The TEM images obtained from the composition of Co-30Ni-10Al-6Ta (at%) alloy, annealed at 800°C for 48 h after solution treatment at 1,290°C for 24 h, are shown in Figure 2A. Fine γ/γ′ two-phase microstructures are observed in it, and Figure 2B is the diffraction pattern along the [001] zone axis and reveals that the cuboidal γ′ precipitates are L1₂-ordered structures. The fine L1₂-ordered γ′ phase is 120 ± 30 nm in size in Figure 2C, distributing throughout the γ matrix homogeneously, which is analogous to the γ/γ′ two-phase microstructure found in Ni-based and Co-based superalloys. Figure 2D shows the EDS mapping of Co-30Ni-10Al-6Ta alloys annealed at 800 °C for 48 h. We can clearly observe that Co tends to partition into the γ matrix, while Ta and Al tend to partition into the γ′ phase as strong γ′-forming elements.

Figure 3A shows the area fraction and Vickers hardness of the Co-30Ni-10Al-6Ta (at %) alloy with the change of aging time from 24 to 240 h. The factor of their decline after a long time of aging may be attributed to changes in the radius of γ′ precipitates and grain sizes under the constant diffusion of elements. We noticed that when the heat treatment time is 30–70h, the alloy has both higher hardness and area fraction. Figure 3B is the result of the lattice misfit study of the alloy after 48 h aging. The γ′ phase lattice constant is 0.3619 nm, the γ phase lattice constant is 0.3579 nm, and the calculation method of the γ/γ′ two-phase lattice misfit is according to the formula   δ = 2 ( a γ ' − a γ a γ ' + a γ ) , showing that the calculation result is, respectively, +1.11%. Figure 3C is the DSC heating curve of the Co-30Ni-10Al-6Ta (at %) alloy after aging at 800 °C for 48 h. The solvus temperature of the γ′ phase is 1, 215°C, and the melting point of the γ phase is 1, 340 °C. The processing window of more than 120 °C means that the alloy has a huge alloying potential to improve alloy defects. Figure 3D shows the fit between the experimental results and the machine learning calculation results. We can find that the prediction has very high accuracy in terms of γ′ solvus temperature and density up to E_r≈0.01%. However, because the γ′ area fraction and alloy hardness will vary greatly with the aging time and temperature, the improvement of prediction accuracy may require more basic data.

The grain boundary and the change of γ′ phase size and shape with aging time are shown in Figure 4, where it is found that no secondary phases emerge in the matrix and grain boundary regions, and γ′ phase size increased with the extension of the aging time, whose shape remains cubic although the lattice misfit is slightly high. It should be noted that cold-rolling is conducted prior to the heat treatment in order to observe the stability of the γ′ phase. This pretreatment seems to shorten the annealing time of the studied alloy, which is required to obtain the thermal equilibrium stage. This cold rolling treatment method is also applied in Co-Al-W-based alloy (Tsukamoto et al., 2010) to obtain the phase equilibrium composition. Figure 5 shows the typical γ/γ′ two-phase microstructure obtained in the cold-rolled Co-30Ni-10Al-6Ta (at%) quaternary alloy, respectively, annealed at 800–1100 °C for 300 h. It can be seen that after the aging treatment, the alloy Co-30Ni-10Al-6Ta (at %) maintain stable γ/γ′ two-phase structure and no harmful impurities such as HCP, TCP, B2, and μ phase are found in the matrix. The composition of γ/γ′ and the partition coefficient are displayed in Table 1. Usually, the partitioning tendency of alloying elements between the γ and γ′ phases can be ascertained by the partition coefficient K_X, where K_X > 1 indicates that X is partitioned to the γ′ phase, while K_X < 1 means that X distributes to the γ phase (Yuechao Chen et al., 2019). Thus, it is clear that the Ta strongly partitions to the γ′ phase, especially at 800°C (K_Ta = 8.45), and the similar effect elements are Ti, W, Nb, etc. (Omori et al., 2013), and the Co partitions to the γ phase, which accords with the reported Co-based superalloys. The effective design of high-performance Co-based superalloys can be achieved by elucidating the role of alloying elements. In Table 1, we found that the Ta element is a strong γ′ phase forming element, its addition may be the key factor for the excellent γ′ phase thermal stability of the alloy. A similar action rule was also found in the study of Suzuki A et al. (Suzuki et al., 2007). We find K_Ta, K_Ni, and K_Al (particularly is K_Ta) change from high to low with increasing temperature, while K_Co is the opposite. The distribution behavior of all elements approaches K_X = 1 with increasing annealing temperature and this trend is also was found in other Co-Al-W-based (Omori et al., 2013) and Ni-Al-based superalloys (Jia et al., 1994).

