Deformation Mechanisms and Processing Maps for High Entropy Alloys (Presentation of Processing Maps in Terms of Zener–Hollomon Parameter): Review

In this review paper, the hot compressive deformation mechanisms and processing maps of high-entropy alloys (HEAs) with different chemical compositions and crystal structures are analyzed. The stress exponent (n1) values measured from the series of compression tests for the HEAs performed at different temperatures and strain rates are distributed between 3 and 35, and they are most populated between 3 and 7. Power law breakdown (PLB) is found to typically occur at T/Tm ≤ 0.6 (where T is the testing temperature and Tm is the melting temperature). In AlxCrMnFeCoNi (x = 0–1) and AlxCrFeCoNi (x = 0–1) HEAs, n1 tends to decrease as the concentration of Al increases, suggesting that Al acts as a solute atom that exerts a drag force on dislocation slip motion at high temperatures. The values of activation energy for plastic flow (Qc) for the HEAs are most populated in the range between 300 and 400 kJ/mol. These values are close to the activation energy of the tracer diffusivity of elements in the HEAs ranging between 240 and 408 kJ/mol. The power dissipation efficiency η of the HEAs is shown to follow a single equation, which is uniquely related to n1. Flow instability for the HEAs is shown to occur near n1 = 7, implying that the onset of flow instability occurs at the transition from power law creep to PLB. Processing maps for the HEAs are demonstrated to be represented by plotting η as a function of the Zener–Hollomon parameter (Z = expQcRT, where R is the gas constant). Flow stability prevails at Z ≤ 1012 s−1, while flow instability does at Z ≥ 3 × 1014 s−1.


Introduction
High-entropy alloys (HEAs) are a new family of solid-solution alloys made of four or more principal alloying elements alloyed in equiatomic or near-equiatomic concentrations (with each constituent element having a concentration from 5 to 35 atomic percent (at.%)) [1,2]. The first approach for designing an HEA was to obtain a single-phase solid solution by maximizing the mixing configurational entropy, but later, new design approaches involving multiple phases and/or intermetallics were explored [1][2][3].
Thermomechanical working at high temperatures is necessary not only to form and shape materials into components but also to produce the desired microstructures and properties of products [4,5]. For this reason, the high-temperature deformation mechanisms and hot workability of HEAs have been studied . Finding the constitutive equations that mathematically depict the material response to the applied hot deformation conditions can be useful in predicting the flow stress or strain rates and identifying the rate-determining deformation mechanisms at different temperatures/strain rates and microstructural parameters. Characterization of hot workability using a processing map is important for the optimization of hot working conditions of materials and fabrication of defect-free components [101]. If a material is processed under unstable flow conditions, adiabatic shear banding or cracking can occur, and if a material is processed under optimal conditions, superior microstructure and mechanical properties can be obtained.
In this work, we have reviewed and analyzed the hot compression data of HEAs available in the literature to elucidate their deformation mechanisms and optimal hot working conditions.

History and Materials
The first paper reporting the hot compression behavior of HEAs was available in 2011, and the first studied HEAs were Nb 25 Mo 25 Ta 25 W 25 and V 20 Nb 20 Mo 20 Ta 20 W 20 alloys [6], where the microstructural change during hot compression at temperatures of 1073-1873 K and at a strain rate of 10 −3 s −1 was examined. The papers published in the literature from 2011 to the present can be categorized into three groups (Figure 1a). The first group of papers reports the hot compressive deformation data of the HEAs in the limited temperature and strain rate range. The second group of papers reports the hot compression data of the HEAs in a wide range of temperature and strain rates, but processing maps are not constructed. The third group of papers reports the hot compression data as well as the processing maps of the HEAs. The number of publications increases almost exponentially with time, indicating that attention to this academic and engineering field has rapidly increased.
Materials 2023, 16, x FOR PEER REVIEW 2 of of defect-free components [101]. If a material is processed under unstable flow conditio adiabatic shear banding or cracking can occur, and if a material is processed under op mal conditions, superior microstructure and mechanical properties can be obtained. In this work, we have reviewed and analyzed the hot compression data of HE available in the literature to elucidate their deformation mechanisms and optimal h working conditions.

