Compositional Dependence of Phase Selection in CoCrCu0.1FeMoNi-Based High-Entropy Alloys

To study the effect of alloy composition on phase selection in the CoCrCu0.1FeMoNi high-entropy alloy (HEA), Mo was partially replaced by Co, Cr, Fe, and Ni. The microstructures and phase selection behaviors of the CoCrCu0.1FeMoNi HEA system were investigated. Dendritic, inter-dendritic, and eutectic microstructures were observed in the as-solidified HEAs. A simple face centered cubic (FCC) single-phase solid solution was obtained when the molar ratio of Fe, Co, and Ni was increased to 1.7 at the expense of Mo, indicating that Fe, Co, and Ni stabilized the FCC structure. The FCC structure was favored at the atomic radius ratio δ ≤ 2.8, valence electron concentration (VEC) ≥ 8.27, mixing entropy ΔS ≤ 13.037, local lattice distortion parameter α2 ≤ 0.0051, and ΔS/δ2 > 1.7. Mixed FCC + body centered cubic (BCC) structures occurred for 4.1 ≤ δ ≤ 4.3 and 7.71 ≤ VEC ≤ 7.86; FCC or/and BCC + intermetallic (IM) mixtures were favored at 2.8 ≤ δ ≤ 4.1 or δ > 4.3 and 7.39 < VEC ≤ 8.27. The IM phase is favored at electronegativity differences greater than 0.133. However, ΔS, α2, and ΔS/δ2 were inefficient in identifying the (FCC or/and BCC + IM)/(FCC + BCC) transition. Moreover, the mixing enthalpy cannot predict phase structures in this system.

The microstructures and crystalline phases present in HEAs are very sensitive to the alloy composition. An α phase appears when the molar ratio of Mo in AlCoCrFeNiMo x alloys exceeds 0.1 [17]. Changes in the molar ratio of Fe, Co, and Cr in AlCoCrFeMo 0.5 Ni alloys affect the crystalline phases and mechanical properties. As the Mo content increases, the volume fraction of the σ phase increases in Ni 2 CrFeMo x alloys [18]. However, the volume fraction of the σ phase is increased with increasing Cr content. Eventually, the dendritic matrix of AlCoCr x FeMo 0.5 Ni HEAs is changed from the ordered B2 phase to the σ phase [19]. As the Co content in AlCo x CrFeMo 0.5 Ni HEAs changes from x = 0.5 to x = 2.0, the phase changes from BCC to BCC + FCC + σ, respectively. Recently, it was found that the precipitation of intermetallic (IM) compounds of σ and µ phases could strengthen CoCrFeNiMo 0.3 alloy without causing serious embrittlement [21]. Moreover, the ordered B2 solid-solution and σ phases were presented in FeAlCrNiMo x HEAs with increasing Mo content [22]. Most previous investigations have focused on the effects of the addition or content change of one or two elements on the microstructure and properties of the HEA. However, studies on the effect of each individual element on the microstructure and phase selection have not yet been reported. Additional systematic research will be necessary in the near future to guide the exploration of HEAs.
Many parameters are related to phase selection in HEAs, including the atomic radii differences (δ), differences in electronegativity (∆X), the valence electron concentration (VEC), the enthalpy of mixing (∆H mix ), and the mixing entropy (∆S mix ) [24][25][26][27][28][29][30][31]. Based on these parameters, many criteria have been proposed for phase prediction in HEAs. Zhang et al. summarized a solid-solution phase-forming rule using δ, ∆H mix , and ∆S mix with δ ≤ 6.6%, −22 ≤ ∆H mix ≤ 7 kJ/mol, and 11 ≤ ∆S mix ≤ 19.5 J/(K·mol) [24]. To limit the target of discussion to simple disordered phases, the conditions are more strict: δ ≤ 4.3%, −15 ≤ ∆H mix ≤ 5 kJ/mol, and 12 ≤ ∆S mix ≤ 17.5 J/(K·mol). Guo proposed that the phase stability of the FCC and BCC solid solution was correlated with VEC; for VEC < 6.87 the BCC phase was stable; for VEC > 8, FCC was [25]. Later, the stability of the σ phase was studied and it was predicted that alloys with 6.88 ≤ VEC ≤ 7.84 were prone to σ phase formation [30]. However, this criterion works well only for Cr-and V-containing HEAs. Recently, complex ordered phases were found to be stable for ∆X > 0.133, except for HEAs containing a large amount of Al [31]. More recently, Wang et al. [32] proposed a new parameter, α 2 , to address the local lattice distortion of crystalline lattices in HEAs. This parameter effectively explained the lattice distortion, intrinsic strain energy, and excess entropy in HEAs.
As mentioned above, the phases present in HEAs are remarkably dependent on the alloy composition. In a previous work, the CoCrCu 0.1 FeMoNi alloy exhibited the duplex microstructure of BCC + FCC [33]. Under compositional change, the microstructural behavior is uncertain: the HEA could retain this simple solid solution mixture or intermetallic (IM) phases could appear. In order to address this question, it is necessary to study the effect of alloy composition on the phase selection of CoCrCu 0.1 FeMoNi alloys. Hence, the present work investigates the partial substitution of Mo by Cr, Co, Ni, and Fe. The effect of the relative contents of Cr, Co, Ni, Fe, and Mo on the microstructure and crystal structures of CoCrCu 0.1 FeMoNi-based HEAs was studied in this work in order to understand the phase selection mechanism in this alloy system.

