Composition Optimization in Alloy Design for Nickel-Based Single Crystal Superalloy: A Review

Abstract

This article presents a review of the composition optimization progress of nickel-based single crystal (SC) superalloy design in recent years in order to obtain better high-temperature performance for the development of the aviation industry. The influence of alloying elements on the creep resistance, microstructure characteristics, oxidation resistance, castability, density, and cost of superalloys is analyzed and discussed. In order to obtain better high-temperature performance, the content of refractory elements (Ta + Re + W + Mo) and Co was increased gradually. The addition of Ru was added in the fourth-generation nickel-based SC superalloy to stabilize the microstructures and suppress the precipitation of the topologically close-packed (TCP) phase. However, the content of the antioxidant element Cr significantly decreased, while the synergistic effect of Al, Cr, and Ta received more attention. Therefore, synergistic effects should also receive more attention to meet the practical needs of reducing the content of refractory elements to reduce costs and density in future single crystal alloy designs without compromising critical performance.

1. Introduction

Nickel-based single crystal (SC) superalloys, known for their exceptional mechanical properties, resistance to oxidation, and corrosion resistance at elevated temperatures, are crucial materials for the manufacturing of advanced aero engines and turbine blades [1]. The composition of SC superalloys is usually complex and contains many elements. Different element types and contents will affect the properties of superalloys [2,3]. The microstructure of materials determines their properties, and the creep properties of SC superalloys are determined by their intrinsic two-phase structure (γ phase and γ′ phase). As the matrix of the SC superalloys, the γ phase is distributed continuously in the alloy. The γ phase has face-centered cubic (FCC) crystal structure like pure Ni, and it forms a solid solution to contain other elements in alloys. The volume fraction of the γ′ phase in the alloy is large, and, as the main precipitated phase of SC superalloys, it is evenly distributed in the matrix [4,5]. The existence of a two-phase structure means that the designers mainly use solid solution and precipitation strengthening to strengthen the alloy, and the development of a single crystal alloy is also mainly focused on how to strengthen the two-phase structure.

The first SC superalloy was PWA1480, reported in the 1980s [6]. In the following decades, TMS, CMSX, and René series have reported SC superalloys with different composition characteristics to improve their mechanical, chemical, and physical properties. The high-temperature performance of SC superalloys is generally judged by the standard of a 137 MPa/1000 h creep fracture [1]. Figure 1 shows the high-temperature capability of some typical SC superalloys [7]. The temperature bearing capacity of SC superalloys in the second generation is roughly 1040 °C, and the corresponding service temperature of SC superalloys in each generation is increased by about 20~30 °C. Each generation of upgrading means a two-fold increase in blade service life. According to this criterion, all kinds of SC superalloys developed at present can be roughly divided into six generations. Among them, the highest generation of SC superalloys, TMS-238, has a high-temperature resistance of 1120 °C [8]. Since the development of TMS-238, no research has shown that a single crystal alloy with higher temperature capability has been developed.

The high-temperature resistance of SC superalloys is mainly determined by its constituent elements. The basic elements in SC superalloys include Ni, Cr, Co, Al, Mo, W, Ti, Ta, Re, and Ru [9]. In addition, a wide variety of alloying element are chosen in these alloys, such as Nb for increasing the internal diffusivity of elements in the alloy [10,11] and Si for improving oxidation performance [12,13,14,15]. These elements can be divided into γ phase elements and γ′ phase elements according to their different functions in strengthening alloys [16,17,18]. STEM-EDS (Scanning Transmission Electron Microscopy–Energy Dispersive Spectrometer) maps (Figure 2) have shown the elemental distribution in γ and γ′ phases of SC superalloys. The “+” in the figure indicates the corresponding positions of γ and γ′. The γ phase elements, such as Co, Cr, Mo, W, Re, and Ru, are mainly distributed in the γ phase and form solid solutions [19]. The addition of these elements significantly strengthens the γ phase by increasing the solidus temperature to enhance thermal stability [20]. Al, Ti, and Ta are the primary components of the γ′ phase. When creating microstructures using these elements, Ni-Ni or X-X structures are substituted with Ni-X bonds (where X represents Al, Ti, or Ta). Strong chemical order in the Ni-X bonds leads to the creation of the structured γ′ phase (L1₂ structure). This distinguishes them from the disordered γ phase with FCC structures [21].

The chemical compositions of the most famous series of single crystal alloys are listed in

Table 1. Chemical compositions (wt.%) of some mainstream series of nickel-based single crystal superalloys. Adapted from Refs. [25,26,27,28,29,30].

