)0.50(PdRh)0.50, all have the B2 (cP2-CsCl) type structure. All these HEAs, with the exception of the most (PdRh)-rich ones, are type-II superconductors (Stolze et al. [128]). The critical temperatures strongly depend on the VEC as well as on the number of constituents. They increase monotonically with decreasing VEC within a series. (NbScZr)0.65(PdRh)0.35 shows with 9.3 K the highest Tc (i.e., the same as elemental Nb).

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For a general review on bcc HEAs, see, e.g., Couzinie & Dirras [20]. In this review, beside mechanical properties also different approaches for the prediction of HEAs are discussed, in particular, the influence of the valence electron concentration, VEC, on the stability of HEAs. The VEC includes additionally to the itinerant electrons also the d-electrons into the electron count. For a collection of values for the yield strength and hardness of R-HEAs see, e.g., Yao et al. [77]. I want to mention here that R-HEA-based ceramic materials, i.e., borides, carbides, silicides, nitrides and oxides with interesting properties have been discovered recently (see Gild et al. [136] and references therein). 5.2.4 R-HEA-aluminides

As in the case of TM-based HEAs, there are also a few aluminides of R-HEAs known. They crystallize predominantly with the B2 (cP2-CsCl) structure type as predicted by thermodynamic calculations (Chen et al. [137]). Examples are AlCrMoTi, AlCrMoNbTi, AlCrMoTaTi and AlMoNbTi (Chen et al. [137]), AlNbTiV and (AlNbTiV)0.89Cr0.11 (Yurchenko et al. [138]).

5.3 Rare-Earth-element-based HEAs (RE-HEAs) Rare-earth (RE) elements, i.e., the lanthanoids (Ln) together with Sc and Y, are characterized by their electronic structure, where the valence electrons are increasingly filling the 4f orbitals of the Ln-elements. Since these are largely screened by their 5s and 5p electrons, their chemical properties are rather uniform, and large stability fields of solid solutions can be expected. Most binary alloys of RE-elements show a bcc solid solution at high temperature (HT) and a hcp one at lower temperatures (LT). Therefore, depending on composition and temperature, the structures of RE-HEAs can have the one and/or the other 18

Journal Pre-proof symmetry. The atomic radii vary between 1.62 and 1.87 Å, if we neglect divalent Eu with 2.0 Å and divalent Yb with 1.94 Å. The Pauling electronegativities are all very similar (1.1 – 1.3) as well as the chemical properties, in particular, for the heavier RE-elements from Gd to Lu. This means that the mixing enthalpy will be small. Indeed, no binary Ln-Ln compounds are known so far. In the PCD there are 73 entries for binary Ln-Ln phases (solid solutions) with the structure types fcc (cF4-Cu), bcc (cI2-W), hcp (hP2-Mg), dhcp (hP4-La) or hR9-Sm. This means that all these binary phases are solid solutions with structures different from those of the two constituents (for more information see Steurer & Dshemuchadse [36]). The systems Ln-Yb all show large miscibility gaps. Since the mixing entropy for RE-elements is very small, it seems to be likely that the 1486 theoretically possible RE-HEAs with 5-11 elements can be realized experimentally (Feuerbacher et al. [139]). Some of them may have interesting magnetic properties. From the mineral monazite, the not so expensive Mischmetall can be extracted, which is already a HEA of composition Ce0.45-0.52La0.20-0.27Nd0.15-0.18Pr0.03-0.05(Sm,Tb,Y)0.01-0.03.

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For the HEA GdDyErHoTb, a giant magnetocaloric effect was observed due to the statistical distribution of magnetic moments, which makes magnetic ordering difficult and leads to a small magnetic hysteresis (Zou [29]). Under pressure, This HEA follows the sequence of phase transformations hcp => hR9-Sm => dhcp => dfcc with correlated s => d charge transfer, which is observed for all the trivalent lanthanoids (Yu et al. [140]).

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Senary RE-HEAs, and even one octonary RE-HEA, were prepared by Qiao et al. [141]. The alloys contained a significant amount of oxides, however, and their stability is unclear.

