Mechanical and Magnetic Properties of the High-Entropy Alloys for Combinatorial Approaches

: This review summarizes the state of high-entropy alloys and their combinatorial approaches, mainly considering their magnetic applications. Several earlier studies on high-entropy alloy properties, such as magnetic, wear, and corrosion behavior; di ﬀ erent forms, such as thin ﬁlms, nanowires, thermal spray coatings; speciﬁc treatments, such as plasma spraying and inclusion e ﬀ ects; and unique applications, such as welding, are summarized. High-entropy alloy systems that were reported for both their mechanical and magnetic properties are compared through the combination of their Young’s modulus, yield strength, remanent induction, and coercive force. Several potential applications requiring both mechanical and magnetic properties are reported.


Introduction
In 2004, Professor Jien-Wei Yeh reported the concept of high-entropy alloys, which are beyond traditional principal-element alloys, with multiple principal elements [1], and Professor Brian Cantor presented the development of equiatomic multicomponent alloys [2]. The results of both investigators created a new direction for the exploration in metallurgy, which is not conventionally categorized by principal elements. For the past fifteen years, high-entropy alloys with potential use for various applications in different groups of metal elements have been developed. In 2016, Miracle and Senkov categorized high-entropy alloys, multi-principal-element alloys (MPEAs), and equiatomic multicomponent alloys in terms of complex, concentrated alloys (CCAs) [3]. Diao et al. also call them metal buffets [4].
The mechanical properties of different families of high-entropy alloys extend the limits of possible operating-environment temperatures of metallic systems to cryogenic [5] and elevated temperatures [6,7]. These large groups of high-entropy alloys possess several fundamental properties, such as those for the cocktail effects. Moreover, the mechanical metallurgy characteristics of these high-entropy alloys are needed for their systematic development. Starting from basic metallurgical principles, Jones and Ashby have summarized the microstructure-insensitive properties of high-entropy

History of High-Entropy Alloys for Combinatorial Approaches
High-entropy alloys are well-known as structural materials for their excellent mechanical properties [3]. Exceptional mechanical properties have been reported for the Cantor alloys [5], dual-phase high-entropy alloys [30], and intermetallics-strengthened high-entropy alloys [31]. For comparison of the mechanical properties of high-entropy alloys relative to the conventional alloys, Figure 1 presents the yield strength and Young's moduli of a few selected representative metals and several high-entropy alloys.
Crystals 2020, 9, x FOR PEER REVIEW 2 of 18 ductility, fracture toughness, and creep and fatigue strength [8]. These properties depend on the heat treatment, mechanical metallurgy, and the specific alloy compositions. For steels, these investigators have concluded that even when the composition is nearly identical, these microstructure-sensitive properties may yet vary, subject to the history of the heat and mechanical treatments of the metallic system [8]. For high-entropy alloys, microstructure-sensitive behavior can be much more complicated. Moreover, Ding et al. showed that the element-dependent local arrangement of the high-entropy alloys, such as staggered positive and negative strain fields at nanoscale, can change the mechanical properties significantly [9]. The composition-structure-property relationships seem infinite for the design of high-entropy alloys [3,10].
With innovations in manufacturing [11,12], characterization [13][14][15][16], high-throughput examinations [17,18], and computation technology [19][20][21][22], the aforementioned complexity seems to become solvable puzzles for materials scientists [23,24]. Systematic investigations into the highentropy enhancement and interplay with microstructure-sensitive and -insensitive properties are expected to yield combinatorial approaches for functional applications, such as for superconductivity [25], catalysts [26], and magnetics [27,28]. As shown in Borkar et al.'s work [29], it is important to consider the combinatorial approaches, especially for mechanical and magnetic properties. This article reviews the history and advances of high-entropy alloys for future high-throughput combinatorial approaches, with a focus on the mechanical and magnetic behavior.
Even before the first two high-entropy alloys published in 2004 [1,2], Professor Yeh and several other teams had already focused on combinatorial approaches for the high-entropy-alloy research and development, as listed in Table 1, which chronically summarizes the early research into high-entropy-alloy combinatorial approaches through 2004. These results are mainly archived from different groups' dissertations and theses. Several potential applications and research areas have been explored. These applications range from thin films [45][46][47][48], magnetic behavior [47], nanowires [49], thermal spray coatings [50,51], plasma spraying [52], corrosion behavior [53,54], welding [55], inclusion effects [56], and wear properties [57,58]. The latest magnetic applications of high-entropy alloys are summarized in the later sections of this manuscript.