Generation	Alloy	Cr	Co	Mo	W	Al	Ti	Ta	Re	Ru	Hf	Ni
1st	PWA1480	10.0	5.0	-	4.0	5.0	1.5	12.0	-	-	-	Bal.
	RR2000	10.0	15.0	3.0	-	5.5	4.0	-	-	-	-	Bal.
	CMSX-2	8.0	5.0	0.6	8.0	5.6	1.0	6.0	-	-	-	Bal.
	René N4	9.0	8.0	2.0	6.0	3.7	4.2	4.0	-	-	-	Bal.
2nd	PWA1484	5.0	10.0	2.0	6.0	5.6	-	9.0	3.0	-	0.1	Bal.
	CMSX-4	6.5	9.0	0.6	6.0	5.6	1.0	6.5	3.0	-	0.1	Bal.
	MC2	8.0	5.0	2.0	8.0	5.0	1.5	6.0	-	-	-	Bal.
	René N5	7.0	8.0	2.0	5.0	6.2	-	7.0	3.0	-	0.2	Bal.
3rd	CMSX-4 Plus	3.5	10.0	0.6	6.0	5.7	0.85	8.0	4.8	-	0.1	Bal.
	CMSX-10	2.0	3.0	0.4	5.0	5.7	0.2	8.0	6.0	-	0.03	Bal.
	René N6	4.2	12.5	1.4	6.0	5.75	-	7.2	5.4	-	0.15	Bal.
	TMS-75	3.0	12.0	2.0	6.0	6.0	-	6.0	5.0	-	0.1	Bal.
	TMS-82	5.0	7.8	3.4	8.7	5.2	0.5	4.4	2.4	-	0.1	Bal.
4th	MC-NG	4.0	0	1.0	5.0	6.0	0.5	5.0	4.0	4.0	0.1	Bal.
	PWA1497/MX-4	2.0	16.5	2.0	6.0	5.6	-	8.3	6.0	3.0	0.15	Bal.
	TMS-138	3.2	5.8	2.9	5.9	5.8	-	5.6	5.0	2.0	0.1	Bal.
	EPM-102	2.0	16.5	2.0	6.0	5.55	-	8.25	5.95	3.0	0.15	Bal.
	TMS-138A	3.2	5.8	2.9	5.6	5.7	-	5.6	5.8	3.6	0.1	Bal.
5th	TMS-162	3.0	5.8	3.9	5.8	5.8	-	5.6	4.9	6.0	0.1	Bal.
	TMS-173	3.0	5.6	2.8	5.6	5.6	-	5.6	6.9	5.0	0.1	Bal.
	TMS-196	4.6	5.6	2.4	5.0	5.6	-	5.6	6.4	5.0	0.1	Bal.
6th	TMS-238	4.6	6.5	1.1	4.0	5.9	-	7.6	6.4	5.0	0.1	Bal.

. The minor elements, such as Nb, C, B, are not included in this table. As an element forming the γ′ phase, the addition of Ti will obviously affect the formation of the eutectic structure. In order to inhibit eutectic structure formation and yield homogeneous constituent distribution, the content of the Ti element should be controlled within a low level [23]. Table 1 shows that the fifth- and sixth-generation SC superalloys no longer contain Ti elements. However, in recent years, researchers have found that the addition of minor (0.5%) Ti elements to new second-generation SC superalloys can significantly enhance resistance to high-temperature creep. The addition of titanium reduces the minimum strain rate during creep to one-third of that of alloys without titanium, resulting in a doubling of the creep rupture life in high-temperature conditions [24].

Nearly ten or more elements make up the possibility of an infinite number of alloy components. Assuming that the content of each added element is within 0–10% and the change step is 1%, there are about 10⁸~10¹⁰ alloy components that can be arranged and combined [16]. Furthermore, each alloy component needs to be tested for melting, heat treatment, and creep properties. Obviously, this is beyond the scope of any practical experimental research program. Therefore, a degree of modeling and theoretical calculation is required to isolate the optimum composition from these alloy components. The evolution of the major compositions of the conventionally cast superalloys and SC superalloys in Table 1 from the first generation to the fifth generation has been shown in Figure 3. The content of refractory elements (Ta + Re + W + Mo) was increased gradually in order to gain better high-temperature properties. Re is one of the alloying elements that greatly improves the high-temperature creep properties in new SC superalloys, as shown by evidence suggesting that the addition of Re leads to a significant increase in creep resistance [6,31,32,33]. Starting with the fourth-generation nickel-based SC superalloy, the additions of Ru are expected to suppress the formation of the topologically close-packed (TCP) phase. The widely acknowledged belief is that the reverse partitioning method involving Ru can enhance the distribution of Re and other resistant elements to γ′ precipitates, ultimately decreasing the likelihood of segregation in the matrix [29,34,35,36,37].

In the process of superalloy development, the concept and method of advanced alloy design play an important role. Over the past few decades, material designers have come up with a variety of ways to design superalloys. Phase computation was pioneered and applied in the design of superalloys as early as the 1960s [38]. The d electron theory proposed by Morinaga in the late 1980s based on molecular orbital energy levels is one of the more mature methods until now [39,40]. In recent years, with the development of computer technology and material science, many new methods of alloy design have emerged, such as the study of phase balance, which has really become a part of the material’s design. By summing up the existing alloy designs, it can be known that no matter what design method is adopted, there is ultimately a return to the relationship of superalloy composition, processing, structure, and properties. It is necessary to study this restriction relationship to lay a theoretical foundation for the optimal design of SC superalloys. At present, nickel-based superalloys have their own alloy design system, as shown in Figure 4. SC superalloys are mainly strengthened by precipitated γ′. Volume fractions and particle sizes of the precipitated γ′ should be optimally designed, as a large amount of fine γ′ is beneficial for interactions between dislocations and γ′, leaving an anti-phase boundary for high-temperature strength [41]. It is worth noting that the heat treatment process is crucial for improving the performance of SC superalloys. The heat treatment process of nickel-based single crystal alloys mainly includes solution treatment and aging treatment. These steps can effectively reduce the segregation of alloying elements and regulate the content, morphology, and size of γ′ phases. Considering the actual service environment of SC alloy, the various mechanical properties of the alloy, as well as its corrosion resistance and microstructure stability, also need to be taken into account. These performance characteristics in Figure 4 need to be considered in the alloy design process.

This review summarizes the design methods of superalloys and the various effects of alloying elements on the microstructure, high-temperature creep properties, casting properties, and oxidation resistance of SC superalloys. We hope it can provide a reference for the design of high-generation nickel-based superalloys.

2. Design Method of Composition Optimization in Superalloy

2.1. Phase Computation

Some early compositions of the superalloy Udimet 700 developed a sigma phase during prolonged elevated temperature service, which resulted in a decrease in rupture life and room temperature ductility [38]. Boesch et al. predicted σ phase formation based on electron holes and pioneered PHACOMP (an acronym for phase computation) in the design of superalloys [38,42]. The basic idea is to use the average electron vacancy number $\overline{N_v}$ in the alloy to predict and control the harmful phase precipitation in the nickel-based superalloy γ matrix phase. $\overline{N_v}$ is given by

$$\overline{N_v}=\sum _{i-1}^n{m}_i{\left(N_v\right)}_i$$

(1)

where $m_i$ is the atomic fraction of each element in an alloy and $N_v$ (see

Table 2. List of N_v for common elements in nickel-based superalloys. Adapted from Ref. [43].