Materials and Methods
The proposed HEAs were prepared via vacuum arc melting in a Ti-gettered Ar atmosphere with subsequent melt solidification in a water-cooled Cu crucible. A mixture of the appropriate amounts of the constituent elements with purities > 99.9 wt % for each alloy was flipped and melted at least four times to ensure thorough chemical homogeneity. Table 1 shows the compositions prepared in this study. As-cast samples were then sectioned and polished for microstructural and compositional characterization using scanning electron microscopy (SEM, JEOL-5410, JEOL Ltd., Tokyo, Japan), energy dispersive X-ray spectrometry (EDS, JEOL Ltd., Tokyo, Japan), and an X-ray diffractometer (XRD, Rigaku ME510-FM2, Rigaku Ltd., Tokyo, Japan) at a scanning speed of 4 • /min and a scanning range from 30 • to 100 • using a Cu target and an applied voltage and current of 30 kV and 20 mA, respectively.

Co a CrCu 0.1 FeMo 2−a Ni Alloys
The microstructures of the Co a CrCu 0.1 FeMo 2−a Ni (a = 1.2, 1.5 and 1.7) alloys are shown in Figure 1. A typical eutectic structure is found in the inter-dendritic region, and the volume fraction of the eutectic mixture is decreased with increasing Co and decreasing Mo. Table 2 shows the actual composition and contents of different regions in the microstructures, as detected by EDS. The dendrites are enriched in Co, Cu, Fe, and Ni, while the contents of Cr and Mo are higher in the inter-dendritic region B. The composition of the inter-dendritic eutectic region B is approximately (CrMo) 54 (CoCuFeNi) 46 according to EDS. This means that the content of Cr and Mo is 54% and that of Co, Cu, Fe, and Ni is 46%. Furthermore, the Cu content in the inter-dendritic region is increased with decreasing Mo content. This is related to the positive ∆H mix between Cu and Mo (+19 kJ/mol). Figure 1d shows the XRD patterns of the Co a CrCu 0.1 FeMo 2−a Ni HEAs. The FCC, σ, and µ phases are detected. The crystal structure of the σ phase is tetragonal with the lattice constants of a = 0.885 nm and c = 0.459 nm, and the σ phase is similar to the binary Co 2 Mo 3 phase. The µ phase is tetragonal with lattice constants of a = 0.7381 nm and c = 1.8504 nm, and probably Co 7 Mo 3 or Fe 7 Mo 6 . Both σ and µ are topologically close-packed (TCP) phases. Obviously, the volume fractions of the σ and µ phases, represented by peaks in the range of 40-50 • , are decreased as the Co content increases and Mo decreases. According to the EDS and XRD results, we can identify the dendrites as the FCC phase, while σ and µ are eutectic structures.    Figure 2a), while the inter-dendritic region (B) is enriched with Co and Mo. However, for the CoCr 1.5 Cu 0.1 FeMo 0.5 Ni alloy (referred to as Cr 1.5 Cu 0.1 Mo 0.5 ), a fully eutectic structure is found, indicating that the alloy has a eutectic composition, probably of (CrMo) 52 (CoCuFeNi) 48 , according to region A in Table 2 as detected by EDS. This means that the content of Cr and Mo is 52%, and that of Co, Cu, Fe, and Ni is 48%.
It is apparent that CoCr b Cu 0.1 FeMo 2−b Ni (b = 1.2 and 1.5) alloys contain FCC, BCC, and TCP phases according to the XRD patterns, as shown in Figure 2c. The TCP phases correspond to the tetragonal σ phase (a = 0.917 nm, c = 0.474 nm) and a hexagonal close-packed (HCP) Laves phase (a = 0.473 nm, c = 0.772 nm). As can be seen in Figure 2c, the volume fraction of the BCC phase increases with increasing Cr, which enhances the formation of BCC phase in CoCr b Cu 0.1 FeMo 2−b Ni alloys (b = 1.2 and 1.5). With increasing Cr and decreasing Mo, the BCC phase appears, and the volume fraction of both TCP phases decreases. According to the EDS and XRD results, the dendrites should be FCC, while the eutectic structures include BCC, σ, and Laves phases.