Mechanical Properties of High-Entropy Alloys
High-entropy alloys have been found to have great mechanical properties [3], especially at cryogenic [5] and elevated temperatures [6]. It has been reported that the temperature-dependent mechanical properties can be influenced by both entropy and element effects [42]. The identification of the high-entropy effects is an emerging research area.
For soft materials, the temperature-associated entropy effects for thermoelastic behavior can be found as follows: where f is the total elastic force, f U is the component of the internal energy, f S is the component of the entropic energy, U is the internal energy, S is the entropy of the system, and T is the temperature. The force at a fixed strain increases with temperature, with the force being nearly proportional to the absolute temperature.
For the deoxyribonucleic acids [63], there could be conformational entropy effects, as presented in Equation (2): where F is the force as a function of the extension, x, A is the length of the deoxyribonucleic acid, k is the Boltzmann's constant, T is the temperature, and L is the molecular contour length. The elastic behavior of Actin networks is an example of such a concurrent effect from the entropy-driven and energy-driven elasticities [64,65]. It is interesting to re-think if these entropy effects act on the high-entropy alloys as well.
For general metallic systems, the deformation mechanisms are functions of their strength and ductility; they are categorized in some classic models, as listed below. For example, a homogeneous plastic response with the irreversible flow of strain hardening indicates the dislocation movement, which can be shown as the Hollomon relationship: where σ true is the true stress, K is a material constant, and n is the strain-hardening coefficient. For a heterogeneous plastic response, the phenomenon could be from twinning and/or a vacancy interaction with dislocations. For a heterogeneous plastic and homogeneous plastic response, there could be dislocation-solute atom interactions showing upper and lower yield strengths as a Lüder band. Specifically, yield strength (σ y ) is a combination of the frictional stress (σ f r ), the effects of solid solutions (σ ss ), dislocation density (σ ρ ), precipitate hardening (σ precipitate ), and grain boundaries (σ gb ), as summarized in the following equation: As mentioned above, the yield and tensile strength, ductility, fracture toughness, and creep and fatigue strengths are microstructure-sensitive mechanical properties [8].
For high-entropy alloys, a major characteristic is its low stacking fault energies (SFE) [21]. Huang et al. examined the SFE as a function of temperature via ab initio calculations [20]. Their models consider chemical, magnetic, and strain contributions. The local structural energies, magnetic moments, and elastic moduli predicted deformation twins and face-centered-cubic to hexagonal-phase transformation under cryogenic conditions [20]. The twinning results agree with earlier experimental results [5]. Their predictions for phase transformation have been experimentally validated [15,[66][67][68].
Niu et al.'s experimental and simulation results depict the possible paths for the aforementioned microstructure-dependent phase-transformation mechanisms [22]. They reveal the interactions between magnetic and mechanical properties of CrCoNi and other equiatomic ternary derivatives of CrMnFeCoNi. Niu et al. demonstrated that magnetically frustrated Mn eliminates the Face-Centered Cubic (FCC)-Hexagonal Closest Packed (HCP) energy difference as an important element effect for high-entropy alloys [22].

