Physical Metallurgy of High-Entropy Alloys

JOM, Vol. 67, No. 10, 2015 DOI: 10.1007/s11837-015-1583-5 2015 The Minerals, Metals & Materials Society Physical Metallurgy of High-Entropy Alloys JIEN-WEI YEH 1,2 1. Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC. 2. e-mail: jwyeh@mx.nthu.edu.tw Two definitions of high-entropy alloys (HEAs), based on composition and entropy, are reviewed. Four core effects, i.e., high entropy, sluggish diffusion, severe lattice distortion, and cocktail effects, are mentioned to show the uniqueness of HEAs. The current state of physical metallurgy is discussed. As the compositions of HEAs are entirely different from that of conventional alloys, physical metallurgy principles might need to be modified for HEAs. The thermodynamics, kinetics, structure, and properties of HEAs are briefly discussed relating with the four core effects of HEAs. Among these, a severe lattice distortion effect is particularly emphasized because it exerts direct and indirect influences on many aspects of microstructure and properties. Because a constituent phase in HEAs can be regarded as a whole-solute matrix, every lattice site in the matrix has atomic-scale lattice distortion. In such a distorted lattice, point defects, line defects, and planar defects are different from those in conventional matrices in terms of atomic configuration, defect energy, and dynamic behavior. As a result, mechanical and physical properties are significantly influenced by such a distortion. Suitable mechanisms and theories correlating composition, microstructure, and properties for HEAs are required to be built in the future. Only these understandings make it possible to complete the physical metallurgy of the alloy world. INTRODUCTION What is physical metallurgy? Physical metallurgy is a science focusing on the relationships among composition, processing, crystal structure, and microstructure, and physical and mechanical properties. 1,2 Figure 1 shows the straightforward correlation. Composition and processing determine the structure and microstructure, which in turn determine the properties. The relationships in the first stage are thermodynamics, kinetics, and deformation theory. The relationships in the second stage are solidstate physics, strengthening, toughening, fatigue, creep, wear mechanisms, etc. Therefore, an understanding of physical metallurgy is very helpful to control and improve materials. The progress of physical metallurgy has occurred over 100 years and the underlying principles were thought to have become mature. 2 However, the progress is based on the observations on conventional alloys. As compositions of high-entropy alloys (HEAs) are entirely different from that of conventional alloys, physical metallurgy principles might need to be modified for HEAs. TWO DEFINITIONS FOR HEAS Before discussing the physical metallurgy of HEAs, two definitions for HEAs are reviewed to avoid misunderstanding and confusion in mutual communications. The first is composition definition which was proposed in the first HEAs concept article in 2004. 3 It defined HEAs as having at least five major metallic elements, each having an atomic percentage between 5% and 35%. That is, n major 5 5 at:% X i 35 at:%: (1) Thus, no element in HEAs exceeds 35 at.%. Under this definition, a HEA system could have three kinds of compositions. For example, Hf-Nb-Ta-Ti-Zr HEA system has one equimolar composition, numerous nonequimolar compositions, and numerous minor additions of other elements. The reason of this definition is to utilize high mixing entropy, which is referred to as the random-solution state, to enhance the formation of solid-solution phases including disordered multielement solid solutions and partially ordered multielement solid solutions at high temperatures. 2254 (Published online August 19, 2015)

Physical Metallurgy of High-Entropy Alloys 2255 Another alternative definition is entropy definition. It defines HEAs as having configurational entropy larger than 1.5 R at the random-solution state. 4 Configurational entropy per mole for an n- element alloy at the random-solution state (such as liquid-solution state or regular solid-solution state) can be calculated with the summation equation. DS conf ¼ R Xn i¼1 X i ln X i (2) where X i is the mole fraction of the ith component and R is the gas constant. If the composition is equiatomic, then the configurational entropy in terms of gas constant R is as listed in Table I. 4 The configurational entropy increases as the number of elements increases. Because the minimum number of major elements in HEAs is five elements and five-element equiatomic alloys have 1.61 R, 1.5 R is a reasonable lower limit for HEAs. At the same time, those between 1 R and 1.5 R are medium-entropy alloys (MEAs), and those smaller than 1 R are low-entropy alloys (LEAs) were defined. 