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There are no RE-HEAs in combination with non-RE-elements known so far, with the exception of two Sm-doped HEAs, AlCoFeNiSm0.1V0.9 and AlCoFeNiSm0.1TiV0.9 (Sarswat et al. [43]). Zr could be a candidate as well, because Dy, Er and Ho, for instance, show up to 40% solubility of the RE-element in Zr. On the other hand, Ho can dissolve up to ≈30% Zr. Sc is fully miscible with Hf, Ti and Zr. Indeed, there are three R-HEAs known with Zr and Sc as one of the constituents.

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High-pressure (HP) induced phase transitions in HEAs have been reviewed by Zhang et al. [8]. All refractory element based HEAs studied are stable under the high pressures applied so far. In contrast, hcp DyGdHoTbY undergoes a whole sequence of phase transitions in the same way as the RE elements themselves. The Cantor alloy, CoCrFeMnNi, shows a sluggish phase transformation fcc => hcp under high pressure. Temperature studies indicate that the fcc phase of the Cantor alloy is stable at lower temperatures and the hcp phase at higher. Functional physical properties of HEAs, such as soft magnetic, magnetocaloric, thermoelectric, superconducting, and hydrogen storage have been discussed in great detail in the review by Gao et al. [142]. The random arrangement of magnetic moments in HEAs favors low coercitivity in combination with high saturation magnetization. The high magnetic entropy due atomic disorder can induce a large magnetocaloric effect. Hindered phonon propagation (related with low thermal conductivity) in combination with metallic electric conductivity is favorable for a large thermoelectric effect, etc.

6 Conclusions There is a hype on HEAs, for sure. Indications are not only the exponential growth of publications on this topic in comparison to the small amount of thermodynamically stable intermetallic single-phase HEAs (≈50) identified so far, but also the many papers that are based on possibly unreliable and unreproducible experimental data from as-cast samples. By definition, HEAs are characterized by a random distribution of their constituting atoms on the lattice sites. Deviations from this ideal structure do have influence on the properties. What is needed, therefore, is a clearly defined protocol for the synthesis and 19

Journal Pre-proof characterization of HEAs, and the only use of thermally equilibrated single-phase samples for the study of their properties. Best would be single-crystalline specimens to eliminate the influence of the microstructure. One of the main tasks beside the search for new HEAs should be the determination of the compositional and thermal stability regions of the HEAs with the most interesting properties and potential for applications. Finally, what is needed at this state of research is a database with all available reliable data about stability, structure and properties of HEAs.

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Acknowlegement: I want to thank Ian Baker and Rachel Osmundsen for their helpful comments.

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29

Journal Pre-proof Table 1 Distribution of the metallic elements constituting the N-ary single-phase HEAs (or HEICs) known so far. In the first row the Mendeleev numbers (on top in each box) [143] and the element symbol are given. A star means that at least one HEA in this system remained stable under annealing, if having been annealed at all. N TM-HEAs AlCoCrCuFeMn AlCoCrCuFeNi* AlCoCrCuMnNi AlCoCrCuNiV AlCoCrFeMn AlCoCrFeMnNi* AlCoCrFeNi* AlCoCrFeNiTi AlCoCrFeNiV* AlCoCuFeMnNi* AlCoCuFeNi* AlCoCuFeNiV AlCoFeMnNi* AlCoFeNiV AlCoFeNiTiV AlCrFeMn AlCrFeMnNi CoCrCuFeMoNi CoCrCuFeNiTi CoCrCuFeNiTiV CoCrCuFeNiV CoCrFeMn CoCrFeMnNi* CoCrFeMnNiV* CoCrFeNi* CoCrFeNiPd* CoCrFeNiSi CoCrFeNiTi CoCrMnNi* CoCuMnNi* CoCuFeMnNiV