Combinatorial Approaches for Magnetic Features
Nowadays, most of the electronics and computational devices facilitate magnetism and magnetic materials as the smart functional materials [71]. The excellent mechanical properties of high-entropy alloys can improve the reliability of these modern devices [72][73][74].
The magnetic materials are classified as either soft or hard from their magnetization hysteresis characteristics.
Ferromagnetic and ferrimagnetic materials contain specific elements that have large magnetic moments. The high-entropy alloys containing these elements and their combinatorial properties focusing on magnetic and mechanical properties are summarized in Table 2.
Here, the magnetic properties of particular concern are the remanent induction (T) and coercive field (A/m). Figure 4 presents a comparison between several commercial magnets and selected high-entropy alloys. The commercial soft and hard magnets are shown in the regions marked with solid lines. The high-entropy alloys are presented in the regions marked with symbols.
The two most important characteristics for applications of soft and hard magnetic materials are the coercivity and what is termed as the energy product, designated as BH max . Soft magnets have low coercive fields and narrow hysteresis loops. Hard magnets have much higher coercive fields. Larger maximum energy products (BH max , unit J m 3 ) are desirable for hard magnets. The maximum energy product depends on the shape of the B-H curve. However, for a given shape, it increases with the product of B R × H C (the diagonals on Figure 4). The remanent induction, B R , is the induction that remains when the field, H, is removed. The coercive field, H c , is the field required to fully magnetize and demagnetize the material. Microstructure and mechanical property of as-cast, -homogenized, and -deformed AlxCoCrFeNi (0 ≤ x ≤ 2) high-entropy alloys [35] AlCoCrCuFeNi Yield Strength

2012
Tensile properties of an AlCrCuNiFeCo high-entropy alloy in as-cast and wrought conditions [36] 2013 Phase composition and superplastic behavior of a wrought AlCoCrCuFeNi high-entropy alloy [37] Young's Modulus 2012 Effect of elemental interaction on microstructure and mechanical properties of FeCoNiCuAl alloys [38] 2008 Effects of Mn, Ti and V on the microstructure and properties of AlCrFeCoNiCu high entropy alloy [39]

Mechanical and Magnetic Maps for the Applications of High-Entropy Alloys
Magnetic materials are important in several areas, such as information storage, superconductivity, electrical-power transmission, high-speed switching, high-speed-signal transmission for computation, and high-speed magnetically-levitated trains. Many of these applications require excellent mechanical properties across various operating temperatures, areas where high-entropy alloys show great potential. For example, there are both active and passive electromagnetic devices for vibration damping and isolation, and the selection criteria for materials and for these devices include the coercivity, remanence, relative permeability, and saturation field [83].
Here, we compare different combinations of mechanical and magnetic properties, and we select several potential applications and their featured combinations of properties. Magnets embedded in the discs for regenerative braking induces a current and allows power to be drawn to the electric motor that drives the wheels. There are several material requirements for this application, such as the density, thermal conductivity, thermal expansion, hardness, Poisson's ratio, and Young's modulus [84], while the maximum energy product (BH max , units J m 3 ) is also important. For these applications, Young's modulus-coercive force and Young's modulus-remanent induction relationships are summarized in Figure 5; Figure 6, respectively.

Discussion and Future Perspectives
As shown by the blue arrow in Figure 2, all of the hard magnets made from commercial alloys have products of the remanent induction (BR) and coercive field (Hc) greater than those of the highentropy alloys. Similarly, as shown by the red arrow, commercial alloys have better soft-magnet performance, with small products of × , as presented by the diagonals in Figure 2.  (Data taken from [5,27,29,33,43,44,72,76,77,79,80]). The data is from the CES EduPack 2009, Granta Design, Limited, Cambridge, UK, 2009.

Discussion and Future Perspectives
As shown by the blue arrow in Figure 2, all of the hard magnets made from commercial alloys have products of the remanent induction (BR) and coercive field (Hc) greater than those of the highentropy alloys. Similarly, as shown by the red arrow, commercial alloys have better soft-magnet performance, with small products of × , as presented by the diagonals in Figure 2.  [5,27,29,33,43,44,72,76,77,79,80]

Br
Edition I Here, the magnetic properties of particular concern are the remanent induction (T) and coercive field (A/m). Figure 2 presents a comparison between several commercial magnets and selected highentropy alloys. The commercial soft and hard magnets are shown in the regions marked with solid lines. The high-entropy alloys are presented in the regions marked with symbols. Larger maximum energy products ( , unit ) are desirable for hard magnets. The maximum energy product depends on the shape of the B-H curve. However, for a given shape, it increases with the product of × (the diagonals on Figure 2). The remanent induction, BR, is the induction that  [27,29,43,[75][76][77]81,82] remains when the field, H, is removed. The coercive field, Hc, is the field required to fully magnetize and demagnetize the material.