4 Both definitions have their own convenience in judging a composition, HEA or not HEA. However, it can be seen that the two HEA fields defined by them are not overlapped in some alloy range. Conceptually, this nonoverlapped alloy range is also of high-entropy alloys. In the broad sense, even those alloys close to any of the two definitions could be regarded as HEAs. ROLES OF FOUR CORE EFFECTS OF HEAS IN PHYSICAL METALLURGY Because of their uniqueness, four core effects of HEAs were proposed in 2006. 5 For thermodynamics, they have high-entropy effect. For kinetics, they have sluggish diffusion effect. For structure, they have severe lattice distortion effect. For properties, they have cocktail effect. Figure 2 shows the influence positions of these four core effects in the scheme of physical metallurgy for HEAs. The high-entropy effect should be involved in thermodynamics to determine the equilibrium structure and microstructure. The sluggish diffusion effect affects kinetics in phase transformation. The severe lattice distortion effect is very broad, not only affecting deformation theory and all the relationships among each property, structure, and microstructure but also affecting thermodynamics and kinetics. As for the cocktail effect, it is the overall effect from composition, structure, and microstructure. Therefore, the physical metallurgy principles of HEAs might be different from that of current physical metallurgy because of these influences. In other words, every aspect of physical metallurgy needs to be rechecked through the four core effects of HEAs, and the four core effects are helpful in understanding the physical metallurgy of HEAs. It can be expected that when the physical metallurgy from conventional alloys to HEAs is built, the whole understanding of the alloy world becomes realized. High-Entropy Effect in Physical Metallurgy The high-entropy effect of HEAs can enhance the formation of multielement solid-solution phases especially at high temperatures. This effect is important in reducing the number of phases in HEAs even at low temperatures. Otherwise, their microstructure would become more complex and brittle because many binary or ternary intermetallic compounds would form. 3 6 The entropy effect is often ignored in the phase prediction of conventional alloys. By thermodynamics, the mixing free energy of a phase in an alloy system could be related to mixing enthalpy and mixing entropy with the equation: DG mix ¼ DH mix TDS mix (3) Because conventional alloys are based on one major element, their phases would have small mixing entropies. Thus, DG mix is approximately equal to DH mix. That is: TDS mix DH mix (4) DG mix DH mix (5) Fig. 1. The scheme of physical metallurgy. Thus, the phase formation is mainly the outcome from the competition between the mixing enthalpies of competing phases. The phases with the lowest overall mixing enthalpy would be the equilibrium Table I. Ideal configurational entropies in terms of R for equiatomic alloys with constituent elements up to 13 4 n 1 2 3 4 5 6 7 8 9 10 11 12 13 DS conf 0 0.69 1.1 1.39 1.61 1.79 1.95 2.08 2.2 2.3 2.4 2.49 2.57

2256 Yeh Fig. 2. The areas of physical metallurgy influenced by four core effects of HEAs. phases based on the second law of thermodynamics. However, the mixing entropies of multielement solid-solution phases in HEAs are much higher than that in conventional alloys. They should be considered in the prediction of their equilibrium phases. This is why the equilibrium phases at high temperatures are mainly multielement disordered solid solutions and partially ordered multielement solid solutions. 7 Of course, a single phase, two phases, or more phases might form depending on the competition between phases under the second law of thermodynamics. The phase formation rule in HEAs is an important issue in physical metallurgy and alloy design. It is similar to Hume Rothery rules for binary alloys, which concern the mutual solubility at high temperatures. Although different rules or criteria were proposed, two representative examples are chosen. In 2008, Zhang et al. first proposed the phase-formation rules of HEAs. 8,9 They used mixing enthalpy, mixing entropy, and atomic size difference d for the prediction. Figure 3a suggests their criteria of forming one or more simple solid solutions, and Fig. 3b suggests criteria for forming a single solid solution. That is, (1) Simple solid solutions (including disordered or partially ordered phases) form when satisfying the criteria: 20 DH mix 5kJ=mol; (6) where 12 DS mix 17:5 J=Kmol; (7) d 6:4%; (8) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X n d ¼ 100 c i 1 r i 2 r i¼1 (9) (2) Simple disordered solid solutions will form when: 15 DH mix 5kJ=mol (10) d 4:6%: (11) Fig. 3. The distribution of HEAs and bulk metallic glasses in (a) DS mix DH mix d diagram and (b) DH mix d diagram. Specific areas for solid solutions are highlighted. 