6 6 6 6 5 6 5 6 6 6 5 6 5 5 6 4 5 6 6 7 6 4 5 6 4 5 5 5 4 4 6

19 Sc

49 Zr

50 Hf

51 Ti

52 Ta

53 Nb

54 V

55 W

56 Mo

Ti V

V

Ti

l a

n r u

o J

Ti Ti

V V

V

Ti

58 Re

Cr Cr Cr Cr Cr Cr Cr Cr Cr

V

V V

57 Cr

Mo

V

30

61 Fe

Mn

Fe Fe

62 Ru

63 Os

Mn Mn

o r p

e Mn

Mn

Mn Mn

Mn Mn Mn

Mn Mn Mn

Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe

Fe

64 Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co

f o

Mn

r P Cr Cr Cr Cr Cr Cr Cr Cr Cr Cr Cr Cr Cr Cr

60 Mn

Co Co Co Co Co Co Co Co Co Co Co Co Co Co

65 Rh

66 Ir

67 Ni

68 Pt

69 Pd

Cu Cu Cu Cu

Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni

Cu Cu Cu

Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni

72 Cu

76 Zn

80 Al

81 Ga

83 Sn

85 Si

Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al Al

Cu Cu Cu Cu

Pd Si

Cu Cu

Journal Pre-proof CoFeMnNi* CoFeMnNiTiV CoTaTiV CrMoTiV CuIrNiPdPtRh* CuMnNiZn CuMnNiZnSn FeGaMnNiSi

4 6 4 4 6 4 5 5

R-HEAs AlCrMoTi* AlCrMoNbTi* AlCrMoTaTi* AlCrMoTiV* AlCrNbTiV* AlHfNbTaTiZr AlHfNbTiZr* AlMoNbTi* AlNbTaTiVZr AlNbTaTiZr AlNbTiV* CrFeMoNiRuW* CrMoReVW* HfMoNbTiZr* HfMoNbZr* HfMoTiVZr HfNbReTiZr HfNbTaTiZr* HfNbTaZr* HfNbTaWZr HfNbTaZr HfNbTiVZr* HfNbTiZr* IrMoRhRuW* IrOsReRhRu* MoNbTaVW* MoNbTaW*

4 5 5 5 5 6 5 4 6 5 4 6 5 5 4 5 5 5 4 5 4 5 4 5 5 5 4

Ti Ti Ti

Mn Mn

V V V

Ta

Mo

Fe Fe

Co Co Co

Ni Ni

Cr Rh Mn Mn Mn

Zr Zr

Hf Hf

Zr Zr

Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti Ti

Nb Ta

Ta

Ta Ta

Nb Nb Nb Nb Nb Nb Nb

V V

Mo

Hf

Ti

Hf Hf Hf Hf Hf Hf Hf Hf

Ti Ti Ti

l a

V V

n r u V

Zr Zr Zr Zr Zr Zr Zr Zr Zr Zr

Mo Mo Mo Mo

Nb Nb

o J Ta Ta Ta Ta

Ti Ti

Nb Nb Nb Nb Nb Nb Nb

W W W

V

Mo Mo Mo Mo Mo

Cr Cr Cr Cr Cr

Ru

Ni

Re

W V Mo Re

Nb Nb

o r p Fe

V

W W

Mo Mo

31

Ru Ru

Os

Pt

Pd

Cu Cu Cu

Zn Zn

Sn Ga

Al Al Al Al Al Al Al Al Al Al Al

Re

W Ta Ta

f o

Ni Ni Ni Ni

e

r P Cr Cr

Fe

Ir

Rh Rh

Ir Ir

Si

Journal Pre-proof MoReRhRu MoReRhRuTi NbPdRhScZr NbPdRhScTaZr NbTaTiV* NbTaTiZr NbTiVZr PdRhScZr

4 5 5 6 4 4 4 4 N

RE-HEAs DyErGdHoTb DyErGdHoLuScTbY DyGdHoLaTbY DyGdHoTbY DyGdLuTbTm* DyGdLuTbY ErGdHoLaTbY GdHoLaTbY

