Recent Progress in Our Understanding of Phase Stability, Atomic Structures and Mechanical and Functional Properties of High-Entropy Alloys

Abstract

This paper reviews a current trend and recent progress in research on phase stability, atomic structures, mechanical and functional properties of high-entropy alloys. The survey is carried out based partly on the special issue published in April, 2020, in Materials Transactions (Vol. 61, No. 4). Research on high-entropy alloys has spread worldwide since the year of 2004, as many of them exhibit attractive properties for structural and functional applications, which have never been achieved in conventional alloys. Significant progress has been made in recent years in our understanding of high-entropy alloys in terms of processing, characterization, modeling and simulation, and so on. Some of them are briefly described in this paper.

Since the concept of ‘high-entropy alloy’ was proposed by J.W. Yeh in 2004,¹⁾ high-entropy alloys have caught significant attention of a tremendous number of materials scientists in the world and the research of high-entropy alloys has become one of the most active areas in materials science today. This paper aims at summarizing recent progress in our understanding of phase stability, atomic structures and mechanical and functional properties of high-entropy alloys.

In addition to some excellent books^2–4) and many review papers,^5–10) many international journals have published special issues on high-entropy alloys. A special issue entitled ‘Materials Science of High-Entropy Alloys’ has been published in April 2020 in Materials Transactions (Vol. 61, No. 4). The special issue includes 8 regular articles in total, covering studies on processing,¹¹⁾ alloy design,¹²⁾ characterization of mechanical properties,^13,14) solidification microstructure,¹⁵⁾ and modelling of mechanical properties,¹⁶⁾ energetics of lattice defects such as vacancies¹⁷⁾ and interstitials.¹⁸⁾ This special issue is intended to provide some preliminary outcomes of a national research project, Grant-in Aid for Scientific Research on Innovative Areas ‘High-Entropy Alloys: New Scientific Principle for Controlling Variety and Inhomogeneity of Elements’, which has been launched in 2018 as a 5-year research project supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

Research on high-entropy alloys has become tremendously popular in the world, as is evident from the annual change in the number of published papers on high-entropy alloys and that of their citations respectively in Figs. 1(a) and (b). The numbers plotted in Figs. 1(a) and (b) are obtained simply by search with Web of Science with ‘high entropy alloys’ as a keyword. The annual numbers of published papers and their citations both increase explosively and exponentially since the first paper by Yeh et al.¹⁾ published in 2004. Accordingly, many international conferences and symposia on high-entropy alloys have been extensively held here and there in the world, in particular in recent several years (Table 1). Some special symposia on high-entropy alloys are annually held not only in TMS Annual Meetings and in MRS Fall and Spring Meetings but also in some other international conferences such as Thermec and Euromat, although the latters are not included in Table 1. A series of International Conferences on High-Entropy Materials (ICHEM) and World Congress on High-Entropy Alloys are held every two and three years respectively.

Fig. 1

(a) The annual change in the number of published papers on high-entropy alloys and (b) that of their citations. The numbers plotted are those obtained by searching with Web of Science with ‘high entropy alloys’ as a keyword.

Table 1 Some important international conferences and symposia on high-entropy alloys since 2016.

Multiple reasons can be found for the very high research activity in the field of high-entropy alloys in recent years. One is obviously scientific curiosity to check the validity of the high-entropy concept based on thermodynamic arguments that the configurational entropy should be very high when the alloy is in a solid-solution in a multicomponent alloy system so that such high entropy promotes a tendency to form a simple solid-solution without forming secondary/tertiary intermetallic phases.¹⁾ Then, a question naturally arises as to what constituent elements form such a solid-solution alloy with either FCC (face-centered cubic), BCC (body-centered cubic) or HCP (hexagonally close-packed) structure, and what atomic structures these high-entropy alloys possess; do they form a completely random structure or comprise some kind of short-range ordering (SRO) or something else? Extraordinary mechanical properties exhibited by some (but not all) high-entropy alloys have also been one of the main reasons for the current high research activity on high-entropy alloys, since the discovery of simultaneous achievement of high strength and high ductility,^19–22) in addition to high fracture toughness,^23,24) in some FCC high-entropy alloys and retention of high strength at high temperatures in BCC high-entropy alloys.^25,26)