8 It is apparent the latter criterion is stricter than the former to obtain a simple disordered solid solution. It should be noted that although Fig. 3b does not use mixing entropy, it already implies the effect of high mixing entropy because those data points including solid solutions, ordered solid solutions, and intermediate phases are HEAs, in which high mixing entropy enhances the solubility of multielements in each type of phases. On the other hand, data points of multicomponent bulk metallic glasses with lower mixing entropy and larger negative mixing enthalpy tend to form intermetallic compounds with low concentrations of other alloying elements after crystallization treatment. Guo et al. proposed another criterion for one or more solid solutions based on Fig. 4. 10,11 It can be seen that their mixing enthalpy criterion is stricter than that proposed by Zhang. That is, solid solutions can form when 11:6 < DH mix < 3:2 kj=mol; (12) d 6:6: (13) It is apparent that different proposed criteria are not consistent with each other. This is due to several reasons: (I) The types of disordered solid solution,

Physical Metallurgy of High-Entropy Alloys 2257 Fig. 4. The distribution of equiatomic and near-equiatomic multicomponent alloys in DH mix d diagram. Solid solutions, intermetallic compounds, and amorphous phases are highlighted by dash-dotted regions. 10,11 ordered solid solutions, or intermetallic compounds are not clearly identified in some references used for the statistical analyses; (II) the database for statistical analyses is still not sufficient; (III) the transformation enthalpy for nonmetallic elements (B, C, N, Si, Ge, and P) is not considered in the calculation of mixing enthalpy; and (IV) the parameters used might not be pertinent to the phase prediction, at least not considering the different mechanisms for forming different types of compounds. Therefore, future research to overcome these drawbacks is needed to build clear-cut rules for phase prediction. As phase diagrams represent the phase equilibria under a set of composition and temperature at ambient atmosphere (not considering pressure and other effects), they are very important for material scientists to understand the equilibrium phases and the tendency toward equilibrium phases. Because the high-entropy effect could enhance the mixing among alloy elements to form body-centered cubic, face-centered cubic (fcc), hexagonal close-packed (hcp) solid solutions, and/or partially ordered solid solutions with binary compound or ternary compound structures, the number of phases in phase diagrams of HEAs is largely reduced. Whether by experimental analyses or by a computer-assisted thermodynamic approach, phase diagrams of HEAs are needed to be built in the future. Sluggish Diffusion Effect in Physical Metallurgy In kinetics, the sluggish diffusion effect of HEAs could lower the diffusion rate of atoms and thus the phase transformation rate in the multielement matrix (or the whole solute matrix) of a phase. The formation of new phases from the old phase requires cooperative diffusion of many different kinds of atoms to accomplish the partitioning of composition. Fig. 5. Temperature dependence of the diffusion coefficients for Co, Cr, Fe, Mn, and Ni obtained from Co-Cr-Fe-Mn-Ni diffusion couple experiments. 12 The diffusion efficiency is expected to be lower than that in traditional alloys based on one major element. Although much evidence suggests the existence of sluggish diffusion effect, direct diffusion study would be more persuasive. The first diffusion study on HEAs was made by using experimental alloys based on near-ideal fcc solid solution CoCr- FeMnNi. 12 In the study, three diffusion couples were prepared to see the pseudo-binary diffusion between Cr and Mn, between Fe and Co, and between Fe and Ni, respectively. Figure 5 shows the plots of log D versus 1/T obtained from the analysis of concentration profiles after diffusion treatment. 12 It can be seen that Mn is the fastest atom, Cr is the second, Fe is the third, Co is the fourth, and Ni is the slowest one. Figure 6 shows the comparison of melting-point normalized activation energies, Q/T m, between fcc HEAs, various stainless alloys, and pure metals. 12 Obviously, HEAs have the highest Q/ T m for each element as indicated by blue color. Four stainless steels are the second as indicated by green color. Three pure metals are the lowest as indicated by red color. It is interesting to see the trend: The higher the entropy, the lower the diffusion rate because stainless steels are MEAs and pure metals are low-entropy ones. Thus, this study confirms the sluggish diffusion effect in this HEA system. As diffusional phase transformation requires cooperative diffusion of different kinds of atoms, sluggish diffusion would reduce the overall transformation rate, and the slowest elements often determine the transformation rate. The diffusion study also proposed the mechanism for sluggish diffusion. 12 Before describing the mechanism, let us observe the local atomic configurations as shown in Fig. 7. Compared with pure