History and Materials
The first paper reporting the hot compression behavior of HEAs was available 2011, and the first studied HEAs were Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 alloys [ where the microstructural change during hot compression at temperatures of 1073-18 K and at a strain rate of 10 −3 s −1 was examined. The papers published in the literature fro 2011 to the present can be categorized into three groups (Figure 1a). The first group papers reports the hot compressive deformation data of the HEAs in the limited temp ature and strain rate range. The second group of papers reports the hot compression d of the HEAs in a wide range of temperature and strain rates, but processing maps are n constructed. The third group of papers reports the hot compression data as well as t processing maps of the HEAs. The number of publications increases almost exponentia with time, indicating that attention to this academic and engineering field has rapidly creased. The f group of papers includes papers that report hot compressive deformation of the HEAs in the limi temperature and strain rate range, the second group of papers provides hot compression data of HEAs over a wide range of temperature and strain rates, but processing maps are not construct and the third group of papers provides hot compression data (over a wide range of temperat and strain rates) as well as processing maps of the HEAs. (b) Three material groups of HEA ma rials studied for hot compression, which are classified by their chemical compositions. (c) HEA m terials studied for hot compression, which are classified by phases (crystal structures).
The HEA materials studied by hot compression can be classified into three grou ( Figure 1b). The first material group is the Cr-Mn-Fe-Co-Ni series HEAs containing Sn, Zr, Sn, C, and N [9,20,23,27,34,37,38,42,45,60,[62][63][64]; the second material group is t Cr-Fe-Co-Ni series HEAs containing Zr, Ta, Nb, Mo, Cu, C, and [13,25,51,53,72,84,92,96,97,100]; and the third material group is the other compositi HEAs, including the materials of TiVNbMoTa, Mn5Co25Fe25Ni25Ti20, MnFeCoNiCu, e [8,11,12,22,29,32,33,40,41,47,52,56,68,71,74,79,91,93,95,99]. Information regarding t chemical compositions of the HEAs, grain sizes, crystal structure, types of phases, te perature and strain rate ranges for hot compression tests are provided in Table 1. Most the HEAs studied for hot compression are as-cast or heat-treated (homogenized) cast w 11   The first group of papers includes papers that report hot compressive deformation of the HEAs in the limited temperature and strain rate range, the second group of papers provides hot compression data of the HEAs over a wide range of temperature and strain rates, but processing maps are not constructed, and the third group of papers provides hot compression data (over a wide range of temperature and strain rates) as well as processing maps of the HEAs. (b) Three material groups of HEA materials studied for hot compression, which are classified by their chemical compositions. (c) HEA materials studied for hot compression, which are classified by phases (crystal structures).

Deformation Mechanisms
The raw data (true stress-true strain curves) in the second and third groups of papers, where a series of hot compression tests were systematically carried out over wide temperature and strain rate ranges, were digitally extracted from the published papers using a software. For example, the true stress-true strain curves for Al 0.7 CrMnFeCoNi HEA [62] at different temperatures and different strain rates are shown in Figure 2a-d.
The hyperbolic sine Garofalo equation has been widely used to describe the steadystate relationship between the flow stress, temperature, and strain rate ( . ε) over a wide range of temperatures and strain rates where power law creep and power law breakdown (PLB) govern plastic flow [4,104], which is expressed as: where A and α are the experimentally determined material constants, n is the stress exponent, and Q c is the activation energy for plastic flow. The hyperbolic sine function is mathematically reduced to the equation describing power law creep at low stresses (Equation (2)) and to the equation describing power law breakdown (PLB) at high stresses (Equation (3)): . .
