{"paper_id":"21f5be0a-b8e6-428c-99a1-024fe30cf1a1","body_text":"Posted on 23 Apr 2025 — CC-BY 4.0 — https://doi.org/10.22541/au.174543474.41741698/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary.\nA brief discussion on High-entropy alloys vs Compositionally\nComplex alloys\nMainak Saha 1\n1Affiliation not available\nApril 23, 2025\n1\n\nA brief discussion on High-entropy alloys vs Compositionally \nComplex alloys \nMainak Saha* \nDepartment of Metallurgical and Materials Engineering, \n National Institute of Technology(NIT) Durgapur, Durgapur-713209, West Bengal, India \nmainaksaha1995@gmail.com \nAbstract \nHigh-entropy alloys(HEAs) are of great interest in the field of materials science \nand engineering. Unlike conventional alloys, which contain a maximum of 2 base \nmetals, this new category of materials consist s of multi-principle elements and \nthe possible number of alloy compositions, in case of HEAs, is outstandingly \nhigher than that for con ventional alloys. Here, a review on the high -entropy \nalloys, has been provided , on the issue whether the earliest definition of High-\nEntropy alloys, proposed in 2004 [2, 4], is consistent with one of the 4-component \nequiatomic Compositionally complex alloys exhibiting a “High-entropy” effect. \n1. Introduction \nSince ancient times, human civilisation has always been striving towards the \ndevelopment of new classes of materials [1], which have played a vital role for \nmore than thousands of years. Since the Bronze age, alloys have been developed \nbased on “base element paradigm” i.e. by using one or at most, 2 base elements, \nfor example iron in steels or Ni in Ni-based superalloys. In 2004, a new paradigm \nof designing alloys, was proposed independently by Prof. J.W. Yeh and Prof. \nBrian Cantor . which eschewed the “base element” approach. Prof. J.W. Yeh \nnamed these materials as “High -entropy alloys” and there is already a high -\nentropy alloy, popularly named as Cantor alloy, after its discoverer, which forms \na single phase FCC solid solution at room temperature. By the term “High -\nentropy”, it is clear that the configurational entropy of this alloy is high due to \nrandom mixing of the elements, in this case. The new theory has basically opened \nup new avenues in research of engineering materials. In conventional ‘base metal’ \napproach, only n different alloys may be obtained with n base metals. However, \nif a combination of p elements are to be selected from a total of n elemen ts, to \nform an equiatomic alloy(p=2,3,4,…..), the total number, N, of the alloys, may \nbe increased from n to N=2 n-n-1.[2] So, from the mathematical expression, when \nn<3, the two approach do not differ considerably. However, with increasing n, \nthe two approach differ largely, due to exponential dependence of N on n[16]. \n2. The concept of HEAs [2][3][4] [5] [6] [7] [8][9] [17] \n\nConsidering an ideal solution, the configurational entropy of mixing per mole, \nmay be expressed as Δ mixS=-RƩCilnCi, where R is universal gas constant and \nequal to 8.314 J/molK, Ci is the mole fraction of ith element and i ranges from 1 \nto n. The closer the alloy composition to the central region, the larger is the value \nof ΔmixSm which reaches a maximum of 9.15 J/molK at the centre. Consequently, \nthe molar entropy of mixing (ΔmixSm), for an equiatomic HEA, is given by \nΔmixS=Rln n \nWith the “High -entropy” effect, the random solid solution may be stabilised \nagainst the intermetallic compounds when numerous elements are mixed in \nequimolar fraction. According to Zhang , et al. two additional parameters have \nbeen proposed for design of HEAs, namely δ(atomic size difference) [2] and ΔmixH \nwhich are mathematically expressed as follows( the binary molar enthalpy of \nmixing, in case of binary system i-j, is given by ΔmixHij[3], calculated accoding to \nthe Miedema model): \n \n𝛿 = √∑ 𝐶𝑖(1 − 𝑟𝑖\n𝑟̅ )2\n𝑛\n𝑖=1\n \n𝑟𝑖 atomic radius of 𝑖𝑡ℎ element \n𝐶𝑖 atom fraction of 𝑖𝑡ℎ element \n𝑟̅ - average atomic radius = ∑ 𝐶𝑖\n𝑛\n𝑖=1 𝑟𝑖 \n \nΔmixHm= ∑ ΩijCiCj\nN\ni=1, i≠j\n= ∑ 4Δ𝑚𝑖𝑥HijCiCj\nN\ni=1, i≠j\n \n𝛺𝑖𝑗 - melt interaction parameter (Miedema[11] model) \nΔ𝑚𝑖𝑥𝐻m - Enthalpy of mixing. This is found to be <0 for compounds and >0 for \nrandom solid solutions, following the Quasi-Chemical theory[11]. \n𝐶𝑖-atom fraction of ith element \nAtomic size mismatch parameter ( 𝝳): This parameter quantifies atomic radius \nmismatch. \nAccording to Yeh, et al.[2] symbolically, for HEAs \nTSsys>>max(|Hi|) (i=1,2,…….m) \n\nwhere S sys is the configurational entropy of the alloy, H i is the enthalpy of \nformation of the ith phase, assuming m phases in total. However, in their early \nwork, Yeh, et al. proposed a criterion Δ mixSm >=1.6R, corresponding to mixing \nof at least 5 elements in equiatomic composition. \nSimilarly, Zhang, et al. proposed another parameter, Ω, [5] showing the relative \ndominance of Enthalpy of mixing (ΔmixHm) given as \nΩ= Tm ΔmixSm/|ΔmixHm| \nWhere, Tm- absolute melting point of the alloy. \nΩ<1: |ΔmixHm| < ΔmixSm , implies that, intermetallic compound formation or \nsegregation is favoured. \nΩ>1: |ΔmixHm| > ΔmixSm, implies that, random solid solution is favoured. \n \nValence electron concentration (VEC) [6]: For electron compounds, VEC is used \nas a useful parameter in finding its formation propensity. This parameter is \ndetermined from the number of electrons in 4s and 3d orbitals of individual \nelements( in ground state) \n𝑉𝐸𝐶 = ∑ 𝐶𝑖(𝑉𝐸𝐶)𝑖\n𝑛\n𝑖=1\n \n(VEC)𝑖 valence electron concentration of element 𝑖. \nElectronegativity (Δχ) [6]: \n𝛥𝜒 = √∑ 𝐶𝑖(𝜒𝑖 − 𝜒̅)2\n𝑁\n𝑖=1\n \nχi – electronegativity of 𝑖𝑡ℎ element.(according toPauling Scale) \nAccording to Hemphill et at. [7] the total entropy of mixing ST per spherefor a hard \nsphere system with different sized particles, may be expressed as follows: \nST(ci,ri,Ɛ)= SC(ci)+ SE(ci,ri,Ɛ) \nWhere, \nSE- excess entropy of mixing \nSC=-kƩCilnCi \nk- Boltzmann constant=1.38*10^(--23) J/K \n\nci, ,ri, Ɛ - atomic concentration, atomic radius and overall packing density, \nrespectively. \n \nФ-parameter[8] \nYe, et al. assumed that Ssys ~ST~ SC-|SE| and accordingly proposed a parameter \nФ, expressed mathematically as: \nФ= (SC- |ΔmixHm|/Tm)/ |SE| \nIf Ф< ФC, HEAs form multiple phases and even an amorphous structure. And if \nФ> ФC, HEAs form single phase solid solution. \n \nIn the strictest sense, a solid solution phase is preferred to an inter metallic phase \nfor a multicomponent alloy if GSS < GIM, where GSS and GIM denote the Gibbs \nfree energy of the solid solution and intermetallic phase, respectively. In terms of \nentropy and enthalpy, this inequality can be written as Hmix -TSmix 1 and \n𝝳<6.6%, simple solid solutions form. Besides, with high VEC, FCC is reported \nto be highly stable and BCC is found to be stable at low VEC. \n3. Major properties of HEAs[10] \nSevere L attice Distortion: This effect arises due to the fact that there exist \nmulticomponent matrices in HEAs mainly due to atomic size difference in \nindividual elements. This leads to severe lattice distortion and not only, affects \nvarious properties like strength, hardness e.t.c but also reduces the thermal effect \n\non properties. By the term ”lattice” in HEAs, the average lattice arising due to \nformation of different solid solutions, is being referred to. Strength is expected \nto increase due to increased solid solution strengthening occurring due to severe \nlattice distortion. Besides lattice distortion, the other factors contributing to the \nsame are: different bonding energies, and difference in crystal structure(arising \ndue to different efficiency of packing). This effe ct is enhanced when relative \ndifference in atomic radii between the individual elements is very high and vice-\nversa. \nSluggish Diffusion Effect: HEAs contain mainly random solid solution, \nintermetallic compounds and/or ordered solid solution. Thus, atomic diffusion in \nwhole-solute matrix is very different than that in a matrix of a conventional alloy. \nA vaca ncy in a whole -solute matrix is surrounded and competed by different \nelement atoms during diffusion, due to large fluctuation in lattice potential \nenergy(LPE) between lattice sites. The abundant low LPE sites may serve as traps \nand hinder atomic diffusion. This causes Sluggish Diffusion Effect. \n4. The concept of Compositional Complexity in alloys \nMany literatures[5][6] report that Compositionally Complex Alloys are those which \nwere initially termed as HEAs, in 2004. According to the earliest definition, \nproposed by Yeh, at al. [2] HEAs must have at least 5 elements in equiatomic or \nnear-equiatomic(~5-35%) proportions, in order to maximise the molar entropy of \nmixing(Δ𝑚𝑖𝑥𝑆m). But, at present, this definition of HEAs is found to be \ninconsistent with the basic notion of maximisati on in molar entropy of \nmixing(Δ𝑚𝑖𝑥𝑆m) and thus, the new term “Compositionally Co mplex alloys” has \nemerged. For instance, a 4-component equiatomic alloy, AlTiVCr was \nreported[15] to possess a single phase B2(ordered BCC solid solution) at room \ntemperature, in its as -cast microstructure, such that the molar enthalpy of \nformation of B2 phase(~Δ𝑓𝐻m=-9.30 kJ/mol) was revealed to be lesser than that \nfor disordered BCC phase(~ Δ𝑓𝐻m=-1.25 kJ/mol) at low temperature, from the \nsame study. Besides, it was also found, from the same study, that, the values of \nΔ𝑚𝑖𝑥𝑆m and Δ𝑚𝑖𝑥𝐻m were in agreement with intermetallic compound formation \nwhereas only the values of 𝝳 and Ω showed that solid solution should form. \nHowever, from the characterisations, carried out later, it was observed that single \nphase B2, in this alloy, was found to be stable over disordered BCC, over a wide \nrange of temperature. Thus, the established fact that AlT iVCr forms a single \nphase B2 over a wide range of temperature, is similar in analogy with respect to \nthe 5 -component equiatomic Cantor alloy [3], CoCrFeMnNi, forming a single -\nphase FCC at room temperature and defies the earliest definition of HEAs where \nat least 5 components are required in equiatomic or near-equiatomic proportions \n\nare required to exhibit the “High -entropy” effect[2] and form only single phase/ \nmulti phase solid solutions or single/multi -phase solid solutions along with \nintermetallic compounds. \n5. Summary and Outlook \nThe advent of HEAs, composed of multiple principle elements unlike \nconventional alloys with mostly, one and very rarely, 2 base elements, has fully \nrevolutionised the concept of alloy designing and also led to a lot of modern \ntheories, methods and even, models of alloy designing which not only apply to \nHEAs but also to conventional alloys . However, these theories and \nmodels(especially, those for atomistic movement governing phase formation [16]) \nneed to be investigated, further, and