5 8 6 5 5 5 6 5

Mo Mo

Ti Sc Sc

Zr Zr

Sc

Zr Zr Zr

19 Sc

20 Lu

Sc

Lu

Lu Lu

Ti Ti Ti

21 Tm

Ta Ta Ta

Nb Nb Nb Nb Nb

22 Er

23 Ho

24 Dy

Er Er

Ho Ho Ho Ho

Dy Dy Dy Dy Dy Dy

Tm Er

Ho Ho

Re Re

Ru Ru

Rh Rh Rh Rh

Pd Pd

Rh

Pd

V

25 Y

Y Y Y Y Y Y

26 Tb

27 Gd

Tb Tb Tb Tb Tb Tb Tb Tb

Gd Gd Gd Gd Gd Gd Gd Gd

l a

f o

33 La

e

o r p

La

r P La La

n r u

o J

32

Journal Pre-proof Table 2 Single-phase HEAs (or HEICs) based on transition elements (groups 3 – 12) without significant amounts of refractory elements (TM-HEAs). The constituents are given in alphabetical order. The year is given when the phase stability of the HEA was studied in greater detail, if at all. ECP…Experimentally confirmed prediction. Nominal composition

Years studied

Thermal history

Comments

References

ECP

[40]

AlCo0.5CrCu0.2FeMn

bcc

2019

?

Al0.3CoCrCu0.3FeNi

fcc

2018

Annealed at 1173-1373 K

Al0.5CoCr0.5CuMnNi

fcc

2019

?

ECP

[40]

AlCo2CrCuNi3V

fcc

2019

?

ECP

[40]

AlCoCrFeMn

bcc

2019

as cast

Cr-Mn pair driven B2-type sro

[101]

Al0.2CoCrFeMnNi

fcc

2018

Annealed at 1173-1373 K

AlCoCrFeNi

bcc

2019

Al0.3CoCrFeNi

fcc

2017

-p

ro of

[100]

[100]

Thermoelectric and magnetocaloric effects

[144]

Annealed at 1523 K

Single crystal by Bridgman as well as floating zone method

[105][75]

2019

as cast

Phase transformations under pressures up to ≈50 GPa

[103],[104]

fcc

2019

?

ECP

[40]

B2

2016

In situ HT study

stable up to 873 K, then beyond phase

[109]

Al(Co0.2Cu0.2Fe0.2Mn0.2Ni0.2)

B2

2019

Annealed at 1373 K

Al occupies always one sublattice

[23]

Al(Co0.25Cu0.25Fe0.25Ni0.25)

B2

2019

Annealed at 1373 K

Al occupies always one sublattice

[23]

Al0.5CoCuFeNiV0.5

fcc

2019

?

ECP

[40]

Al(Co0.25Fe0.25Mn0.25Ni0.25)

B2

2019

Annealed at 1573 K

Al occupies always one sublattice

[23]

AlCoFeNiSm0.1TiV0.9

fcc

2019

As cast

Selective Laser melting,

[43]

lP na fcc,

Al1-xCoCrFeNix (x = 0.5,0.75)

hcp, bcc

Jo

Al0.2CoCr0.5Fe2NiTi0.25

ur

AlxCoCrFeNi (x = 0, 0.1, 0.3, 0.75, 1.5)

AlCoCrFeNiV

re

Annealing at 1073 K leads to a secondary fcc phase

33

Journal Pre-proof

AlCoFeNiSm0.1V0.9

fcc

2019

As cast

Selective Laser melting

[43]

Al0.3Cr2Fe0.5Mn0.8

bcc

2019

?

ECP

[40]

Al0.075Cr0.06Fe0.404Mn0.348Ni0.113

fcc

2016

As cast

C-doped between 0% and 1.1%

[4]

Co1.7CrCu0.1FeMo0.3Ni

fcc

2018

As cast

CoCrCuFeNiTi0.4

fcc

2019

?

CoCr0.5Cu0.5FeNi2Ti0.5V0.5

fcc

2019

?

CoCr0.3Cu0.2FeNiV0.5

fcc

2019

?

CoCrFeMn

fcc

2019

As cast

CoCrFeMnNi

fcc

2004, 2019

[145]

CoCrCu0.1Fe1.7Mo0.3Ni CoCrCu0.1FeMo0.3Ni1.7 [40]

ECP

[40]

ECP

[40]

Co-Cr pair driven sro

[101]

Cantor alloy

[80],[62],[82]

-p

ro of

ECP

fcc

2019,

na

Co0.10Cr0.15Fe0.35Mn0.05Ni0.25V0.10

lP

re

Annealed between 1073 and 1473 K

Annealed between 1173 and 1373 K

Single-phase region in phase diagram calculated

[146],[147]

fcc

2019

Single crystal by Bridgman

Phase transformation at 500 K

[32], [75], [62]

fcc

2018

As cast and also annealed

Also highpressure study

[65], [49]

CoCrFeNiSi0.6

fcc

2019

?