5 of 20 where A 1 , A 2 , and β are the material constants and n 1 is the stress exponent, which is ideally equal to n, but can be different). The constants α in Equation (1), n 1 in Equation (2), and β in Equation (3) can be related by β = αn 1 [4,104]. The hyperbolic sine Garofalo equation has been widely used to describe the stea state relationship between the flow stress, temperature, and strain rate ( ) over a w range of temperatures and strain rates where power law creep and power law breakdo (PLB) govern plastic flow [4,104], which is expressed as: = sinh( ) exp − where A and α are the experimentally determined material constants, n is the stress ponent, and Qc is the activation energy for plastic flow. The hyperbolic sine function mathematically reduced to the equation describing power law creep at low stresses (Eq tion (2)) and to the equation describing power law breakdown (PLB) at high stres (Equation (3)): , and β are the material constants and n1 is the stress exponent, which ideally equal to n, but can be different). The constants α in Equation (1), n1 in Equat (2), and β in Equation (3) can be related by β = αn1 [4,104].  ε − log(sinh(α σ)) curves represent the n value at each temperature. Figure 3d shows the plot of log(sinh(α σ)) − 1000 T , of which the slope (= ∂ ln(sinh(α σ)) ∂( 1000 T ) . ε ) represents the s value at each strain rate. The Q c value can be calculated by using the average (N) of the n values measured at different temperatures and the average (S) of the s values measured at different strain rates as follows: It is well-known that a value of n 1 represents a specific deformation mechanism; Haper-Dorn creep and diffusional creep are associated with n 1 = 1 [105][106][107][108], grain boundary sliding is associated with n 1 = 2 [109,110], solute drag creep is associated with n 1 = 3 [111], dislocation climb creep is associated with 5-7 [112,113], and power law breakdown occurs when n 1 > 7 [4]. Jeong and Kim [62] analyzed the tensile, compressive, and creep data of CrMnFeCoNi and Al 0.5 CrMnFeCoNi HEAs with various grain sizes and proposed the constitutive equations that can quantitatively predict their flow stresses as a function of strain rate, temperature, and grain size ( Table 2). Figure 4a [114], where c i is the atomic percentage of the ith component and (T m ) i is the melting point of the ith component of the alloy. The plots in Figure 4a,b show that the hot compression tests for the HEAs have been conducted in the temperature range between 873 K and 1573 K, corresponding to the T/T m range between 0.4 and 0.9. The n 1 value is distributed between 3 and 35, and the n 1 values are most populated between 3 and 7. As T and T/T m decrease, n 1 tends to increase, and at T/T m ≤ 0.6, the number of the data associated with n 1 ≥ 7 sharply increases. In the T/T m range between 0.6 and 0.9, the fraction of the data associated with n 1 ≥ 7 is 0.17, while in the T/T m range between 0.4 and 0.6, the fraction of n 1 ≥ 7 is 0.66. This result indicates that PLB dominates plastic flow below 0.6 T/T m , while power law creep dominates plastic flow above 0.6 T/T m . It should be noted that the HEAs that show the lowest n 1 of~3 are the Al x CoCrFeNi and Al x CoCrFeMnNi HEAs with BCC or BCC + FCC (minor) phases, containing an Al element. Figure 4c shows that the n values of the HEAs are slightly smaller than their n 1 values. They mostly range between 2.5 and 5. The n tends to increase as T/T m decreases, but it is not as sensitive as n 1 to T/T m variation. It is well-known that a value of n1 represents a specific deformation mechanis Haper-Dorn creep and diffusional creep are associated with n1 = 1 [105][106][107][108], grain boun ary sliding is associated with n1 = 2 [109,110], solute drag creep is associated with n1 [111], dislocation climb creep is associated with 5-7 [113,112], and power law breakdow occurs when n1 > 7 [4]. Jeong and Kim [62] analyzed the tensile, compressive, and cre data of CrMnFeCoNi and Al0.5CrMnFeCoNi HEAs with various grain sizes and propos the constitutive equations that can quantitatively predict their flow stresses as a functi of strain rate, temperature, and grain size ( Table 2). Figure 4a  Diffusional creep Nabarro-Herring [105,106] .
