Metastable high entropy alloys

In contrast to conventional alloys, which consist of one or two dominant metals with a pinch of other alloying elements, high entropy alloys (HEAs) are a new family of alloys usually made up of five or more metallic elements in approximately equal proportions to maximize the configurational entropy, hence also termed as the multi-principal-element alloys or complex concentrated alloys. Such an innovative design paradigm proposed by Yeh et al. opened a giant composition space for alloy design,^1,2 which fertilizes great opportunities to break the property bottleneck of conventional materials. More importantly, these compositionally complex alloys often tend to form a single-solid solution rather than a multi-phase microstructure, especially in the as-processed condition or at elevated temperatures, since the Gibbs free energy is lowered by the high configuration entropy in the complex concentrated solid solution. As a result, there are severe lattice distortions and sluggish atomic diffusion due to the differences in atomic size and chemistry among the multiple constituents in HEAs, which in turn gives rise to a series of thrilling properties, such as ultrahigh ductility and fracture toughness at cryogenic temperatures,³ unprecedented softening resistance and microstructural stability at high temperatures,⁴ and exceptional irradiation resistance.⁵ The unique features of structure and property render HEAs exciting potential for structural and functional applications, particularly for those cases under extreme conditions, which spark intense research activities in this area, from the fundamental issues, such as phase formation and stability, to the engineering-related problems, such as fabrication, processing, and usage performance. HEAs are currently the focus of intense research in the fields of materials science and condensed matter physics. Although great progress has been made in this rapidly developing area, challenges remain in our fundamental understanding of metastability related phenomena and their underlying mechanisms in HEAs.

From the topological perspective, the intrinsically heavy lattice distortion is intuitively expected to induce the lattice/structural metastability of HEAs, since the presence of local strain/stress fields caused by the lattice distortion surely leads to excess free energy. On the other hand, the distinct difference in chemistry among multiple elements leads to strong chemical interactions and, thus, the propensity to develop appreciable local chemical fluctuation or ordering, making the randomly elemental distribution unfavorable. Therefore, the metastability, both compositional as well as structural, should be inherent in many HEAs. Furthermore, this inherent metastability in HEAs can be designed and exploited for achieving enhanced mechanical and functional properties and forms the basis of this special topic collection. Compositional metastability in HEAs typically leads to decomposition of the complex concentrated solid solution via thermally activated processes (e.g., diffusion), which results in the development of local chemical ordering, the precipitation of second (or more) phases, and the formation of a complex multi-phase microstructure. Structural metastability in HEAs often leads to stress-induced martensitic transformation and/or deformation twinning, which are responsible for transformation induced plasticity (TRIP) and twinning induced plasticity (TWIP) in HEAs, respectively. In fact, metastability engineering via manipulating chemical and structural stability has been proven to be an effective strategy to design high-performance HEAs.^6–8 

This special topic collection on metastable high entropy alloys was proposed to attract much attention on recent advances and to hopefully stimulate and guide further research activities in this rapidly growing area. It includes 42 articles related to the following aspects: (1) theoretical/computational or experimental design of metastable HEAs;^9–20 (2) advanced characterization, such as synchrotron and neutron scattering, three-dimensional atom probe tomography (3D-APT), and transmission electron microscopy (TEM);^21–26 (3) thermodynamics, phase stability, kinetics, and phase transformation mechanisms related to precipitation of second (or more) phases, martensitic transformation, and TRIP/TWIP effects in HEAs; and their influences on mechanical behavior;^{19,21,23,25–38} (4) mechanical behavior, such as deformation, fracture, and micro/nano-mechanics of the metastable HEAs;^37,39–45 and (5) functional properties, such as magnetic, super-elastic, shape memory, and catalytic behaviors, of the metastable HEAs.^46–50 

In addition to adopting the empirical models (e.g., electronic negativity and atomic size difference) for experimentally predicting phase formation in HEAs,^51,52 theoretical calculations and modeling have been extensively used to help design metastable HEAs, among which density function theory (DFT)-based simulations and machine learning (ML) techniques are the most popular tools in dealing with these chemically complex alloys. For example, Zhang et al. investigated the characteristic chemical short-range order (CSRO) and its effects on mechanical properties in the TiZrHfNb alloy by DFT-based Monte Carlo simulations.⁹ Wu et al. proposed an approach combining mean-field DFT with the ML approaches to explore the chemical ordering and phase partitioning in the refractory AlMo_0.5NbTa_0.5TiZr HEA.¹⁰ These studies have important implications in the understanding and design of compositionally metastable HEAs. Sun et al. developed an interpretable extreme gradient boosting (XGBoost) ML model to predict the hardness of Ti–Zr–Nb–Ta HEAs by combining phase diagram calculations (CALPHAD) with experimental data,¹¹ which provides a feasible guidance for the structure-property design of HEAs. Experimentally, Li et al. proposed a grouping strategy via the d-orbit energy level to design eutectic HEAs.¹² Islam et al. developed a dimensionless number defined by global energy density, thermal diffusivity, latent heat of fusion, and mass flow rate in the directed energy deposition (DED) process to predict both macro- and meso-scale features in DED additive manufacturing, which is helpful for the high-throughput design of HEAs.¹⁵ Tsao et al. developed platinum-group-metals-containing HEAs,¹⁷ which exhibited superior resistance against thermal softening.