ECP

[40]

CoCr1.5Fe1.5NiSi0.2

fcc

2019

?

ECP

[40]

CoCr0.5Fe2NiTi0.25

fcc

2019

?

ECP

[40]

CoCrMnNi

fcc

2018

Annealed at 1273 K

G-x curves calculated

[93]

Co10Cu20Mn30Ni40

fcc

2020

Annealed at 873 – 1173 K

Phase diagram calculated

[56]

CoCuFeMnNiV0.5

fcc

2019

?

ECP

[40]

CoFeMnNi

fcc

2014

Annealed at 1373 K

CoFeMnNiTi0.5V0.5

fcc

2019

?

(CoCrFeNi)100-xPdx

Jo

CoCrFeNi

ur

2017

Anti-Invar system

34

[88] ECP

[40]

Journal Pre-proof Co0.2TaTiV

bcc

2019

?

ECP

[40]

CrMoTiV

bcc

2019

?

ECP

[40]

CuIrNiPdPtRh

fcc

2017

annealed

[95], [96]

Cu2MnNiZn

fcc

2019

As cast

[97]

Cu2MnNiSn0.2Zn

fcc

2019

As cast

[97]

Fe0.267Ga0.156Mn0.20Ni0.267Si0.11

bcc

2020

Annealed at 700 K

[94]

Year studied

Thermal history

Annealed at 1473 K

Comments

-p

Nominal composition

ro of

Table 3 Single-phase HEAs (or HEICs) based on refractory elements (R-HEAs). Elements of the same column in the periodic table are listed in parentheses. The year is given when the phase stability of the HEA was studied in greater detail, if at all. ECP…Experimentally confirmed prediction.

B2

2019

AlTiNb(CrMo)

B2

2019

AlTiTa(CrMo)

B2

2019

Annealed at 1773 K

[137]

AlTiV(CrMo)+

bcc

2018

As cast

[148]

AlTi(VNb)Cr0.5

B2

2018

Annealed at 1473 K

Al0.4(TiZrHf0.6)(NbTa)+

bcc

2014

As cast

[149]

re

AlTi(CrMo)

Annealed at 1573 K

[137], [148]

[137]

lP

na

ur

Alx(NbTiZrHf)100-x, 0≤x≤7 Alx(TiZrHf)3(100-x)/4Nb(100-x)/4

Below 1123 A15 (cP8Cr3Si) type phase forms

References

Quasi-binary phase diagrams

[138]

2018

Annealed at 1273 K

[150]

B2

2019

Annealed at 1773 K

[137]

Al (Ti1.5Zr0.5)(Nb1.5Ta0.5)+

bcc

2014

As cast

[149]

AlTi(VNb)

B2

2018

Annealed at 1473 K

[138],[70]

Al0.3(Ti1.4Zr1.3)(V0.2NbTa0.8) +

bcc

2014

As cast

[149]

Cr21Fe20Mo6Ni38Ru13W2

fcc

2018

Annealed at 1523 K

(CrMoW)VRe

bcc

2019

Annealed at 1273 K

(TiZrHf)NbMo

bcc

2016

Annealed at 1973 K

No phase transition up to 1743 K

[112],[151]

(Ti2ZrHf)V0.5Mo0.2

bcc

2019

As cast

Irradiation resistance

[132]

(ZrHf)NbMo

bcc

2016

Annealed at 1973 K

(Ti0.11Zr0.11Hf0.11)Nb0.11Re0.56

hcp

2019

As cast

Superconducting

[64]

(Ti20Zr20Hf23)Nb21Re16

bcc

2018

As cast

Superconducting

[123]

AlTiNbMo

Jo

bcc

35

Predicted by CALPHAD, High corrosion resistance

[92]

[115]

[112]

Journal Pre-proof (ZrHf)(NbTa)

bcc

2016

Annealed at 2073 K

sro determined, B2 phase precipitation

[31]

(ZrHf0.5)(NbTa)W0.5

bcc

2019

?