Element	Cr	Co	Mo	W	Al	Ta	Re	Ru	Hf	Ni
Electron vacancy number	4.66	1.71	4.66	4.66	7.66	5.66	3.66	2.66	6.66	0.61

) is the number of electron vacancies in the metal d band of each element in an alloy. When the average number of electron holes is higher than a certain value (the critical value), the alloy tends to form a topologically close-packed (TCP) phase. In contrast, when the average electron hole number is lower than this value, the alloy does not form a TCP phase.

After deducting only the alloying element content consumed by the γ′ phase, the average number of electron holes in the remaining matrix is calculated according to the above formula, and the critical value is 2.32 [38]. In addition to this, after deducting the contents of various alloying elements consumed by the γ′ phase, borides, and carbides, the average number of electron holes is calculated for the remaining matrix components according to the above formula. By comparing the calculation and experimental results of more than 500 commercial and experimental alloys, it is found that the $\overline{N_v}$ critical value for forming the σ phase is 2.45~2.52 and that for forming the Laves phase is 2.30 [44]. A low-cost second-generation SC superalloy, DD6, has been developed with the help of PHACOMP. The value of the $\overline{N_v}$ of DD6 is 1.869, which is smaller than the critical value (2.32) for alloy microstructure stability while significantly reducing the cost [45].

The PHACOMP method can be used according to the predetermined working conditions to extract some aspects of the new alloy and then determine the content of some main alloying elements. The addition amounts of other elements can be determined through PHACOMP, which can keep the structure of the alloy stable while maintaining the performance requirements of the certificate owner and avoid the topological dense phase in service. However, this method also has its limitations, mainly due to its narrow application scope. It can only provide good results for nickel-based superalloys and has poor or even no effect on systems like cobalt-based and iron-based superalloys. Furthermore, the number of electron holes of individual elements varies with the composition. Factors like composition segregation in casting superalloys cannot be considered. It is not possible to predict the properties of the existing alloys only by estimating whether the brittle phase appears or not.

2.2. d-Electrons Concept

The d-electrons concept was developed by analyzing electronic structures through molecular orbital calculations [39,40,46]. Two alloying parameters have been identified through molecular orbital calculation ($DV$-$X_a$ cluster calculation) in relation to this concept. Two key electronic parameters are primarily used for designing alloys based on this principle. One factor is the bond strength between an alloying element and nickel atoms (hereafter referred to as $Bo$), while another is the d-orbital energy level of the alloying element (referred to as $Md$).

Table 3. List of $Md$ and $Bo$ for common elements in nickel-based superalloys. Adapted from Refs. [39,47].

Element		$\mathit{M}\mathit{d}$ (eV)	$\mathit{B}\mathit{o}$	Element		$\mathit{M}\mathit{d}$ (eV)	$\mathit{B}\mathit{o}$
3d	Ti	2.271	1.098	4d	Mo	1.550	1.611
	Cr	1.142	1.278		Ru *	1.006 *	-
	Mn	0.957	1.001	5d	Hf	3.020	1.518
	Fe	0.858	0.857		Ta	2.224	1.670
	Co	0.777	0.697		W	1.655	1.730
	Ni	0.717	0.514		Re	1.267	1.692
	Cu	0.615	0.272	Other	Al	1.900	0.533

* Courtesy of Pr. M. Morinaga.

lists the values of $Bo$ and $Md$ for each element in nickel-based superalloys. For an alloy, the average d values of $Bo$ and $Md$ are defined by calculating the compositional average, and $\overline{Bo}$ and $\overline{Md}$ are represented as follows:

$$\overline{Bo}=\sum x_i{·\left(Bo\right)}_i$$

(2)

$$\overline{Md}=\sum x_i{·\left(Md\right)}_i$$

(3)

where x is the atomic fraction of component $i$ in the alloy and ${\left(Bo\right)}_i$ and ${\left(Md\right)}_i$ are the $Bo$ and $Md$ values for component $i$, respectively.

The molecular orbital approach is highly important in creating and advancing nickel-based superalloys used in industrial turbine applications [39]. TUT series SC superalloys with properties comparable to the second-generation SC superalloys PWA1484 and CMSX-4 have been successfully designed using the d-electrons concept [48]. The theory has evolved to introduce a new concept of alloying vectors for d-electrons [49]. By utilizing this concept, a clear understanding of how the alloying elements are distributed between the γ and γ′ phases can be consistently achieved. Additionally, a nickel-based superalloy was developed using the d-electrons concept, with 5.4% Re and 3.8% Cr, showing superior creep rupture strength and resistance to high-temperature corrosion compared to the second-generation SC superalloy [40]. The study demonstrated the effectiveness and feasibility of applying the d-electrons alloy design concept to develop a high-performance, corrosion-resistant SC superalloy, showcasing its potential for designing better hot corrosion resistance in nickel-based superalloys [50,51,52].

Utilizing the d-electrons concept enhances the efficiency and precision of alloy design in contrast to current methods that rely on numerous empirical rules and trial and error experiments [49]. In contrast to the PHACOMP method, the d-electrons concept is more rigorous and more widely used, and it can predict the properties of designed alloys.

2.3. The Calculation of the Phase Diagram

Superalloys can gradually reach phase equilibrium at high temperature or medium temperature for a long time, so the study of the equilibrium microstructure at service temperature is of great significance for the design of superalloys. Phase diagrams play an important role in material design. With the improvement of the calculation method, database, and calculation software, the calculation method of phase diagram (CALPHAD) has become an important tool for the simulation of materials design, metallurgy, and the chemical industry, and the study of phase balance has really become a part of the material’s design. In most cases, CALPHAD utilizes the Gibbs energy or another appropriate thermodynamic state function. The Gibbs energy of a system can be used to determine a range of properties, such as the state of equilibrium in specific conditions, various stable and metastable phase diagrams, thermochemical and thermophysical properties, and the driving forces for reactions in systems that are not in equilibrium [53].