Discussion
Two eutectic phases are found in the Cr 1.5 Cu 0.1 Mo 0.5 and Cu 0.1 Fe 1.2 Mo 0.8 HEAs, with probable eutectic compositions of (CrMo) 51-54 (CoCuFeNi) 46-49 . Similarly, fully eutectic structures have been obtained in CoFeNi x VMo y HEAs at both CoFeNi 1.4 VMo and CoFeNiVMo 0.6 [14]. Recently, Lu et al. [34] have proposed a strategy to design eutectic high-entropy alloys (EHEAs) based on ∆H mix . They selected Zr, Nb, Hf, and Ta to replace Al in a previous AlCoCrFeNi 2.1 EHEA, based on the relationship of ∆H mix for various atomic pairs. Unfortunately, no regularities have yet been found in the current HEA system. Further research is ongoing to clarify this relationship in the future.
The phase selection mechanism in the CoCrCu 0.1 FeMoNi-based HEAs can be understood using the parameters listed in Table 3. Based on alloy composition, a simple FCC structure is obtained only when the CoCrCu 0.1 FeMoNi-based HEAs contain higher contents of principal elements, such as Fe/Co/Ni. This suggests that Fe, Co, and Ni are FCC stabilizers in the CoCrCu 0.1 FeMoNi-based alloys. It can be found that a simple FCC structure is favorable for alloys with the smallest δ, ∆X, and ∆S. Conversely, alloys with large VEC values favor the formation of simple FCC structures, while TCP phases develop in alloys with smaller VEC values. TCP phases are found when the ∆H of the alloys is largely negative, with the exception of Cu 0.1 Mo 0.3 Ni 1.7 . Furthermore, alloys with small α 2 favor the formation of a single-phase FCC structure. In the current work, the FCC structure is stable when δ ≤ 2.8, FCC+BCC is favored when 4.1 ≤ δ ≤ 4.3, and FCC or/and BCC + IM is found when 2.8 ≤ δ ≤ 4.1 or δ > 4.3, with the only exception of AlCoCrCuFeNiMo 0.2 . As shown in Figure 5c, the FCC structure is stable when VEC ≥ 8.27, but there is an overlap between the mixture types of FCC+BCC and FCC or/and BCC + IM. The IM phase is favored when ∆X > 0.133 only with the exceptions of the CoCrCu 0.1 FeMoNi and CoCrCu 0.3 FeMoNi alloys.
The results are well fitted with the criterion proposed by Lu et al. As shown in Figure 5b,f, the FCC structure is stable when ∆S ≤ 13.037 and α 2 ≤ 0.0051; however, the (FCC+BCC)-type phase-forming ∆S and α 2 ranges show overlaps with those of the (FCC or/and BCC + IM)-type. All the calculated values of ∆H are in the range −15 ≤ ∆H mix ≤ 5 kJ/mol (Figure 5a), and except for FCC and BCC, IM phases are still found, indicating that the phase structures of the listed alloys cannot be distinguished by ∆H.
Singh demonstrated that a simple solid solution as obtained when ∆S mix /δ 2 > 0.96, IM compounds when ∆S mix /δ 2 < 0.24, and a mixture thereof when 0.24 < ∆S mix /δ 2 < 0.96 [36]. As can be seen in Figure 5e, a large ∆S/δ 2 value favors the formation of a single FCC phase. As the value of ∆S/δ 2 decreases, more phases appear, and smaller ∆S/δ 2 values favor the BCC phase. For CoCrCu 0.1 FeMoNi-based alloys, the simple FCC phase structure is favored when ∆S/δ 2 > 1.7, while multiphase structures containing (FCC or/and BCC + IM) are found when 0.549 ≤ ∆S/δ 2 ≤ 1.28, and the (FCC+BCC)-type phase-forming ∆S/δ 2 range shows an overlap with that of the (FCC or/and BCC + IM)-type. The former famous criterion for phase-forming in HEAs cannot be used effectively in this system. Thus, new rules or parameters must be considered in the future.

Conclusions
Eutectic or dendritic microstructures were observed in as-solidified Moreover, a simple FCC structure was found in the alloys with the smallest δ, ∆X, and ∆S values. Conversely, alloys with higher VEC were simple FCC structures, while TCP phases appeared to develop in alloys with decreased VEC. TCP phases were found with large negative ∆H values, with the exception of the Cu 0.1 Mo 0.3 Ni 0.7 alloy. Furthermore, the value of α 2 is smaller when a simple FCC structure is obtained.
For CoCrCu 0.1 FeMoNi-based alloys, the FCC structure was stable when δ ≤ 2.8, VEC ≥ 8.27, ∆S ≤ 13.037, α 2 ≤ 0.0051, and ∆S/δ 2 > 1.7; the mixture of FCC+BCC is favored when 4.1 ≤ δ ≤ 4.3 while the (FCC or/and BCC + IM) mixture is found when 2.8 ≤ δ ≤ 4.1 or δ > 4.3. IM phases are favored when ∆X > 0.133. However, some overlap remained in parameters including VEC, ∆S, α 2 , and ∆S/δ 2 . This indicated that these parameters are not sufficient to distinguish (FCC or/and BCC + IM) from (FCC+BCC) phase formation behaviors, and new rules or parameters must be considered for the described system. Moreover, ∆H could not predict phase structures in the current work. In summary, the phase selection behaviors in CoCrCu 0.1 FeMoNi-based HEAs can be well delineated by δ and ∆X.

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