ECP

[40]

(Ti0.11Zr0.14Hf0.08)(Nb0.33Ta0.34)

bcc

2014

Annealed at 2523 K

Superconducting

[121]

(TiZrHf)(NbTa)

bcc

2019

Annealed at 1373 K

Phase decomposition at T < 973 K; Superior hydrogen storage

[117], [116], [152], [153], [154]

(TiZrHf)x(NbTa)1−x

bcc

2018

As cast

superconducting (ScCr), (Y-Mo), and (ScMo) substitution

[127]

(Ti1.5ZrHf0.5)(Nb0.5Ta0.5)

bcc

2018

Anealed at 1273 K

(Ti0.15Zr0.24Hf0.21)(V0.15Nb0.25)

bcc

2019

Anealed at 1073 K

(Ti2ZrHf0.5)(VNbx), x = 0, 0.25, 0.5, 0.75, 1

bcc

2019

As cast

(TiZrHf)(VNb)

bcc

2018

Annealed at 1773 K

(TiZrHf)Nb

bcc

2014

Annealed at 1573 K

[156]

(Mo20W11.5) Ru20(Rh22.5Ir26) (Mo20W9.5) Ru25(Rh20Ir25.5)

hcp

2019

Annealed at 2373 K

[134]

(Mo5W5) Ru15.3(Rh37.4Ir37.4)

fcc

2019

Re0.21(Ru0.19Os0.22)(Rh0.20Ir0.19)

hcp

2017

MoReRhRu

Hcp

(MoReRhRu)0.9Ti0.1 (VNbTa)(MoW)

[118]

ro of

Superconducting

[155] [119], [120]

[135]

Annealed at 1500 K

Stable up to 45 GPa; electrocatalytic activity in methanol oxidation

[157]

2019

As cast

superconducting

[129]

Hcp

2019

As cast

superconducting

[129]

bcc

2016

Annealed at 2073 K

[112], [158]

bcc

2016, 2019

Annealed at 2073 K

[112], [159], [160],[76],[158]

bcc

2019, 2018

Annealed at 1973 K

[59], [51]

bcc

2019

As cast + ball milling

Hydrogen storage material

[133]

(Ti0.15Zr0.15)(Nb0.35Ta0.35) bcc + second phase at grain boundaries

2018

As cast

Superconducting

[125]

Ti(VNbTa)

ur Jo

(NbTa)(MoW) (NbTa)(MoWx)

na

Annealed at 2373 K

ECP

lP

re

-p

Superior hydrogen storage

[124]

(TiZr)(VNb)

Table 4 Single-phase HEAs based on rare-earth elements (Lanthanoids) (RE-HEAs). The HEAs and elements are arranged in alphabetical order. The year is given when the phase stability of the HEA was studied in greater detail. Nominal composition

Year studied

Thermal history

Comments

References

Giant magnetocaloric effect

[29]

DyErGdHoTb

hcp

2017

As cast

DyErGdHoLuScTbY+

hcp

2018

As cast

36

[141]

Journal Pre-proof DyGdHoLaTbY+

hcp

2018

As cast

DyGdHoTbY

hcp

2015, 2017

As cast

DyGdLuTbTm+

hcp

2014

Annealed at 1173 K

[161]

DyGdLuTbY+

hcp

2014

As cast

[161]

hcp

2018

As cast

[141]

As cast

[162]

ErGdHoLaTbY

+

GdHoLaTbY+

hcp

Phase transitions under pressure,

[139], [140]

ro of

2016 +small amount of oxides or other precipitates

[141]

Number of publications on HEAs per year 1000

-p

900

700

lP

600 500

300 200 9

13

na

400

27

27

33

48

438 294 238 93

123

41

99

119

146

ur

6 58 49 19 7 3 2 2 1 1 1 0 0 0 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2

Jo

0

783

re

800

100

918

All HEA papers

Single-phase HEA papers

Fig. 1 Total number of publications on high-entropy alloys (HEAs) per year (blue) and number of papers on single-phase HEAs (orange) according to a Web of Science search. The exponential growth is a first sign of a hype (see, e.g., [163]). For 2019, the growth rate of the papers is declining already.