Grain boundary sliding (GBS) Lattice-diffusioncontrolled [109] . ε 3 = k 3 D L /d 2 (σ/E) 2 6.4 × 10 9 3.1 × 10 8 6.7 × 10 8 Pipe-diffusion-controlled [110] . 4 3.2 × 10 11 1.6 × 10 10 3.4 × 10 10 Grain-boundarydiffusion-controlled [109] . 2 5.6 × 10 8 1.9 × 10 7 5.9 × 10 7 Slip creep Harper-Dorn [108] . ε 6 = k 6 D L /b 2 Eb 3 /kT (σ/E) 1.7 × 10 −11 1.7 × 10 −11 1.7 × 10 −11 Lattice-diffusion-controlled dislocation climb creep [112] . ε 7 = k 7 D L /b 2 (σ/E) 5 1 × 10 11 2.6 × 10 9 1.5 × 10 9 Pipe-diffusion-controlled dislocation climb creep [112] . 7 5 × 10 12 1.1 × 10 9 3.9 × 10 9 Solute drag creep [111] .    ε − log σ curves for the Al x CrMnFeCoNi (x = 0-1) [9,27,34,42,63] and Al x CrFeCoNi (x = 0-1) HEAs [13,25,51,53,72,84,92,96] at a given temperature of 1173 K. The n 1 value decreases from 5 to~3 as x increases. This result indicates that as the amount of BCC phase (rich with Al) increases, the characteristics of viscous glide creep associated with n 1~3 become more pronounced. Jeong and Kim [42] analyzed the deformation behavior of the AlCrMnFeCoNi HEA and found that aluminum, which is largest in size among the constituent elements [42], acts as a solute that causes solute drag creep and showed that the solute drag creep model proposed by Hong and Weertman [111] for conventional metals can quantitatively explain the deformation behavior of the AlCrMnFeCoNi HEA with reasonable assumptions on the diffusivity of Al in the HEA. From the plots in Figure 5a,b, it should also be noted that flow stress tends to decrease the added amount of Al increases especially at low strain rates, indicating that the BCC phase deforming under solute drag creep is weaker than the FCC phase deforming under dislocation climb creep. man [111] for conventional metals can quantitatively explain the deformation behavior of the AlCrMnFeCoNi HEA with reasonable assumptions on the diffusivity of Al in the HEA. From the plots in Figure 5a,b, it should also be noted that flow stress tends to decrease the added amount of Al increases especially at low strain rates, indicating that the BCC phase deforming under solute drag creep is weaker than the FCC phase deforming under dislocation climb creep. Deformation mechanism maps represent the dominant deformation mechanism for a given metallic material under different conditions. Figure 6a,b shows the deformation mechanism maps as a function of strain rate (10 −5 to 10 s −1 ) and temperature (873 and 1573 K) at a given (coarse) grain size of 100 μm for CoCrFeMnNi and Al0.5CoCrFeMnNi. On the maps, the data of the CoCrFeMnNi and Al0.5CoCrFeMnNi HEAs are loaded. For the CoCrFeMnNi HEA, at high temperatures, dislocation climb creep controlled by lattice diffusivity (DL) governs plastic flow, but when the temperature is low, the rate-controlling mechanism changes to dislocation climb creep controlled by Dp (or PLB). As the strain rate increases, the region associated with Dp-controlled dislocation climb creep (or PLB) expands to a higher temperature. For the Al0.5CoCrFeMnNi, solute drag creep appears in the bottom right corner of the map. Jeong and Kim [62] showed that when the grain size is sufficiently small, grain boundary sliding mechanism can play a more important role than solute drag creep in the Al0.5CoCrFeMnNi HEA. Deformation mechanism maps represent the dominant deformation mechanism for a given metallic material under different conditions. Figure 6a,b shows the deformation mechanism maps as a function of strain rate (10 −5 to 10 s −1 ) and temperature (873 and 1573 K) at a given (coarse) grain size of 100 µm for CoCrFeMnNi and Al 0.5 CoCrFeMnNi. On the maps, the data of the CoCrFeMnNi and Al 0.5 CoCrFeMnNi HEAs are loaded. For the CoCrFeMnNi HEA, at high temperatures, dislocation climb creep controlled by lattice diffusivity (D L ) governs plastic flow, but when the temperature is low, the rate-controlling mechanism changes to dislocation climb creep controlled by D p (or PLB). As the strain rate increases, the region associated with D p -controlled dislocation climb creep (or PLB) expands to a higher temperature. For the Al 0.5 CoCrFeMnNi, solute drag creep appears in the bottom right corner of the map. Jeong and Kim [62] showed that when the grain size is sufficiently small, grain boundary sliding mechanism can play a more important role than solute drag creep in the Al 0.5 CoCrFeMnNi HEA. Figure 7a shows the Q c values of HEAs calculated using Equation (4). The Q c value is in the range between 150 and 600 kJ/mol, and the data distribution is most populated in the range between 300 and 400 kJ/mol. The activation energy of the tracer diffusivity of elements in the HEAs ranges between 240 and 408 kJ/mol [115,116], implying that the activation energy of plastic flow for the HEA is related to the atomic diffusivity of elements constituting the HEAs. Figure 7b shows the relation between n 1 and Q c for the HEAs. A smaller Q c is obtained at smaller n 1 , and this is more apparent near n 1~3 , where solute drag creep governs the deformation mechanism. It is worthwhile to note that the activation energy for the solute diffusion (Q solute ) of magnesium in aluminum (136 kJ mol −1 ) is lower than the activation energy for self-diffusion in pure aluminum (142 kJ/mol) [117].  