2258 Yeh Fig. 8. Illustration of an atom vacancy pair (A V) and their neighboring atoms in an fcc lattice: A1 7, atoms adjacent to A only, type 1; V1 7, atoms adjacent to V only, type 2; and S1 4, atoms adjacent to both A and V, type 3. 12 Fig. 6. Normalized activation energies of diffusion for Cr, Mn, Fe, Co, and Ni in different matrices. 12 Fig. 9. Schematic diagram showing the fluctuation of lattice potential energy along the diffusion path for an atom in the lattice. Fig. 7. Comparison of the nearest neighbors around an atom among (a) pure metals, (b) binary alloys, and (c) HEAs. metal and binary alloy (Fig. 7a and b), HEAs have a large variety of atomic configuration in their wholesolute matrices (Fig. 7c). It is apparent that such a large variety would make the diffusion of vacancies or atoms not regular in their diffusion path. Considering the local configuration for a pair of atom A and vacancy V in the whole solute matrix, as shown in Fig. 8, when A and V exchange with each other, the binding energies before and after the exchange are different due to different nearest neighboring bondings they encounter. 12 This means atom A would experience fluctuated lattice potential energy along its diffusion path in the lattice. In the diffusion path shown in Fig. 9, there are deep traps marked by circles. Larger fluctuation would cause larger diffusion barrier. This is like a rugged road. The car driven along it would consume more energy than that driven along a smooth road. For a detailed discussion, the reader is referred to Ref. 12. However, this article is based on the alloy system Co-Cr- Fe-Mn-Ni, which exhibits a single fcc structure. 12 Other alloy systems and other crystal structures also need to be studied to check the sluggish diffusion effect. Even better mechanisms for explaining sluggish diffusion through lattice, grain boundary, and dislocation are demanded in physical metallurgy. Severe-Lattice-Distortion Effect in Physical Metallurgy In structure, there is severe lattice distortion in the whole solute matrix because every atom in the lattice site has different kinds of atoms in its first neighboring, and thus suffers lattice distortion. As mentioned previously, the lattice distortion effect is very broad, not only affecting microstructure and properties, but also affecting thermodynamics and kinetics. The following physical metallurgy issues need to be clarified: What are the atomic configuration, and atomicscale stress and strain around vacancy, dislocation, stacking fault, grain boundary, and twin boundary in the distorted lattice? What are the defect energies and behaviors of vacancy, dislocation, grain boundary, and twin boundary in the lattice? What are the diffuse scattering of x-ray beams and phonons resulting from the distorted lattice?

Physical Metallurgy of High-Entropy Alloys 2259 Fig. 10. Schematic diagram showing the various interactions as dislocations, electrons, phonons, and x-ray beam passing through the severely distorted lattice. What are the influences on melting range, lattice constant, Young s modulus, thermal expansion, and electrical and thermal conductivities of a HEA by its distortion energy and mixing enthalpy? What are the influences on nucleation, growth, and coarsening rates of precipitates and grains by the severely distorted lattice? What is the temperate effect on the effect of lattice distortion? Figure 10 shows that the interactions will occur when dislocations, electrons, phonons, and x-ray beams passing through the distorted lattice. Basically, hardness and strength effectively increase because of large solution hardening in the distorted lattice. Electrical and thermal conductivities significantly decrease due to increased electron and phonon scattering. X-ray diffraction (XRD) peak intensity decreases due to increased x-ray diffuse scattering. We also find that all these properties become insensitive to temperature. This is explainable since the thermal vibration amplitude of atoms is relatively small as compared with atom position deviations from lattice sites in the severe lattice distortion. But all these need theoretical models and theory to verify the interactions and outcomes. OBSERVATIONS ON LATTICE DISTORTION EFFECT IN NI-CO-FE-CR-MN ALLOY SERIES To understand more about lattice distortion effect, a series of Ni-Co-Fe-Cr-Mn alloys with a single fcc structure were chosen for experimental study. Besides pure Ni, they included one LEA CoNi, two MEAs CoFeNi and CoCrFeNi, and one HEA CoCrFeMnNi. They were investigated on crystal structure, XRD intensity, mechanical properties, and stacking fault energy (SFE). 