Advanced characterization methods, particularly the state-of-the-art techniques with high temporal-spatial resolution and in situ testing ability, play an important role in understanding phase stability, defect structures, and the associated structural and functional properties in the metastable HEAs. In this special topic collection, the underlying mechanisms of phase decomposition in the CrMnFeCoNi Cantor alloy were revealed at the atomic scale using 3D-APT.²¹ In situ neutron diffraction measurements were exploited to investigate the stacking fault evolution in the Fe_38.5Mn₂₀Cr₁₅Co₂₀Si₅Cu_1.5 metastable HEA²² and martensitic transformation behaviors of the NiCorCr alloy at the temperature of 140 K.²³ Fang et al. studied the effects of temperature on deformation behavior, particularly dislocation behavior, in CrCoNi-based high entropy alloys by in situ ambient and cryogenic TEM analyses.²⁴ With a combination of TEM and APT analyses, Dasari et al. investigated proton irradiation induced chemical ordering behavior in the Al_0.3CoFeNi HEA and found that high-fluence proton irradiation promotes the transformation of the pristine metastable single face-centered cubic (FCC) solid-solution to a more stable structure with L1₂ precipitates embedded within the FCC solid solution matrix.²⁵ Wei et al. established the compositional dependence of FCC to HCP (hexagonal close-packed) martensitic transformation in FeMnCo medium entropy alloys and revealed the underlying transformation mechanisms by comprehensive studies of in situ electron backscatter diffraction, aberration-corrected scanning transmission electron microscopy, and synchrotron x-ray diffraction experiments.²⁶ 

Phase transformation behaviors and mechanisms and TRIP/TWIP effects have been becoming the most active subjects in the metastable HEA community, as evidenced by the fact that more than half of the articles in this special topic collection focus on phase transformation and its effects on mechanical behavior.^{19,27–30,32–38,42} Fu et al. found that the martensitic transformation can be suppressed due to the antiferromagnetic ordering of Mn under cooling in the dual-phase Fe₅₀Mn₃₀Co₁₀Cr₁₀ TWIP HEA.²⁹ The high-temperature phase stability and evolution of the duplex microstructure of AlMo_0.5NbTa_0.5TiZr refractory HEA during aging were investigated in depth by both experiments and modeling.^32,33 Considerable efforts have been made to improve mechanical properties via manipulating precipitated phases and microstructure in metastable multi-principal element alloys.^{28,30,34,36–38} For instance, via doping interstitial carbon, Cao et al. modulated the fraction of FCC and HCP phases in FeCoCr-based medium-entropy alloys and thereby achieved the significantly improved strength without scarifying ductility.²⁸ Similarly, Kwon et al. increased the yield strength from 600 MPa to 1.07 GPa in the C-doped Co_18.5Cr₁₂Fe₅₅Ni₉Mo_3.5C₂ alloy by modulating the recrystallized microstructure.³⁴ Moreover, the strategy of hetero-deformation-induced (HDI) plasticity by hetero-structuring to induce strengthening and strain hardening was applied for a simultaneous increase in both yield strength and ductility,³⁶ and TRIP effects were used to ductilize metastable refractory HEAs.³⁸ 

Deformation behaviors are commonly accompanied by phase transformation in metastable HEAs. Therefore, it is actually difficult to separate the articles on mechanical behaviors from those on phase transformation. Here, we just highlighted several representative ones to show the trend of research in this area. Stacking fault energy (SFE) play a critical role in deformation modes of metal alloys, which is also the focus of intense research in metastable HEAs.^40,42,44 Li et al. revealed the effect of Si and Ge on the plastic deformation modes in Co–Cr–Fe–Mn–Ni system alloys via calculating the dependence of SFE on Ge and Si.⁴⁰ Zheng et al. studied effects of SFE on the deformation behavior of CoNiCrFeMn high entropy alloys.⁴⁴ They found that the SFE decreased with increasing Co concentration, leading to the continuous stacking fault networks on which multiple plastic deformation carriers including stacking faults, dislocations, twins, and martensitic transformation were activated sequentially. There is increasing research focusing on the influence of SROs on mechanical behaviors in HEAs. Liu et al. found that the SROs facilitated the FCC–BCC–HCP phase transformation and mechanical twining, which results in an enhanced yield strength in NiCoFeCr HEAs.³⁹ In addition, effects of strain rate and temperature on deformation mechanisms were also investigated.^41,45

Functional properties and their applications of HEAs are expected to be the promising research directions in the near future, which are important to extend the applications of HEAs from structural materials to functional ones. In this regard, superelasticity, magnetocaloric effect, conductivity, and catalytic property were reported in this special topic collection. Huang et al. studied the vibrational entropy effect on magnetocaloric properties of Mn-rich HEAs.^46,47 Raghuraman et al. investigated electrical conductivity of several HEAs by first-principles calculations.⁴⁹ HEA catalysts exhibit the overwhelming advantages (e.g., the superior catalytic activity) over conventional one- or two-element based catalysts due to the synergetic effects of different constituents in the multi-principal component HEAs.^48,53 Zhang et al. revealed the orientation-dependent super-elasticity of the Fe_43.76Ni_27.5Co_16.5Al₁₀Ta_2.2B_0.04 metastable HEA.⁵⁰ 

In summary, this Special Topic has collected papers related to the recent advancements in alloy design, advanced characterization, phase transformation, mechanical behavior, and functional properties in metastable HEAs. Based on the recent progress and development trends in this area, the following research directions are expected to be worthy of study in the future: (1) structural and chemical heterogeneities at multiple length scales and their impact on properties, (2) unusual phase transformation pathways and deformation mechanisms and their interplay, (3) influence of complex concentrated solid solutions and ordered precipitates on functional properties and their application, and (4) data-driven alloy development. We hope this collection not only provides the reader an opportunity to appreciate the recent advancements in metastable HEAs, but also stimulates further research activities in this rapidly growing area.

We would like to thank all the authors who have contributed to this Special Topic as well as the journal editors and staff who helped us put this great collection together.