Figure 6 shows the γ′ solvus temperature and density comparisons of Co-30Ni-10Al-6Ta (at%) alloy, Co-Ni-Al-V-based (Yuechao Chen et al., 2019), Co-Ni-Al-Mo-based (Makineni et al., 2015b), Co-Ni-Al-W-based (Qu et al., 2019), Co-Ti-based (Zenk et al., 2017), and Ni-based (Baldan et al., 2013) superalloy. It is obvious from the figure that the γ′ solvus temperature of this alloy is much higher than that of the aforementioned Cobalt-based alloys and comparable to commercial nickel-based superalloy M-Mar-247. The reason may be that Ta is a strong γ′-phase former element, and the addition of this element can increase the solvus temperature of the γ′ phase. However, we should also note that Ta as a heavy element can also sharply increase the alloy density, which is consistent with the calculation results in Figures 1C, D. When considering the lightweight design of the alloy, the addition of Ta or W element should be appropriate.

Figure 7 shows the lattice misfit comparisons of Co-30Ni-10Al-6Ta (at%) alloy with other Co-based superalloys; it is found that this alloy has a high lattice misfit (+1.11%) compared to Co-12Ti alloy and Co-12Ti-4Mo alloy, and Co-Ni-Al-W-based alloys exhibit a suitable lattice misfit around 0.5% (Zenk et al., 2017). The morphology of the γ′ phase in new Co-based superalloys is closely related to the lattice misfit of the two γ/γ′ phases: when the lattice misfit is 0–0.2%, 0.5–1.0%, and higher than 1.25%, the shape of the γ′ precipitates is spherical, cubic, and plate. A too high lattice misfit may cause the precipitated γ′ phase of the alloy to be unstable at high temperatures, the alloy rafting phenomenon is a good proof in Co-12Ti alloy (Zenk et al., 2017), and it can affect the mechanical properties. Therefore, a suitable lattice misfit is critical for subsequent alloy designers. Compared to Co-30Ni-12Al-4Ta (at%) alloys, we found that an increase in the Ta/Al ratio leads to an increase in the γ/γ′ lattice constants. However, as a strong γ′ phase forming element, the Ta element is more inclined to be distributed in the γ′ phase (Table 1), which causes a sharp increase in the γ′ phase lattice constant, and leads to an increase in the γ/γ′ lattice misfit. But it is worth noting that the Cr element, as a γ phase forming element, can effectively increase the lattice constant of the γ phase. The addition of the Cr element maybe is an effective way to improve the defect for alloys with excessive lattice misfit. This method is a good embodiment of the Co-Ti-based alloy (Zenk et al., 2017).

Figure 8 is a graph showing the relationship between yield strength and temperature of this alloy. In this study, part of Co-Ni-Al-V-based (Yuechao Chen et al., 2019), Co-Ni-Al-Mo-based (Makineni et al., 2015c), Co-Al-W-based (Suzuki et al., 2007), Co-Ti-based (Zenk et al., 2017), and Ni-based (Sims et al., 1987) polycrystalline superalloys are listed as comparative alloys. What can be seen from Figure 7 is that the alloy in this study exhibit excellent yield strength (950–1220Mpa) in the low and medium temperature range (20–700 C), which far exceeds other new Co-based superalloys and Ni-based polycrystalline superalloy M-Mar-247. However, the yield strength of this alloy in the middle and high-temperature range (700–900 C) has a relatively obvious and rapid decline, and it is equivalent to the comparison alloys of various series above 800 C. Gerold (Gerold and Haberkorn, 2010) pointed out in the study of the relationship between alloy strengthening and dislocations, elastic stress fields that when the dislocations pass through the precipitation phase particles by cutting, the mathematical formula for the increase in yield strength due to coherent strain strengthening is Δτ = AGε^3/2 (r₀f/b)^1/2, where A is a constant, G is the shear modulus, ε is the degree of lattice misfit, r₀ is the average radius of the precipitated phase particles, f is the volume fraction of the precipitated phase, and b is the primary Gus vector. This mathematical formula clearly shows that the increase in yield strength due to precipitation strengthening increases with the increase in ε, r₀, and f at room temperature. The alloys that use this mechanism for strengthening include GH4169, GH2706, and Inconel718.

Under high-temperature conditions, the grain boundary strength decreases rapidly as the temperature rises, especially the lateral grain boundary becomes a weak link. Above the isothermal strength, the superalloys that do not strengthen the grain boundary are prone to fracture along the grain under high-temperature stress conditions. Therefore, a small amount of grain boundaries strengthening elements such as C and B can be added to improve the high-temperature creep performance of polycrystalline alloys (Reed, 2008). On the other hand, the reason that yield strength decreases rapidly under high temperature may be that the slip on the octahedral plane is activated, the interaction mechanism between the 1/3 [112] partial dislocations and the γ′ phase particles changes from the “cut-through” mechanism to “bypass” mechanism (Suzuki et al., 2007).