In the early days, many investigations on high-entropy alloys focused on finding out proper alloy systems to form high-entropy solid-solution alloys at and near equiatomic compositions and identifying suitable descriptors (materials parameters) to deduce a criterion for the formation of high-entropy alloys, as summarized in the early review papers.^5–7) Many materials parameters are used to deduce these criteria and those include mixing (configurational) entropy,^1,27–30) mixing enthalpy,^27–30) atomic size difference,^27,31) valence electron concentration (VEC)^31,32) and so on. Usually, multiple materials parameters are used to constitute a descriptor and the formation of high-entropy alloys is predicted with either single¹⁾ or multiple^27–32) descriptors in each criterion. The mixing enthalpy is usually used with the mixing entropy in the form of their ratio to express the energy gain as the entropy relative to that of enthalpy.^27–30) The atomic size difference among the constituent elements is in line with one of the Hume-Rothery rules that a solute that differs in its atomic size by more than about 15% from the host is likely to have a low solubility in that metal. VEC is of particular interest as it can predict the formation of high-entropy alloys with different crystal structures when used as a descriptor with a parameter ϕ that contains the ratio of the entropy and enthalpy.^31,32) High-entropy alloys with FCC and BCC structures are shown indeed to form around VEC of 8.5(± 1.0) and 5.0(± 0.7), respectively.^31,32) In fact, CrMnFeCoNi is known to form a quinary equiatomic FCC high-entropy alloy,³³⁾ while TiZrNbHfTa^34–36) and VNbMoTaW^33,34) are known to form quinary equiatomic BCC high-entropy alloys.³²⁾ All of them satisfy the above VEC criterion and they have been treated as a kind of prototypic FCC and BCC high-entropy alloys since their discovery. Recently, Niitsu et al.³⁷⁾ proposed to use mean-square atomic displacement (MSAD), instead of the parameter ϕ, together with VEC for better prediction of the formation of FCC non-equiatomic high-entropy alloys in the Cr–Mn–Fe–Co–Ni system. On the other hand, the formation of high-entropy alloys with the HCP structure is predicted to occur around VEC of 2.8(± 0.2).^31,32) Indeed, some HCP high-entropy alloys that satisfy the VEC criterion are found in Y–Gd–Tb–Dy–Lu and Gd–Tb–Dy–Tm–Lu rare-earth systems.³⁸⁾ More recently, Takeuchi et al.^39,40) have found some new HCP high-entropy alloys in the Ir–Mo–Rh–Ru–W system located in another VEC (7.855–7.865) region (Fig. 2). Of notice, however, is that these HCP high-entropy alloys are formed in non-equiatomic compositions and prototypic quinary equiatomic HCP high-entropy alloys have yet to be identified.

Fig. 2

Gibbs free energy calculated with Thermo-Calc 2019a and TCHEA database at 2100 K along the cross-sectional composition line of Ir_{0.415254(100−2x)}Rh_{0.415254(100−2x)}Ru_{0.169492(100−2x)}W_xMo_x.⁴⁰⁾

Many investigations on high-entropy alloys in the early days assumed a priori a completely random atomic structure for multi-component concentrated solid-solution alloys with the emphasis on severely distorted crystal lattice as one of the most remarkable features in atomic structures of high-entropy alloys. However, many conventional alloys including dilute binary alloys are known to generally exhibit some non-random atomic structures accompanied by short-range ordering (SRO) and short-range clustering (SRC) of the constituent elements with the degree of SRO and SRC varying with heat treatment.^41–44) The occurrence of SRO in these conventional alloys is usually proved by x-ray and electron diffraction^41,42) as well as by electrical resistivity and specific heat measurements^43,44) and how the alloy strength is affected by the evolution of SRO has been investigated for many alloy systems.⁴⁵⁾ According to Cohen et al.,⁴⁵⁾ the overall strength is not affected significantly with the presence of SRO, except that yield drop is observed in the stress-strain curve with the extent of yield drop depending on the degree of SRO. This is believed due to the quick decay of high resistance arising from SRO to the dislocation motion by the passage of the first several dislocations that destroy SRO on the slip plane. Then, subsequent dislocations move on the same slip plane experiencing less resistance for their motion and forming coarse slip. As the formation of SRO and SRC is simply a result of the mixing enthalpy contribution to the Gibbs free energy, high-entropy alloys are also considered to possess non-random atomic structures as characterized by SRO and SRC. The occurrence of SRO is pursued also for high-entropy alloys by x-ray diffraction⁴⁶⁾ and electron diffraction^47,48) and much intensively by theoretical calculations based on density-functional theory (DFT).^49–52) A substantial increase in strength in the presence of SRO is suggested by DFT calculations due to local fluctuations in stacking fault (SF) energy^50–52) and is claimed to occur experimentally in a CrCoNi polycrystal subjected to furnace cooling from 1273 K.⁵⁰⁾ However, some other experiments made on CrCoNi polycrystals⁵³⁾ and CrMnFeCoNi single crystals⁵⁴⁾ claim no significant increase in strength in the presence of SRO. To note is that all these experiments were made by assuming the evolution of SRO with low-temperature annealing but the occurrence of SRO was not proved by experiment. More work is needed to explore the effect of SRO on the strength of high-entropy alloys.