Figure 7a shows the Qc values of HEAs calculated using Equation (4). The Qc value is in the range between 150 and 600 kJ/mol, and the data distribution is most populated in the range between 300 and 400 kJ/mol. The activation energy of the tracer diffusivity of elements in the HEAs ranges between 240 and 408 kJ/mol [115,116], implying that the activation energy of plastic flow for the HEA is related to the atomic diffusivity of elements constituting the HEAs. Figure 7b shows the relation between n1 and Qc for the HEAs. A smaller Qc is obtained at smaller n1, and this is more apparent near n1~3, where solute drag creep governs the deformation mechanism. It is worthwhile to note that the activation energy for the solute diffusion (Qsolute) of magnesium in aluminum (136 kJ mol −1 ) is lower than the activation energy for self-diffusion in pure aluminum (142 kJ/mol) [117].  (a) (b) Figure 6. Deformation mechanism maps as a function of strain rate and temperature at a given grain size of 100 μm for (a) CoCrFeMnNi and (b) Al0.5CoCrFeMnNi. Reproduced/modified with permission from [62], Elsevier. Figure 7a shows the Qc values of HEAs calculated using Equation (4). The Qc value is in the range between 150 and 600 kJ/mol, and the data distribution is most populated in the range between 300 and 400 kJ/mol. The activation energy of the tracer diffusivity of elements in the HEAs ranges between 240 and 408 kJ/mol [115,116], implying that the activation energy of plastic flow for the HEA is related to the atomic diffusivity of elements constituting the HEAs. Figure 7b shows the relation between n1 and Qc for the HEAs. A smaller Qc is obtained at smaller n1, and this is more apparent near n1~3, where solute drag creep governs the deformation mechanism. It is worthwhile to note that the activation energy for the solute diffusion (Qsolute) of magnesium in aluminum (136 kJ mol −1 ) is lower than the activation energy for self-diffusion in pure aluminum (142 kJ/mol) [117].  (4) and (b) the relation between n 1 and Q c for the HEAs. The activation energy (Q * L ) of tracer diffusivity of elements in the Al x CoCrFeMnNi and Al x CoCrFeNi HEAs ranges between 240 and 408 kJ/mol (shaded area by blue color): Q * L = 323 ± 5 kJ/mol for Cr, Q * L = 303 ± 3 kJ/mol for Fe, Q * L = 240 ± 20 kJ/mol for Co, Q * L = 253 ± 8 kJ/mol for Ni in CrFeCoNi, Q * L = 313 ± 13 kJ/mol for Cr, Q * L = 272 ± 13 kJ/mol for Mn, Q * L = 309 ± 11 kJ/mol for Fe, Q * L = 270 ± 22 kJ/mol for Co, and Q * L = 304 ± 9 kJ/mol for Ni in CrMnFeCoNi [115]. Q * L = 263 kJ/mol for Al, Q * L = 288 kJ/mol for Cr, Q * L = 315 kJ/mol for Fe, Q * L = 258 kJ/mol for Co, Q *

Processing Maps
A processing map, which is useful in finding the optimal condition for hot forging or extrusion, is composed of a power dissipation map and a flow instability map. According to Prasad et al. [101], the total power, P, absorbed in a material is divided into the power dissipation content (G), which represents the power dissipated by plastic deformation giving rise to a temperature increase in the workpiece and the power dissipation co-content (J), which represents the power dissipated by a change in its microstructure, such as dynamic recovery and dynamic recrystallization [101].
The efficiency of power dissipation, η, which represents the power dissipation efficiency due to a change in microstructure during plastic flow, is defined as [101]: where J max is the maximum J value (=P/2). The strain rate sensitivity, m, which is equal to 1/n 1 , can be calculated by: When m is assumed to be constant over the investigated strain rate range (as assumed by Prasad et al. [101]), η = 2m m+1 , but when m is not constant (as considered by Murty et al. [118]), η can be directly determined from Equation (6) by calculating . ε 0 σd . ε through the numerical integration procedure, using Equation (8): In drawing the flow instability map, Ziegler's plastic flow theory is used, and according to Murty et al. [119] (when m is not a constant), When ξ is negative, deformation in the material is predicted to be unstable, such that localized flow, adiabatic shear banding, or cracking can take place.