13 Figure 11 shows the room-temperature XRD patterns of the alloy series in their as-homogenized state obtained by water quenching after the treatment at 1100 C for 6 h. 13 It reveals that all metals from pure Ni to quinary alloy are simply a single fcc solid-solution phase despite different crystal Fig. 11. X-ray diffraction patterns of the Ni-Co-Fe-Cr-Mn alloy series in the as-homogenized state. 13 structures between elements. Furthermore, full annealing still keeps single fcc phase. This is due to the high-entropy effect, small mixing enthalpy, and atomic size difference as explained with the phase formation rules mentioned in Figs. 3 and 4. In addition, peak intensity in Fig. 11 decreases as the number of elements increases. This demonstrates that the degree of diffuse scattering increases and thus suggests that lattice distortion increases with an increasing number of elements. 13 What are the factors affecting lattice distortion? I propose that not only atomic size difference but also crystal structure difference and bonding strength difference have an effect on lattice distortion. The first is topological distortion related to distortion strain, and x-ray and electron scatterings, the second and third are physicochemical distortions mainly related to scatterings, but relating to distortion strain in a minor way. Thus, different elements have different reasons to cause lattice distortion. As a result, even Co and Ni have the same size and bond strength; there is a large distortion that is mainly attributable to the crystal structure difference: Co is hcp and Ni is fcc. This understanding is very important to explain the trends of diffusion scattering, thermal conductivity, stacking fault energy, and strength. Figure 12 shows the variation of SFE measured by the XRD method, which compares diffraction patterns from stress-relief powders filed from bulk alloy and cold-rolled alloy. 13 We can see SFE decreases largely from Ni to CoNi but then slowly with an increasing number of elements. The reason has been discussed and related to the combined effect of an increased energy level of the distorted matrix and the increased strain energy relief of stacking fault by in situ atom position adjustment because both factors could reduce the SFE. 14 In general, adding more elements in the alloys is suggested to give a larger effect in these two aspects. But it needs theoretical derivation and explanation.

2260 Yeh Fig. 12. Stacking fault energies of Ni, CoNi, CoFeNi, CoCrFeNi, and CoCrFeMnNi alloys. 13 Fig. 14. Stacking fault energies 15 and atomic size differences of nonequiatomic and equiatomic Co-Cr-Fe-Mn-Ni alloys. Fig. 13. Stacking fault energies of equiatomic fcc metals from pure Ni to NiFeCrCoMn measured by XRD methods combined with different simulations. 15 Koch s group used a mechanical alloying method to prepare another set of equiatomic alloy series and derived SFE by XRD methods and different simulations. The results show that SFE decreases with an increased number of elements, and the five-element alloy has the lowest SFE (see Fig. 13). 15 It is noted that there is a larger discrepancy between the SFEs of equiatomic CoCrFeMnNi in Figs. 12 and 13. Hence, further clarification is required. In addition, by varying Ni content and Cr content, Kock s group found that Ni 14 Fe 20 Cr 26 Co 20 Mn 20 alloy has an extremely low SFE 3.5 mj/m 2. 15 If we make the possible correlation between SFEs and atomic size difference (one of lattice distortion factors) calculated with Eq. 9 for these Co-Cr-Fe-Mn- Ni alloys, as shown in Fig. 14, the trend seems to rationalize the combined effect of increased energy level of the distorted matrix and the increased strain energy relief of stacking fault by in situ atom position adjustment, just mentioned above because Fig. 15. Yield strength, ultimate tensile strength, and elongation as a function of number of elements in the alloy series: Ni, CoNi, CoFeNi, CoCrFeNi, and CoCrFeMnNi. 13 a larger atomic size difference could enhance these two factors. Similarly, all these phenomena still require new models and theories to explain. Figure 15 shows yield strength, ultimate strength and elongation as a function of number of elements in the Co-Cr-Fe-Mn-Ni alloy series. 13 As the number of elements increases, all yield strength, ultimate tensile strength, and elongation increase. This suggests solution hardening in fcc metals is superior over many hardening mechanisms because its elongation could be simultaneously increased. This further demonstrates that increased lattice distortion has a positive effect on the mechanical properties. As for strengthening and toughening mechanisms with lattice distortion, it has been proposed that they could be attributable to the decreased SFE, which enhances twining and the strain-hardening rate. But more evidence and detailed theories are required.