It is difficult to obtain reliable experimental results of the equilibrium phase for the multi-component system of a nickel-based superalloy. Therefore, the use of the phase diagram calculation method to analyze the precipitated phase in multi-component alloys and, on this basis, predict the physical properties of alloys has become the focus of research. The CALPHAD method has been widely utilized in computational design to create a stable and appropriate microstructure for nickel-based superalloys [54]. CALPHAD can provide information on phase fractions at equilibrium, solvus and solidus temperatures, lattice mismatches, and corrosion resistance [16,55,56,57]. Furthermore, as shown in Figure 5, CALPHAD is utilized in the development of nickel-based superalloys (Ni-Al-V-Nb-Cr systems) with stable D0₂₂ γ″ precipitation at high temperatures, and two specific alloys were experimentally validated through microstructure analysis to confirm the effectiveness of the CALPHAD design [54]. For a fixed concentration of Nb, increasing the addition of V can make δ disappear due to conversion to γ″. Using the CALPHAD method which is linked with the Gibbs free energy of the γ and γ′ phases in a nickel-based superalloy system (Ni–Al–Re–Ta) by a four-sublattice model, the phase-field method can be used to simulate multi-component diffusion in a nickel-based superalloy [58]. CALPHAD design techniques can assist in creating new nickel-based superalloys with high strength and long-term high temperature performance while also cutting down on the time and cost of experiments.

2.4. Regression Analyses Method

The multiple regression analyses method is based on regression formula rather than theoretical formula. The regression equation is a mathematical expression that quantitatively describes the statistical relationship between variables. In the design of a nickel-based superalloy, the design idea of the multiple regression method is reflected in the following steps: the regression equation is established on the basis of the experimental law and experimental parameters, the alloy’s composition is designed through the regression equation and the relevant mechanical properties are calculated, and, finally, the optimal alloy is selected. At present, this method has made great progress in application and is relatively mature.

By using regression analysis on the data provided, it became possible to calculate the phases of components and predict the properties of the alloys, and a system for designing alloys has been developed for nickel-base superalloys that harden through γ′ precipitation [59]. The schematic diagram illustrating the process of searching for alloys with specific properties is depicted in Figure 6. Around 100 alloys were created using the system and tested in various ways, with a few demonstrating favorable characteristics in terms of tensile strength, resistance to hot corrosion, or resistance to creep rupture. Subsequent regression analyses were conducted on the aforementioned alloy properties we created and tested, revealing a strong correlation with structural elements like alloy makeup, γ′ content, and γ′ composition. The resulting equations from the analyses have been utilized in alloy design to produce high-quality alloys.

The regression analyses method has been also used in the design of TMS series SC superalloys with excellent properties [60]. During the design process, the composition of the γ′ phase, except Ni and Al, was first determined, and then the composition of the γ′ phase was determined according to the empirical regression equation obtained from a large number of experiments [61]. Then, based on the experimental law and experimental parameters, the alloy’s composition was determined through a series of regression formulas, and the mechanical properties and related data of the alloy were calculated. Finally, the optimal single crystal alloy was selected.

If all data points are distributed near a line among a group of data of variables with correlation, it can be observed through the scatter plot. Multiple lines satisfying the above conditions can be drawn, and it is hoped that one of them can best reflect the relationship between variables. That is, it is possible to find a line that best reflects the characteristics of the known data points. The advantage of the regression analyses method is that when there is no obvious relationship between variables, it is easy to find the relationship between the performance to be predicted and the preset variables through linear regression analysis. However, it is too simplistic to assume a linear relationship between performance and composition when looking at actual data. At the same time, different elements may interact with each other, and a change in the content of one element may affect the relationship between the properties to be predicted and other elements. Therefore, the accuracy and reliability of the method in the design of nickel-based superalloy are lower than in theory due to various complex factors.

The National Institute for Materials Science (NIMS) has created an in-house program, NIMS-ADP, using statistical and systematic experiments to analyze a vast amount of data and develop fifth-generation nickel-based SC superalloys through multiple regression analysis [62]. Alloy designers can use this tool to determine compositions by adjusting various parameters, including the volume fraction of γ′, lattice misfit, the density of the alloy, the stability of phases, and creep rupture life. NIMS has effectively created several fifth-generation SC superalloys, including TMS-162, TMS-173, and TMS-196, with the assistance of NIMS-ADP, reaching a creep life of 1000 h at 1100 °C/137 MPa [62,63]. TMS-196 is a fifth-generation superalloy with increased levels of Re and Ru (6.4 wt.% Re and 5.0 wt.% Ru) for enhanced mechanical characteristics and improved oxidation resistance through the addition of Cr. Furthermore, as shown in Figure 7, TMS-238 was created with the assistance of NIMS-ADP to achieve mechanical characteristics comparable to TMS-196 while enhancing resistance to oxidation and hot corrosion by decreasing Mo and W contents and increasing Co and Ta contents [8]. TMS-238 stands out for its exceptional and harmonious mechanical and environmental characteristics compared to other superalloys currently available. The success of these instances demonstrates that using regression analysis is viable when designing nickel-based superalloys.

3. Key Factors of Composition Optimization in the Alloy Design Process

Due to the complex composition of nickel-based SC superalloys, many factors need to be considered in the process of alloy design, and it is necessary to discuss the influencing factors. Factors like creep resistance, microstructure characteristics, oxidation resistance, casting performance, density, and the cost of the alloy can establish the corresponding model, and the performance design index of the alloy can be obtained according to the specific requirements of the performance, while the result can be obtained through simulation calculation. In the following sections, the key factors for the design of nickel-based SC superalloys and the methods through which these key properties can be estimated are presented.