Kim and Jeong [120] suggested an empirical equation for η by analyzing the behavior of η values of many metals calculated by following the numerical method proposed by Murty (Equation (8)) as a function of n 1 : By using this equation, the η value can be easily obtained once n 1 is known without numerically solving Equation (8). Kim and Jeong [121] also presented a simple form of the flow instability criterion based on the observation that unstable flow occurs in many metals when n 1 is larger than 7 (i.e. when PLB governs plastic flow): ξ = 7 − n 1 < 0 or η < 0.285 (11) Unlike in the procedure for determining n 1 for calculating Q c (Figure 3a), where a linear fitting is applied to the data in the plot of log . ε − log σ, the n 1 value as a function of strain rate, temperature, and strain, which is necessary for constructing processing maps, has often been determined using a third-or fourth-order polynomial fitting to the data in the plot of log . ε − log σ. This polynomial fitting curve, however, sometimes has difficulty describing the power law creep. This example is shown in Figure 8. Thus, Kim and Jeong [121] proposed the exponential fitting method for the determination of the m from the plot of log . ε − log σ. According to the method, = 7 − < 0 or < 0.285 (11) Unlike in the procedure for determining for calculating (Figure 3a), where a linear fitting is applied to the data in the plot of log − log , the value as a function of strain rate, temperature, and strain, which is necessary for constructing processing maps, has often been determined using a third-or fourth-order polynomial fitting to the data in the plot of log − log . This polynomial fitting curve, however, sometimes has difficulty describing the power law creep. This example is shown in Figure 8. Thus, Kim and Jeong [121] proposed the exponential fitting method for the determination of the m from the plot of log − log . According to the method, log = a + c exp log − + exp log − (12) Figure 8. Polynomial fitting and exponential fitting to the data points in the plot in Figure 3a. Reproduced/modified with permission from [63], Elsevier.
When Equation (12) is used, m can be calculated by Equation (13): As observed in Figure 8, the exponential fitting, where m tends to decrease gradually with increasing strain rate, provides a better fit to the series of data compared with the polynomial fitting, which sometimes creates uncertain fluctuation between the data points. Figure 9a-c shows the η values of the HEAs calculated by Murty's method (Equations (6) and (8)) as a function of n1 for the three material groups of HEAs. It is obvious that the η values of all the three material groups of HEAs follow Equation (10) well in the entire range of n1, regardless of the differences in composition and crystal structure. Furthermore, it is observed that the flow instability condition determined by Equation (9) When Equation (12) is used, m can be calculated by Equation (13): As observed in Figure 8, the exponential fitting, where m tends to decrease gradually with increasing strain rate, provides a better fit to the series of data compared with the polynomial fitting, which sometimes creates uncertain fluctuation between the data points. Figure 9a-c shows the η values of the HEAs calculated by Murty's method (Equations (6) and (8)) as a function of n 1 for the three material groups of HEAs. It is obvious that the η values of all the three material groups of HEAs follow Equation (10) well in the entire range of n 1 , regardless of the differences in composition and crystal structure. Furthermore, it is observed that the flow instability condition determined by Equation (9) occurs at n 1 ≈7, supporting that the onset of flow instability occurs at the transition from power law creep to PLB (Equation (11)). Figure 10a-d shows the processing maps for Al 0.5 CrMnFeCoNi and Al 0.3 CrFeCoNi HEAs constructed based on Murty's approach and Kim and Jeong's approach. A good match is observed between the two methods in power dissipation maps as well as flow instability maps. However, some mismatch is observed for the Al 0.3 CrFeCoNi HEA in the flow instability at low strain rates and at low temperatures. This occurs because in Murty's method, the material is assumed to follow the power law creep at low strain rates below . ε min (Equation (8)), but this assumption can be wrong at low temperatures if PLB governs plastic flow below . ε min . occurs at n1≈7, supporting that the onset of flow instability occurs at the transition from power law creep to PLB (Equation (11)).
Materials 2023, 16, x FOR PEER REVIEW 13 of 21 Figure 10. 2D processing maps for (a,c) Al0.5CrMnFeCoNi and (b,d) Al0.3CrFeCoNi constructed based on Murty's approach and Kim and Jeong's approach using the raw data from [62] (for Al0.5CrMnFeCoNi) and [92] (for Al0.3CrFeCoNi). Figure 11a,b shows the plots of n1 as a function of the Zener-Hollomon parameter (Z = exp ( )) for Al0.5CrMnFeCoNi and Al0.3CrFeCoNi. There is a good correlation between n1 and Z, indicating that as strain rate increases and temperature decreases (i.e., as Z increases), n1 tends to increase. This occurs because according to the deformation mechanism maps (Figure 6a,b), as strain rate increases and temperature decreases, the deformation mechanism changes from solute drag creep (associated with n1 = 3) to dislocation climb creep (associated with n1 = 5) and then power law breakdown (associated with n1 > 3). is a function of n1 according to Equation (10). Hence, can also be expressed as a function of Z. Figure 11c,d shows the plot of as a function of Z for Al0.5CrMnFeCoNi and Al0.3CrFeCoNi, where a good correlation between and Z is observed. tends to decrease as Z increases. In addition, most of the data belonging to the flow instability  There is a good correlation between n 1 and Z, indicating that as strain rate increases and temperature decreases (i.e., as Z increases), n 1 tends to increase. This occurs because according to the deformation mechanism maps (Figure 6a,b), as strain rate increases and temperature decreases, the deformation mechanism changes from solute drag creep (associated with n 1 = 3) to disloca-tion climb creep (associated with n 1 = 5) and then power law breakdown (associated with n 1 > 3). η is a function of n 1 according to Equation (10). Hence, η can also be expressed as a function of Z. Figure 11c,d shows the plot of η as a function of Z for Al 0.5 CrMnFeCoNi and Al 0.3 CrFeCoNi, where a good correlation between η and Z is observed. η tends to decrease as Z increases. In addition, most of the data belonging to the flow instability condition (determined by Murty's approach using Equation (9)) are positioned below η = 0.285, supporting the validity of Equation (11). Some mismatches are observed between Equation (9) and Equation (10) and this can be attributed to the aforementioned assumption of power law creep below . ε min in Murty's method.