Although extraordinary mechanical properties are observed in many high-entropy alloys, not all of them exhibit such excellent mechanical properties. In fact, the range of mechanical properties exhibited by high-entropy alloys is comparable to that covered by many conventional alloys (see Figs. 1–3 of Ref. 10)), so that their mechanical properties are described by models already proposed for the deformation behavior of conventional solid-solution alloys^55–57) with some modifications to take into account of the presence of high local complexity of high-entropy alloys.^49–51) The most striking feature of the mechanical properties of FCC high-entropy alloys is excellent combinations of high strength and high ductility,^19–22) as deduced for the CrMnFeCoNi quinary equiatomic high-entropy alloy and quaternary and ternary equiatomic alloys of its sub-systems by George and his colleagues.^19–22,58) They made a systematic study on tensile properties of polycrystals of these equiatomic alloys in a wide temperature range of 77–673 K and found a strong temperature dependence of yield stress below room temperature and an increased tensile ductility at 77 K than at room temperature for most of these alloys.^19,20,58) The occurrence of deformation twinning at low temperatures through a dynamic Hall-Petch effect is believed responsible for their increased tensile ductility.^21,22) The temperature dependence of yield stress of these alloys is well interpreted in terms of thermally-activated dislocation glide, as in conventional solid-solution hardened alloys.^19,20,59)

The high strength of these high-entropy alloys must be related to their severely distorted crystal lattice and some models are proposed to correlate the strength with some appropriate parameters that describe the distorted crystal lattices.^60–63) MSAD is proposed as a materials parameter to scale the strength of high-entropy alloys^37,63) (Fig. 3(a)) and this has been further confirmed recently with molecular dynamic simulations using some different interatomic potentials (Fig. 3(b)).¹⁶⁾ There is a linear correlation between critical resolved shear stress (CRSS) and MSAD once they are normalized respectively to shear modulus (μ) and Burgers vector (b). Although the model based on MSAD lacks a connection to a specific dislocation mechanism, it correctly predicts the magnitudes of solid-solution strengthening of not only high-entropy alloys but also conventional binary alloys.⁶³⁾ This may indicate that MSAD represents the severely distorted crystal lattices for dislocation motion in high-entropy alloys very well. Indeed, a linear correlation is found between MSAD and misfit volumes in high-entropy alloys by theoretical assessment.⁶⁴⁾ Some excellent theoretical models that incorporate the solute-dislocation interaction energy resulting from solute misfit volumes, as is assumed for most existing models of solid-solution hardening applicable to dilute binary alloys,^56,57) are available for describing strengths of high-entropy alloys.^60,61) However, the predicted strength based on these models is rather temperature-insensitive, underestimating the low-temperature strength,⁶¹⁾ as seen in Fig. 4. The excellent low-temperature tensile ductility, on the other hand, is believed due to the occurrence of deformation twinning.^{21,22,58,65–71)} Since the twinning propensity generally increases with the decrease in stacking fault (SF) energy, the tuning of SF energy is important in controlling the ductility of high-entropy alloys.^72–75) Twins formed by deformation at 77 K in a $[\bar{1}23]$-oriented single crystal of CrMnFeCoNi are shown in Fig. 5 at different length scales. Twins formed are generally very thin, 2–3 nm on average.⁷²⁾ The results from polycrystals^21,22) and $[\bar{1}23]$-oriented single crystals^70,71) of CrMnFeCoNi and CrCoNi indicate consistently that the twinning stress increases with decreasing SF energy. This is completely opposite to what is long believed for conventional FCC alloys.^76–78) More work is needed to explore how the twining stress changes with temperature and SF energy in high-entropy alloys.

Fig. 3

Correlation between CRSS (normalized to shear modulus (μ)) and MSAD (normalized to Burgers vector (b)). CRSS data were taken from (a) experiment of Ref. 20)⁶³⁾ and (b) molecular dynamic simulation.¹⁶⁾

Fig. 4

Comparison of temperature dependence of CRSS of the quinary CrMnFeCoNi equiatomic high-entropy alloy deduced by experiment⁷⁰⁾ and that predicted by theory.⁶¹⁾

Fig. 5

Twins formed in a $[\bar{1}23]$-oriented single crystal of CrMnFeCoNi deformed at 77 K.⁷⁰⁾