Mechanical and Magnetic Maps for the Applications of High-Entropy Alloys
Magnetic materials are important in several areas, such as information storage, superconductivity, electrical-power transmission, high-speed switching, high-speed-signal transmission for computation, and high-speed magnetically-levitated trains. Many of these applications require excellent mechanical properties across various operating temperatures, areas where high-entropy alloys show great potential. For example, there are both active and passive electromagnetic devices for vibration damping and isolation, and the selection criteria for materials and for these devices include the coercivity, remanence, relative permeability, and saturation field [83].
Here, we compare different combinations of mechanical and magnetic properties, and we select several potential applications and their featured combinations of properties. Magnets embedded in the discs for regenerative braking induces a current and allows power to be drawn to the electric motor that drives the wheels. There are several material requirements for this application, such as the density, thermal conductivity, thermal expansion, hardness, Poisson's ratio, and Young's modulus [84], while the maximum energy product ( , units ) is also important. For these applications, Young's modulus-coercive force and Young's modulus-remanent induction relationships are summarized in Figure 3; Figure 4, respectively.   For magnetic applications requiring high strength, such as magnetic windings, a higher strength is needed before mechanical failure. Furthermore, low heat generation during operation while maximizing the magnetic field is required. For these multiple constraints [85], high-entropy alloys also show great potential [86]. Figures 5 and 6 exhibit the yield strength-coercive force and yield strength-remanent induction relationships, respectively.  [27,29,34,35,40,43,75,76,78,80]

Discussion and Future Perspectives
As shown by the blue arrow in Figure 4, all of the hard magnets made from commercial alloys have products of the remanent induction (B R ) and coercive field (H c ) greater than those of the high-entropy alloys. Similarly, as shown by the red arrow, commercial alloys have better soft-magnet performance, with small products of B R × H C , as presented by the diagonals in Figure 4.
However, when applications require a specific function needing more than the optimization of a single property, high-entropy alloys present combinatorial advantages since the alloys are much more diverse, as demonstrated in Figure 5, Figure 6, Figure 2, Figure 3, as compared with the narrow regions shown in Figure 4.
Specific functional applications need different combinatorial advantages. For example, to improve the thermoelastic-type shape memory, metallic systems require slow diffusion and resistance to plastic deformation. Moreover, it is important for shape-memory alloys to accumulate more reversible martensitic deformation. Firstov et al. [87] reported TiZrHfCoNiCu high-entropy alloys for the shape-memory effect. The mechanisms of the reversible-deformation-induced martensitic transformation of the Al 0.6 CoCrFeNi high-entropy alloy were revealed by in situ synchrotron X-ray measurements [88].
Another example is the development of high-entropy alloys for thermoelectric applications. Specifically, to satisfy the thermoelectric functions, one criterion for selecting the material is the low thermal conductivity for improving the Seebeck coefficient. Fan et al. showed that the severe lattice distortion of high-entropy alloys has strong potential in this regard [89].
Finally, the developments of the additive manufacturing enable the metals for better performance [90]. The additive manufacturing brings high degrees of geometrical freedom to the production of alloy components [91]. The advantages of the additive manufacturing, such as customized geometry [92], fast cooling for intermediate phase effects [93], mixing of metallics-ceramics powders [94,95], and anisotropic effects [96], are well known. For additive manufacturing, high-entropy alloys also show great potentials [97][98][99][100].

Conclusions
This article explores the state of high-entropy alloys and their combinatorial approaches mainly for magnetic applications. Several earlier high-entropy-alloy studies in the areas of thin film, magnetic behavior, nanowires, thermal-spray coating, plasma spraying, corrosion behavior, welding, inclusion effects, and wear properties are summarized. High-entropy alloy systems that were reported for both their mechanical and magnetic properties were compared via the combination of their Young's modulus, yield strength, remanent induction, and coercive force. Several potential applications requiring both mechanical and magnetic properties were reported. The objective of this article was to review the reported mechanical and magnetic properties of high-entropy alloys for more combinatorial advances. Several advanced measurements using neutron and synchrotron were also included, along with examples of machine learning used for the design of high-entropy alloys.