a lthough, there has been a lot of work on \nmechanical, physical as well as chemical properties of HEAs, but a lot remains \nto be done, primarily because of two reasons: firstly, the formation of different \nphases in HEAs, needs to be explored, in depth, although a certain amount of \nwork has been done on the phase stability of HEAs and secondly, a very large \nnumber of possible combinations in HEAs. The latter may prove to be useful but \nthe major challenge lies in identifyin g the useful alloy composition for a \nparticular application, through trial and error method, which turns out to be a \nhighly cumbersome and even, a non -economic task[5]. Besides, the new concept \nof “Compositional complexity” also needs to be explored, in d epth, in order to \ndraw a proper conclusion as to whether the old concept of “High-entropy alloys” \nmay be completely, replaced by the new definition of “Compositionally Complex \nalloys” and if exceptions exist, then which compositions are those? and why are \nthey exceptional? However, in spite of all challenges, HEAs are found to possess \nexcellent novel properties such as high specific strength, superconductivity, \nsuperparamagnetism, excellent mechanical properties at elevated temperature, \nexcellent ductility and fracture toughness at cryogenic temperature [4]. For \ninstance, HEAs, as light as Al, but stronger than Metallic glasses, have been \ninvestigated to be useful for transport and energy sectors where “lightweight” \nmaterials have a huge demand due to reduction in fuel consumption and thus, \nminimising the energy requirements [16]. Refractory HEAs find application in \nhigh-temperature applications like gas turbines, rocket nozzles, nuclear \nconstruction e.t.c whereas, Lightweight refractory HEAs find applications in \naerospace applications like re -entry nosecones. In view of the promising \napplications, HEAs, with promising properties, may be designed with further \nadvancements, thereby promoting their usage in industries, which is limited, even \ntill today. \nAcknowledgement \n\nThe author is grateful to all the faculty members and Ph .D scholars from the \ndepartment of Metallurgical and Materials Engineering, NIT Durgapur, for their \nextreme support and dedication to carry out fruitful discussions in the p resent \nregard. \nReferences \n[1] R.E. Hummel, Understanding Materials Science, second ed., Springer-Verlag, \n2004. \n[2] J.W. Yeh, et al. Adv. Eng. Mater. 6 (5) (2004) 299. \n[3] B. Cantor, et al. Mater. Sci. Eng. A 375–377 (2004) 213. \n[4] Y.F. Ye, et al. Scripta Mater. 104 (2015) 53. \n[5] Y. Zhang, et al. Progr. Mater. Sci. 61 (2014) 1. \n[6] B. Gludovatz, et al. Science 345 (6201) (2014) 1153. \n[7] M.A. Hemphill, et al. Acta Mater. 60 (16) (2012) 5723. \n[8] S.Q. Xia, et al. JOM (2015) 1. \n[9] Y. Zhang, et al. Adv. Eng. Mater. 10 (6) (2008) 534. \n[10] R.A. Swalin, Thermodynamics of Solids, Wiley, 1962. \n[11] K. Guan-Yu, et al., FCC and BCC equivalents in as-cast solid solutions of \nAl[x]Co[y]Cr[z]Cu[0.5]Fe[v]Ni[w] high-entropy alloys, Cachan, France, 2006.p. \n669. \n [12] H.Y. Ding, K.F. Yao, J. Non-Crystal. Solids 364 (1) (2013) 9. \n[13] J.Y. He, et al. Acta Mater. 62 (2014) 105. \n[14] O.N. Senkov, et al. Nat Commun. (2015) 6. \n[15] Y. Qiu, et al. Acta Mater. 123 (2017) 115-124. \n[16]. Y.F. Ye, et al. Materials Today 19 (2016) 349-362. \n[17]. M. Saha, K. Guruvidyathri, A. Karati, B.S. Murty,”Sequence of \nPrecipitation of sigma phase in CoCrCuMnNi High-Entropy Alloy”, MSE Book \nof Abstracts, NMD-ATM,2017, 07","source_license":"CC-BY-4.0","license_restricted":false}