BCC high-entropy alloys also exhibit very high strength compared to conventional BCC metals and solid-solution alloys.^{8,25,26,34–36)} The strength of these BCC high-entropy alloys is claimed to be scaled well with a materials parameter to describe the lattice distortion⁶²⁾ as in FCC high-entropy alloys.^62,63) In addition to high strength, retention of such high strength up to high temperatures is a striking feature in the mechanical properties of BCC high-entropy alloys,^25,26) which is not the case for conventional BCC metals and alloys.^79–81) In these conventional BCC alloys, the deformation is controlled by the Peierls mechanism through the motion of screw dislocations and hence the strength decreases with increasing temperature due to thermal activation for dislocation motion.^79–81) Such a striking feature of retention of high strength up to high temperatures is found to occur in the VNbMoTaW quinary equiatomic BCC high-entropy alloy and some of quretrnary and ternary alloys of its subsystems.^25,26) Recently, a model based on edge (instead of screw) dislocation strengthening is proposed to account for retention of high strength up to high temperatures observed for some BCC high-entropy alloys.^82–85) The edge (but not screw) strengthening is in line with the scaling of strength with a materials parameter to describe the lattice distortion⁶²⁾ in BCC high-entropy alloys. One of the drawbacks for these high-strength BCC high-entropy alloys is lack of tensile ductility at low temperatures including room temperature.^25,26) TiZrNbHfTa, another prototypic quinary equiatomic BCC high-entropy alloy, on the other hand, exhibits rich deformability so as to be cold-rolled to a sufficiently high reduction even at room temperature. But, the temperature dependence of strength for TiZrNbHfTa is more or less similar to that for conventional BCC metals and alloys.^34–36) A criterion is proposed based on the average VEC value to predict the ductility of BCC high-entropy alloys; those alloys with VEC lower than 4.5 are ductile while those having VEC above 4.5 is brittle.⁸⁶⁾ This accounts indeed for the difference in tensile ductility observed for TiZrNbHfTa and VNbMoTaW, although the criterion based on VEC lacks a connection to a specific dislocation mechanism. More recently, a criterion that can be connected to specific dislocation and fracture mechanisms is proposed to predict the ductility of BCC high-entropy alloys based on the ratio of stress intensity factor for cleavage fracture to that for dislocation emission.⁸⁷⁾

Most alloys in practical structural applications are rarely single-phased but are usually of multi-phased in order to achieve a good balance of mechanical properties.^59,88–90) The secondary/tertiary phase is incorporated mainly for strengthening and optimization is made for their microstructures via various processing routes. This is also the case for high-entropy alloys for better balanced mechanical properties. Therefore, may recent studies have focused on alloy design^12,91–94) including atomic (defect) structure and phase stability,^95–108) processing,^{11,109–119)} characterization of resultant microstructures^120–127) and mechanical properties,^{13,14,128–138)} and modelling of resultant microstructures^139–142) and mechanical properties,^{16,143–147)} pursuing the achievement of better-balanced mechanical properties. Indeed, some excellent examples can be found for achieving fabulous balanced mechanical properties through utilizing TRIP (transformation-induced plasticity) and TWIP (twinning-induced plasticity) effects by tuning SF energy,^148,149) through tuning heterogeneous (bimodal) microstructures^150,151) and through utilizing secondary/tertiary-phase precipitates.^152,153) These studies have indicated that some high-entropy alloys may find a wide range of structural applications, for example, in bio,^{112–114,123)} shape-memory^91,135) and nuclear^{136,137,145,147)} technologies in the future.

While vast majority of research has devoted to the understanding of peculiar atomic structures and mechanical properties of high-entropy alloys in structural applications, functional properties are emerging subjects of high-entropy alloys, which are rapidly growing recently.⁸⁾ The subjects of scientific and technological interest for functional properties of high-entropy alloys include hydrogen storage,^116,154) catalysis^155–160) and so on. The research area is expanding to include not only metallic systems as mentioned above but also some ceramic (oxide, nitride, carbide and boride) systems in earnest since 2015 when entropy-stabilized oxides with the NaCl structure was discovered.¹⁶¹⁾ The functional properties of interest for high-entropy ceramics span a wider range including thermal and environmental protection, thermoelectricity, water-splitting, catalysis, energy storage and so on. Some excellent review papers are available also for high-entropy ceramics.^162–165)

Acknowledgements

This work was supported by Grant-in-Aids for Scientific Research on Innovative Areas on High Entropy Alloys through the grant number JP18H05450 and JP18H05451, in part by JSPS KAKENHI (grant numbers JP18H05478 and JP19H00824), the Elements Strategy Initiative for Structural Materials (ESISM) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan (grant number JPMXP0112101000), and JST CREST (grant number JPMJCR1994).

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