3.1. Creep Resistance

The creep fracture life is a crucial factor that indicates the mechanical characteristics of superalloys, serving as a key metric for evaluating their performance at elevated temperatures in various stages, such as alloy development, testing, and utilization. Creep properties depend on the degradation rate of the initial microstructures, which are highly influenced by external factors, such as temperature and stress, applied to the alloy. Due to the lack of clear definition of the composition dependence of the rate-controlling steps, there is currently no existing fundamental theory that can predict the creep resistance of superalloys based on an initial estimate of the chemical composition [16,64]. Instead, it is more common to use regression analysis and neural networks in the alloy design process [61,65,66]. As shown in Figure 8, the Bayesian neural network using Markov chain Monte Carlo (MCMC) methods successfully predicted the creep rupture life of SC superalloys, achieving a high multiple correlation coefficient (MCC) of 0.932 in a test using reserved data [66].

In addition to the above method, there is another way to simulate creep properties. As shown in Figure 9, the accumulation of creep strain was caused by the migration of dislocations through a process involving both climb and glide, with a significant thermally activated component [67]. Based on the above considerations, a merit index for creep resistance [16], denoted by $M_{creep}$, is given by

$$M_{creep}={\sum }_i{x}_i/{\tilde{D}}_i$$

(4)

where $x_i$ is the atom fraction and ${\tilde{D}}_i$ is the appropriate interdiffusion coefficient of solute $i$ present in the alloy. It is crucial to maximize the time to 1% strain in gas turbine engineering for practical reasons. The suggested merit index, $M_{creep}$, shows a favorable comparison with existing data on the time to 1% creep strain in various experimental SC superalloys [68,69]. The data confirm the feasibility of using $M_{creep}$ to describe creep properties in alloy design.

Creep deformation is associated with the development of rafted structures, which is observed as the directional coarsening of γ′ precipitates at high temperatures (over 1000 °C and even 1100 °C) [70,71]. At low stress levels, dislocation motion is limited within the matrix, with dislocations moving through the γ′ precipitates via climbing and gliding mechanisms [72]. The heightened dislocation movements within the matrix lead to the development of intricate dislocation networks, which will be discussed in detail in Section 3.2.2. Rafted structures significantly increase the length of γ channels for dislocation climbing. Therefore, the rate of creep may decrease to an extremely low value [73]. The secondary creep stage, known as the creep in this phase, is the most significant part of the entire creep life and considered a crucial factor influencing the creep life of SC superalloys. Re segregates strongly to the γ phase, where dislocation movements primarily occur. The addition of Re in the nickel-based SC superalloy of the second generation can slow down dislocation movements, resulting in improved resistance to creep and longer rupture life [32,74]. W and Mo have a large atomic radius, a slow diffusion rate, and high solid solution strengthening. They are the key alternative elements of Re. The coupling adjustment of W and Mo is expected to reduce the cost of alloy while maintaining creep resistance of the SC superalloys [75]. Increasing the resistance of dislocations moving into the precipitates is essential for improving the internal creep resistance of γ′ precipitates. Adding Ta and Ti to the alloy can effectively boost the anti-phase boundary energy, strengthening the γ′ precipitates against dislocations and enhancing the creep resistance of SC superalloys [76,77,78].

The microstructure evolutions occur during creep, and change begins with cuboidal γ′ precipitates and progresses to rafting during the incubation period, as illustrated in Figure 10. Following a period of incubation in the initial creep phase, the substance begins to deform gradually before the rate of creep strain accelerates continuously, until it reaches failure [79]. In the creep process, after complete γ′ rafting (see Figure 10 for t/tr > 0.15), when the ratio of t to tr is greater than 0.15, the rate of strain due to creep decreases significantly, indicating the start of the secondary creep stage. During the tertiary creep stage, the raft’s configuration is completely disrupted by a significant topological reversal, leading to sudden acceleration in the rate of strain accumulation. Because of the numerous γ′ precipitate interconnections (see the microstructure after t/tr = 0.60 in Figure 10), it is so massive that no rafts can be identified anymore by this time. The microstructure’s stability is closely related to misfit, which will be discussed in detail in Section 3.2.3. From the process of microstructure evolutions, the method to improve creep resistance in alloy design is to slow down the degradation of the γ/γ′ microstructure during creep, especially the rafting of γ′ precipitates. Accumulated plastic stains in γ channels promote rafting, and alloying elements, such as Re, W, and Mo, can help restrict dislocation movements, ultimately slowing down the plastic flow generation and rafting process. The addition of these elements will be considered as a key consideration in composition optimization.

3.2. Microstructure Characteristics

The initial microstructure of nickel-based SC superalloys is sensitive to the external conditions of temperature and stress acting on the alloy, and the degradation rate of the microstructure directly determines the creep properties of the alloy. It is clear that increasing stress and temperature on the alloy results in a quicker degradation rate and less creep life [80]. The design of the microstructure is an essential factor to obtain the best creep resistance, so consideration of microstructure stability plays a crucial part in the design of superalloys. This section provides a detailed discussion of three key microstructural features that affect the creep behavior of nickel-based SC superalloys, including the volume fraction of the γ′ phase, the lattice misfit of γ/γ′ phases, and the tendency to form TCP phases, all of which are influenced by the a function of alloy chemistry [16]. Predictions of multiphase, multi-component equilibria in nickel-based superalloys can be made using Thermo-calc software and the database [53,81,82].