Materials 2023, 16, x FOR PEER REVIEW 14 of 21 Figure 11. Plot of n1 and as a function of Z for (a,c) Al0.5CrMnFeCoNi [34] and (b,d) Al0.3CrFeCoNi [25]. Open and solid symbols represent the flow stability and instability conditions (determined by Equation (9)), respectively. A red horizontal line represents = 0.285 (Equation (11)). Figure 12a-c shows the plots of processing maps for the three material groups of HEAs expressed as a function of Z using each Qc value of the HEAs (Table 1), and Figure  12d shows the plot where all the data in Figure 12a-c overlap. The η values of each material are well correlated as a function of Z, and the data for each group converge to a common curve. Also, it is observed that all the data of the three groups converge to a single common curve. According to the plot in Figure 12d, flow stability is nearly guaranteed at Z ≤ 10 12 s −1 , while flow instability is nearly inevitable at Z ≥ 2 × 10 15 s −1 . At 10 12 s −1 ≤ Z ≤ 2 × 10 15 s −1 , flow stability and instability conditions coexist, and flow instability becomes more dominant as Z increases. Open and solid symbols represent the flow stability and instability conditions (determined by Equation (9)), respectively. A red horizontal line represents η = 0.285 (Equation (11)).
The plots in Figure 11c,d represent the "processing maps expressed as a function of Z" because if one knows the temperature and strain rate, the Z value can be calculated, and then the power dissipation efficiency and flow (in)stability can be readily determined from the plot. Figure 12a-c shows the plots of processing maps for the three material groups of HEAs expressed as a function of Z using each Q c value of the HEAs (Table 1), and Figure 12d shows the plot where all the data in Figure 12a-c overlap. The η values of each material are well correlated as a function of Z, and the data for each group converge to a common curve. Also, it is observed that all the data of the three groups converge to a single common curve. According to the plot in Figure 12d, flow stability is nearly guaranteed at Z ≤ 10 12 s −1 , while flow instability is nearly inevitable at Z ≥ 2 × 10 15 s −1 . At 10 12 s −1 ≤ Z ≤ 2 × 10 15 s −1 , flow stability and instability conditions coexist, and flow instability becomes more dominant as Z increases. AlxCrFeCoNi (x = 0-1) [13,25,51,53,72,84,92,96,97,100], and (c) CrMnFeCoNiSn0.5, etc. [22,47,54,60,61,64], expressed as a function of Z using each Qc value of the HEAs (Table 1) and (d) the plot where all the data in (a-c) overlap. Open and solid symbols represent the flow stability and instability conditions (determined by Equation (9)), respectively. A red horizontal line represents = 0.285 (Equation (11)). Figure 13a-c shows the plots of processing maps for the three material groups of HEAs constructed as a function of Z using the average Qc value of all the HEAs (317.2 kJ/mol), and Figure 12d shows the plot where all the data in Figure 13a-c overlap. Note that all the data lie close to a common curve. According to the plot in Figure 12d, flow stability prevails at Z ≤ 10 12 s −1 , while flow instability prevails at Z ≥ 3 × 10 14 s −1 . By plotting in this fashion, one can easily compare the η values of the different HEAs at a given temperature and strain rate as well as predict the optimum hot working conditions of the HEAs with unknown Qc values.  [13,25,51,53,72,84,92,96,97,100], and (c) CrMnFeCoNiSn 0.5 , etc. [22,47,54,60,61,64], expressed as a function of Z using each Q c value of the HEAs (Table 1) and (d) the plot where all the data in (a-c) overlap. Open and solid symbols represent the flow stability and instability conditions (determined by Equation (9)), respectively. A red horizontal line represents η = 0.285 (Equation (11)). Figure 13a-c shows the plots of processing maps for the three material groups of HEAs constructed as a function of Z using the average Q c value of all the HEAs (317.2 kJ/mol), and Figure 12d shows the plot where all the data in Figure 13a-c overlap. Note that all the data lie close