37

Journal Pre-proof

12 Li 1.0 11 Na 0.9 10 K 0.8 9 Rb 0.8 8 Cs 0.7 7 Fr 0.7

2

3

77 3.01 Be 4.90 1.52 1.5 1.11 73 2.85 Mg 3.75 1.86 1.2 1.60 16 2.42 Ca 2.20 2.27 1.0 1.97 15 2.34 Sr 2.00 2.48 1.0 2.15 14 2.18 Ba 2.40 2.66 0.9 2.17 13 Ra 0.9 2.15

* Lanthanoids

3.34 1.61 3.19 1.78 3.10 1.87

51 Ti 1.4 49 Zr 1.4 50 Hf 1.3

5

3.45 1.45 3.64 1.59 3.80 1.56

54 V 1.6 53 Nb 1.6 52 Ta 1.5

6

3.60 1.31 4.00 1.43 4.11 1.43

57 Cr 1.6 56 Mo 1.8 55 W 1.7

7

3.72 1.25 3.90 1.36 4.40 1.37

60 Mn 1.5 59 Tc 1.9 58 Re 1.9

8

3.72 1.37 1.35 4.02 1.37

61 Fe 1.8 62 Ru 2.2 63 Os 2.2

9

4.06 1.24 4.50 1.33 4.90 1.34

64 Co 1.8 65 Rh 2.2 66 Ir 2.2

10

4.30 1.25 4.30 1.35 5.40 1.36

67 Ni 1.8 69 Pd 2.2 68 Pt 2.2

11

4.40 1.25 4.45 1.38 5.60 1.37

72 Cu 1.9 71 Ag 2.4 70 Au 2.4

4.48 1.28 4.44 1.45 5.77 1.44

12

13

76 Zn 1.6 75 Cd 1.7 74 Hg 1.9

80 Al 1.5 81 Ga 1.6 79 In 1.7 78 Tl 1.8

4.45 1.34 4.33 1.49 4.91 1.50

14

15

84 3.20 Ge 4.60 1.22 1.8 1.23 83 3.10 Sn 4.30 1.63 1.8 1.41 82 3.20 Pb 3.90 1.70 1.8 1.75

88 Sb 1.9 87 Bi 1.9

16

3.23 1.43

4.85 1.45 91 4.69 Po 1.55 2.0 1.67

1.88

32 31 Ce Pr 1.1 1.87 1.1 1.82 47 46 Th Pa 1.3 1.88 1.5 1.80

30 29 Nd Pm 1.1 1.81 1.1 1.63 45 44 U Np 1.4 1.39 1.4 1.30

28 18 27 26 24 23 22 21 17 20 Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 1.2 1.62 1.2 2.00 1.2 1.79 1.1 1.76 1.2 1.75 1.2 1.74 1.2 1.73 1.3 1.72 1.1 1.94 1.3 1.72 43 42 41 40 39 38 37 36 35 34 Pu Am Cm Bk Cf Es Fm Md No Lr 1.3 1.51 1.1 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3

re

-p

+ Actinoids

19 Sc 1.3 25 Y 1.2 33* La 1.1 48+ Ac 1.1

4

ro of

1

Jo

ur

na

lP

Fig. 2 Periodic Table of metallic elements. Listed are: Mendeleev numbers (on top left in each box) [143], indicator in which kind of HEA this element is used (TM transition metal, R refractory element, RE rare earth element), (on top right in each box), element symbol, Pearson absolute electronegativity, [eV] [164] next to the element symbol, Pauling electronegativities c (relative to F= 4.0) (bottom left in each box) [165], and atomic radii (half of the shortest distance between atoms in the crystal structure at ambient conditions) (bottom right in each box) of the metallic elements (taken from [36]).

38

Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Jo

ur

na

lP

re

-p

ro of

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

39