3.2.1. Volume Fraction of the γ′ Phase

Dislocations find it difficult to penetrate the γ′ precipitate phase during creep deformation. Creep resistance is significantly influenced by the γ′ precipitate phase’s impenetrability, as dislocations are forced to move through the γ matrix via Orowan bowing [4]. A dynamic creep equation for precipitation-strengthened alloys has been developed based on the climb/glide particle bypass micro-mechanism, which helps with measuring the changes in dislocation and particulate microstructures as well as stress redistribution between the phases. The basic model of the creep deformation rate in nickel-based superalloys is given below [83]:

$$\dot{\epsilon }={\displaystyle \frac{1.6}{\overline{M}}}\rho \left(1-{\varphi }_p\right)[{\left({\displaystyle \frac{\pi }{4\varphi }}\right)}^{{\displaystyle \frac{1}{2}}}-1]c_j{D}_s\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}[{\displaystyle \frac{(\sigma -{\sigma }_i-{\widehat{\sigma }}_{net})b^2{\lambda }_p}{\overline{M}kT}}]$$

(5)

where $\overline{M}$ is the Taylor factor ($\widetilde{=}$3), $\rho$ means the mobile dislocation density, ${\varphi }_p$ and ${\mathsf{\lambda }}_p$ are the volume fraction and interparticle spacing of the γ′ phase respectively, $D_s$ is the volume diffusion coefficient, and $c_j$ is the dislocation line jog density. The above equation proves that the volume fraction of γ′ precipitates can affect the creep property of the alloy by influencing the creep rate.

Obviously, a significant proportion of the γ′ precipitated phase plays a crucial role in improving creep resistance. Al, Ti, and Ta have the ability to enhance the formation of the structured γ′ phase in SC superalloy [29,84]. Figure 11 shows the correlation between the volume fraction of the γ′ phase and the duration of creep rupture life. From Figure 11a, it is evident that the creep resistance does not consistently improve as the γ′ phase increases, and the volume fraction of γ′ precipitates must be carefully managed within a suitable range, typically between 60% and 70% for SC superalloys [5,85]. After the optimal value is reached, creep performance will begin to decline. In the SC superalloy of this study, the alloys with 0–60% γ′ phase have an almost homogeneous microstructure; however, there are inhomogeneities in the dendrite and interdendritic regions in the alloys with 80–100% γ′ phase [5]. The curves in Figure 11b show creep properties for the superalloy at l000 °C and 148 MPa as a function of the initial γ′ size, and the optimal initial size of the cuboids is ~0.5 μm [86,87]. Furthermore, the cuboidal shape shows the longest creep lifespan compared to other shapes. Hence, researchers must determine the best volume fraction and initial size of the γ′ phase during alloy design.

3.2.2. The Lattice Misfit of the γ/γ′ Phase Microstructure

The resistance to high temperatures of SC superalloy is determined by the coherence of the interfaces, typically characterized by lattice misfit [72,88]. High temperatures lead to the coarsening of the γ′ phase due to interfacial energy, influenced by coherency stress from lattice misfit [89]. The phase stability is significantly influenced by the variation in the γ/γ′ microstructure due to changes in lattice misfit. In the process of designing alloys, it is crucial that the γ′ phase is shaped in a strict cuboidal form to minimize strain energy and improve phase stability. However, the morphology of the γ′ phase does not regularly change with lattice misfit; an additional increase in misfit may result in the irregular coalescence of γ′ particles, causing a reversed spherical transformation and a decrease in creep strength [90,91]. The above relationship between lattice misfits and the shape of the γ′ phase prevalently exhibited in many other commercial superalloys and the smaller dislocation spacing was correlated with the larger absolute value of misfits (shown in Figure 12) [30,92,93,94].

Through the design of the alloy’s composition, the lattice misfit can be adjusted to obtain a more cuboidal γ′ morphology and produce large random stress in the matrix, which helps to impede the movement of dislocations and ultimately obtain better microstructure stability and creep resistance. As shown in Figure 13, there is a linear relationship between dislocation spacing and the minimum creep rate in these SC superalloys. Finer interfacial dislocation networks are better at preventing slip dislocations in the γ channel from getting close or breaking them [96,97]. Furthermore, as shown in Figure 14, the dislocation density is greater in TMS-138 compared to TMS-75(+Ru), which aligns with the strains seen in the creep curve shown in Figure 13. The significant lattice misfit in TMS-138 primarily contributes to the easier formation of γ/γ′ interfacial dislocation networks compared to TMS-75(+Ru). The impeccable γ/γ′ interfacial dislocation network in TMS-138 successfully hinders the movement of dislocations in the γ channels, thus preserving the rafted γ/γ′ structure [98]. This correlation between lattice misfit and high-temperature, low-stress creep strength is reaffirmed through the enhancement of superalloy TMS-162 achieved by augmenting the quantities of Mo and Ru present in TMS-138. Enhancing lattice mismatch is a successful strategy for enhancing the strength of superalloys during the alloy design process [30]. In combination with Figure 13 and Figure 14, it is concluded that with the increase in lattice misfit (absolute value), finer interfacial dislocation networks were formed to hinder the slip of the dislocation in the γ channel, resulting in a lower creep rate and increased creep life.

3.2.3. The Formation of TCP Phases

The presence of solid solution strengthening elements like Cr, Re, Mo, and W makes many contemporary nickel-based SC alloys thermodynamically unstable, leading to the formation of TCP phases [99]. The rapid increase of these elements in alloys speeds up the formation of the TCP phase, including σ phases, P phases, μ phases, and R phases [99,100,101,102,103,104]. Of all of the alloying elements in SC superalloys, Re intensively promotes the formation of TCP phases [105]. Re enhances the partitioning behavior of W and Cr, leading to higher supersaturation of TCP-forming elements and promoting the nucleation of TCP phases [106]. Both Mo and W have significant impacts on promoting the precipitation of the μ phase, with Mo also aiding in the formation of the P phase [107,108,109]. Mo improves the dispersion of Re, W, and Cr in the γ phase by affecting element segregation, with W specifically segregating at the γ/γ′ interface as the γ′ phase coarsens, ultimately resulting in the creation of TCP phases [107,110]. The main advantage of Cr is in aiding the formation of the σ phase and encouraging the growth of TCP particles instead of the nucleation of TCP phases [111]. Co helps reduce the segregation tendencies of Re, W, Mo, and Cr, and it is known to inhibit the formation of the TCP phase [112,113,114]. However, in some alloying systems, compared with Co-free alloys, the addition of Co leads to the precipitation of the TCP phase [115]. Co’s addition may increase the average electron vacancy number, $\overline{Nv}$, which increases the precipitation tendency of the TCP phase. The strong partitioning of Ru to the γ matrix results in a lower partitioning coefficient for refractory elements in the γ matrix, ultimately improving the stability of SC superalloys [35]. Controversially, many studies have found that reducing lattice misfit through the addition of Ru may enhance the formation of TCP phases [116,117]. Figure 15 summarizes the effects of the above elements on the TCP phases.