to a common curve. According to the plot in Figure 12d, flow stability prevails at Z ≤ 10 12 s −1 , while flow instability prevails at Z ≥ 3 × 10 14 s −1 . By plotting in this fashion, one can easily compare the η values of the different HEAs at a given temperature and strain rate as well as predict the optimum hot working conditions of the HEAs with unknown Q c values. Figure 13. Plots of processing maps for (a) AlxCrMnFeCoNi (x = 0-1) [9,23,34,42,45,63], (b) AlxCrFe-CoNi (x = 0-1) [13,25,51,53,72,84,92,96,97,100], and (c) CrMnFeCoNiSn0.5, etc. [22,47,54,60,61,64], expressed as a function of Z using the average Qc value of all the HEAs (317.2 kJ/mol) and (d) the plot where all the data in (a-c) overlap. Open and solid symbols represent the flow stability and instability conditions (determined by Equation (9)), respectively. A red horizontal line represents = 0.285 (Equation (11)).

Conclusions
The hot compressive behaviors of the HEA materials with different chemical compositions and crystal structures and processing maps were analyzed, and the following observations were made.
1. Hot compression tests on many HEAs have been conducted in the temperature range between 873 K and 1573 K, corresponding to the T/Tm range between 0.4 and 0.9. The n1 values are most populated between 3 and 7. 2. As T/Tm decreases, n1 tends to increase, and power law breakdown typically occurs at T/Tm ≤ 0.6. 3. In AlxCrMnFeCoNi (x = 0-1) and AlxCrFeCoNi (x = 0-1) HEAs, n1 tends to increase as the concentration of Al increases, implying that Al acts as a solute atom that exerts a drag force on dislocation slip motion. 4. The activation energy for plastic flow (Qc) in the HEAs is calculated to be in the range between 150 and 600 kJ/mol, and the data distribution is populated in the Qc value range between 300 and 400 kJ/mol. The average Qc value for all the HEAs is 317 kJ/mol. 5. The value of the HEAs can be expressed as a function of n1 only. Flow instability is shown to occur near n1 = 7, implying that the onset of flow instability occurs at the transition from power law creep to PLB. 6. Processing maps for all the HEAs are demonstrated to be constructed using the Zener-Hollomon parameter (Z = exp ( )). According to the analysis result, flow stability prevails at Z ≤ 10 12 s −1 in all HEAs.  (9)), respectively. A red horizontal line represents η = 0.285 (Equation (11)).

Conclusions
The hot compressive behaviors of the HEA materials with different chemical compositions and crystal structures and processing maps were analyzed, and the following observations were made.

1.
Hot compression tests on many HEAs have been conducted in the temperature range between 873 K and 1573 K, corresponding to the T/T m range between 0.4 and 0.9. The n 1 values are most populated between 3 and 7.

2.
As T/T m decreases, n 1 tends to increase, and power law breakdown typically occurs at T/T m ≤ 0.6.

3.
In Al x CrMnFeCoNi (x = 0-1) and Al x CrFeCoNi (x = 0-1) HEAs, n 1 tends to increase as the concentration of Al increases, implying that Al acts as a solute atom that exerts a drag force on dislocation slip motion. 4.
The activation energy for plastic flow (Q c ) in the HEAs is calculated to be in the range between 150 and 600 kJ/mol, and the data distribution is populated in the Q c value range between 300 and 400 kJ/mol. The average Q c value for all the HEAs is 317 kJ/mol.

5.
The η value of the HEAs can be expressed as a function of n 1 only. Flow instability is shown to occur near n 1 = 7, implying that the onset of flow instability occurs at the transition from power law creep to PLB. 6.
Processing maps for all the HEAs are demonstrated to be constructed using the Zener-Hollomon parameter (Z = exp Q c RT ). According to the analysis result, flow stability prevails at Z ≤ 10 12 s −1 in all HEAs. Data Availability Statement: The raw/processed data required to reproduce these findings cannot be shared at this time, as the data also form part of an ongoing study.

Conflicts of Interest:
The authors declare no conflict of interest.