Physical Metallurgy of High-Entropy Alloys 2261 investigate the physical metallurgy of HEAs! 17 That means suitable mechanisms, theories, and simulations are waiting for our future works. Only this understanding can make it possible to complete physical metallurgy of the alloy world. Fig. 16. (a) Grain structure, composition analysis, and x-ray diffraction analysis on CoCrFeMnNi. (b) Stress strain curves of CoCrFeMnNi obtained at 77 K, 200 K, and 293 K. 16 In September 2014, a paper on HEAs written by Oak Ridge National Laboratory and Lawrence Berkeley National Laboratory was published in Science. 16 The experimental HEA alloy is CoCr- FeMnNi. The alloy is single fcc and has many annealing twins as shown in Fig. 16a. When conducting the tensile testing from room temperature to 77 K, they found that both strength and ductility of CoCrFeMnNi increase as the temperature decreases (see Fig. 16b). Their explanation is that low SFE enhances mechanical nanotwinning deformation with decreasing temperature, which results in continuous steady strain hardening and enhanced ductility. However, the exact theory is not detailed and thus needs to be established in the future. As mentioned above, the evolution of various properties from conventional alloys to MEAs and to HEAs is very clear, but related mechanisms are still lacking. Beside this, lots of phenomena in the aspects of properties and phase transformation reported for HEAs in last decade (2004 2014) are generally not understood yet. Therefore, it is time to CONCLUSION The four core effects of high-entropy alloys influence many aspects of physical metallurgy. The highentropy effect enhances the formation of solid-solution phases and should be involved in thermodynamics to determine the equilibrium structure and microstructure. The sluggish diffusion effect lowers the diffusion rate and phase transformation rate, thus affecting kinetics in phase transformation. The severe lattice distortion effect not only affects deformation theory and all the relationships among each property, structure, and microstructure but also affects thermodynamics and kinetics. The cocktail effect is the overall effect on properties from composition, structure, and microstructure. It is time to investigate the physical metallurgy of HEAs and thus to understand, control, and improve HEAs more efficiently. Four core effects are helpful for the investigation and understanding. It can be expected that when physical metallurgy from conventional alloys to HEAs is built, the whole understanding of the alloy world can be realized. REFERENCES 1. R.E. Reed-Hill and R. Abbaschian, Physical Metallurgy Principles, 3rd ed. (Boston, MA: PWS Publishing Company, 1994), pp. xiii xv. 2. R.W. Cahn and P, Haasen, eds., Physical Metallurgy, 3rd ed. (New York: Elsevier Science Publishers, 1983), pp. 1 35. 3. J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, and S.Y. Chang, Adv. Eng. Mater. 6, 299 (2004). 4. J.W. Yeh, JOM 65, 1759 (2013). 5. J.W. Yeh, Ann. Chim. Sci. Mater. 31, 633 (2006). 6. Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, and Z.P. Lu, Prog. Mater Sci. 61, 1 (2014). 7. L.J. Santodonato, Y. Zhang, M. Feygenson, C.M. Parish, M.C. Gao, R.J.K. Weber, J.C. Neuefeind, Z. Tang, and P.K. Liaw, Nat. Commun. 6, 5964 (2015). 8. Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, and P.K. Liaw, Adv. Eng. Mater. 10, 534 (2008). 9. Y. Zhang, Z.P. Lu, S.G. Ma, P.K. Liaw, Z. Tang, Y.Q. Cheng, and M.C. Gao, MRS Commun. 4, 57 (2014). 10. S. Guo, Q. Hu, C. Ng, and C.T. Liu, Intermetallics 41, 96 (2013). 11. S. Guo, J. Mater. Sci. Tech. 31, 1223 (2015). 12. K.Y. Tsai, M.H. Tsai, and J.W. Yeh, Acta Mater. 61, 4887 (2013). 13. C. Lee (Master s thesis, National Tsing Hua University, 2013). 14. P.P. Bhattacharjee, G.D. Sathiaraj, M. Zaid, J.R. Gatti, C. Lee, C.W. Tsai, and J.W. Yeh, J. Alloy. Compd. 587, 544 (2014). 15. A.J. Zaddach, C. Niu, C.C. Kock, and D.L. Irving, JOM 65, 1780 (2013). 16. B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, and R.O. Ritchie, Science 345, 1153 (2014). 17. M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, High-Entropy Alloys: Fundamentals and Applications (Cham: Springer, 2015).