The presence of these refractory elements leads to the consumption of the strengthening elements and disruption of the original cross-networks in the surrounding area during the formation of the TCP phase [123]. Additionally, there is a significant discrepancy between the TCP phases and the γ phases, leading to the creation of elevated localized stress along the interfaces. The stress concentration in this case focuses on the interface area, facilitating the formation of micro-cracks near TCP phases under high temperatures. Moreover, the TCP phase may serve as an obstacle to the movement of dislocations within slip systems. Dislocations gather at the boundary of the TCP phase, leading to the formation and spread of micro-cracks along the TCP phase as the dislocations move [124]. The critical damage of the alloy is mainly caused by the serious nucleation and propagation of microcracks. As shown in Figure 16, near the TCP phases, researchers found dense microcracks and pores, confirming the negative impact of TCP phases on mechanical properties [118]. During service, when the damage accumulates to a certain extent, the alloy eventually breaks. Therefore, in the design of SC superalloys, suppressing the precipitation of the TCP phase is important to maintain the stability of the microstructure and the high-temperature properties of superalloys.

To describe the tendency of formation of the TCP phase in alloy design, various methods, such as the d-electrons concept [39,40,47] and phase computation [38,42], are used, which have been described in detail in Section 2.1 and Section 2.2. From the principle of TCP phase formation and the calculation process of these methods, it can be summarized that reducing the content of solid solution strengthening elements can effectively reduce the tendency of TCP phase precipitation.

3.3. Oxidation Resistance

The oxidation reaction of a nickel-based superalloy will inevitably occur when it is in service at high temperatures. During the service of nickel-based superalloys, a layer of anti-corrosion and anti-oxidation thermal barrier coating usually covers the surface [125,126,127,128,129]. However, after the thermal barrier coating is peeled off, the alloy will be directly exposed to oxidation and a corrosive environment. At ultra-high temperatures (800–1100 °C), the alloy will oxidize quickly, and the oxidized part will not only greatly decrease its mechanical properties but also become the source of defects and cracks more easily [130,131]. In addition, during the high-temperature service of turbine blades, the high-temperature gas in the channel inside of the blades can also produce internal oxidation. The oxidation resistance of SC superalloys in alloy design needs to be discussed. Therefore, the design of the nickel-based SC superalloy also needs to focus on improving the oxidation resistance and coordinating the oxidation resistance and mechanical properties [132]. Figure 17 shows the oxidation kinetics curves from the second generation to the fifth generation of SC superalloys [133]. It can be seen from isothermal oxidation curves at 750 °C that the oxidation rate of superalloys gradually increases from the second to the fourth generation and decreases again in the fifth generation of SC superalloys. As it can be seen from cyclic oxidation curves at 1100 °C, the amount of oxidative spalling gradually increased, while in the fifth generation the SC superalloy began to improve and the amount of oxidative spalling approached that of the second-generation SC superalloy. This shows that fifth-generation SC superalloys have better oxidation resistance.

The oxide layer structure of nickel-based superalloys is generally composed of three layers, as shown in Figure 18a. The outermost layer is NiO, the middle layer comprises some oxides of heavy metal elements and spinel phases (NiCr₂O₄, NiAl₂O₄, etc.), and the innermost layer is an oxide formed by Al elements [134]. The nominal composition of this alloy is as follows: 4.3 Cr, 9.0 Co, 2.0 Mo, 8.0 W, 7.5 Ta, 5.6 Al, 0.1 Hf, 2.0 Re, 0.5 Nb, and balanced Ni (mass fraction, %). Meanwhile, the oxidation mechanism model is presented in Figure 18b,c [135]. The structure of the oxide layer will be affected by the different composition of alloy elements or the different content of alloying elements. The oxidation reaction of superalloys slows down as Al₂O₃ forms [7,136,137,138,139,140]. It is evident that the stable Al₂O₃ oxide improves the oxidation resistance of nickel-based SC superalloys. In the composition of SC superalloys (Table 1), Al is added usually at a concentration of about 6 wt.% to guarantee the formation of Al₂O₃ protective oxide.

Similarly to Al, Cr is also a favorable element for the oxidation resistance of SC superalloys, which can form a relatively continuous oxide film and limit the diffusion of elements, thereby improving the oxidation resistance. These two elements have lower Gibbs free energy to form oxides; that is, the partial pressure of oxygen required to form oxides is lower, so they can react more easily with O. Due to the faster diffusion rate of the Cr element, it is more inclined to form oxides near the interface. In addition, when oxidized above 1000 °C, Cr may form volatile CrO₃, reducing the density of the oxide film and thus worsening the oxidation resistance of the alloy. It is observed that more holes were formed on the oxide’s surface due to the volatilization of CrO₃ [141]. The diffusion rate of Ta element is relatively slow, and it is mainly distributed near the interface of internal Al₂O₃ particles, which affects the growth of Al₂O₃ particles [142]. The addition of Ta can also reduce the number of holes in the inner oxide layer so as to obtain a high-density oxide layer and reduce the oxidation rate of the alloy [143]. The sixth-generation nickel-based SC superalloy TMS-238 is noteworthy for its impressive combination of resistance to creep and oxidation. This alloy is characterized by high Ta content, which helps reduce the usual decline in oxidation resistance seen in superalloys with a high concentration of refractory elements [8].

In addition to the oxidation reaction of alloying elements, SC superalloys also have oxidation behaviors, such as volatilization of oxides [144,145,146], solid reaction of oxides [147,148,149], and peeling of oxide layers [150,151,152]. Because of these behaviors, besides the above three elements (Al, Cr, and Ta), other elements can indirectly affect the oxidation resistance of the SC superalloy. Different elements may interact with each other, so it is difficult to elucidate the coupling of elements and design alloys with excellent oxidation resistance. It can be believed that the above-mentioned concerns are the key issues to be considered in the development of alloy design.

3.4. Castability

As for nickel-based SC superalloy, it is believed that the castability is controlled by resistance to freckling. The formation of freckles is facilitated by the lightening of the inter-dendritic liquid due to the partitioning of heavier elements into the dendrite cores [16]. Nevertheless, the castability model does impose restrictions on the development of innovative advanced alloys. The improved regression formulas for the solid–liquid distribution ratios of the key elements in freckle formation include, specifically, Ta, W, and Re. Increasing the overall Mo content in high-refractory nickel-based SC superalloy improves the casting performance of the alloy during solidification and decreases the micro-segregation of dense refractory elements W and Re [153]. Consequently, the following phenomenological equation is used to describe the castability of nickel-based SC superalloy:

$$M_{castability}={\displaystyle \frac{w_{Ta}+0.5w_{Mo}}{1.2w_{Re}+w_W}}$$

(6)

where $w_{Ta}$, $w_{Mo}$, $w_{Re}$, and $w_W$ correspond to the mean weight fractions of Ta, Mo, Re, and W, respectively, in the alloy.

The castability of the alloy improved with the increase of the $M_{castability}$ value. Therefore, the content of Ta and Mo elements can be increased appropriately and the content of Re and W element can be reduced under the premise of ensuring the phase stability and properties of alloys. The rise in Re and W content not only reduces the M value but also intensifies their partitioning to the solidifying material and that of Al to the liquid, ultimately reducing the solute of dense elements needed to prevent freckle formation [153]. It is not possible to simply increase the content of Ta or Mo to increase the $M_{castability}$ value. It is necessary to consider that the increase in Mo content will affect the microstructure stability of the alloy and promote the precipitations of the TCP phase. While increasing the Mo content, Ru can be considered to improve the microstructure stability of the alloy and inhibit TCP phase precipitation so as to improve the overall performance [63,99]. However, as shown in Figure 19, with the addition of Ru, γ′ was separated from the matrix, which created γ/γ′ eutectic, leading to an increase in the volume fractions of eutectic in dendrite regions [154]. Alloys containing a medium fraction of eutectic material are prone to hot cracking because of the lack of intergranular solid bridges and liquid feeding [155]. Therefore, in the alloy’s design, it is necessary to consider the synergistic effect of various elements on castability performance.

3.5. Density and Cost

With the increase in the content of refractory elements in the SC superalloys, the initial melting temperature of the alloy increases gradually. However, the increase in alloy density caused by the increase in refractory elements is not conducive to the enhancement of the thrust–weight ratio. At the same time, the high density will pose new challenges to the strength of the turbine disk. According to the design requirements of the engine blade, the alloy density used in the blade should be controlled within the theoretical limit. The density of pure nickel is 8.907 g/cm³, but the SC superalloys contain more than 10 alloying elements and have a high degree of alloying, and their density is obviously different from this value. The data for density are given in Figure 20a, and data for the density of a number of third-generation and fourth-generation SC superalloys shown in Figure 20 are distributed from 7.87 to 9.07 g/cm³ [16].

During the alloy design process, the density of a novel SC superalloy can be initially predicted by utilizing the pure element values according to a mixture rule. It should be noted that this technique underestimates the actual density by approximately 5% because of varying bonding properties [1]. Therefore, the correction factor needs to be taken into account, and, after using the correction factor, the density can be accurately estimated to within 1%.

The cost of an SC superalloy prototype is determined based on cost estimates of the raw elements employed. Due to the fluctuation of the market price of the metal element raw material, the cost of the alloy will also be affected by the trend of the metal market. The values used for the calculations are given in Figure 20c [16].

The data for the density, cost, and creep behavior of various third-generation and fourth-generation SC superalloys are shown in Figure 21. It can be seen that the creep resistance is related to the density and cost of the alloy, and it is clear that enhanced creep resistance is achieved through higher density (by increasing dense elements like Re), resulting in increased costs. Among them, the density of the high-generation SC superalloy even exceeds 9 g/cm³, and the cost is almost five times that of the lower-generation SC superalloy. This is mainly due to the addition of a large number of rare and refractory elements, such as Re and Ru, in high-generation SC superalloys. The sum of Re and Ru content even exceeds 11% in the fifth-generation nickel-based SC superalloys [62,63]. Therefore, considering the cost and density of SC superalloys, it is necessary to properly reduce the content of refractory elements in the design of alloys, thereby reducing the density and cost of alloys.

4. Summary and Perspective

4.1. Summary

After decades of development, the theoretical level of superalloy design has been greatly improved, and the properties of designed superalloys have also made great progress. The composition of nickel-based superalloy has also been updated and optimized many times. The summary of the important characteristics and design methods of composition optimization to obtain optimal performance in SC superalloys is shown in Figure 22. The details are summarized below.

• The design methods for composition optimization for superalloy mainly include PHACOMP, the d-electrons concept, CALPHAD, and the regression analyses method. One or more of the above design methods may be used in the composition design process of SC superalloys. With the help of these methods, many kinds of SC superalloys with excellent performance have been designed, such as TMS series, CMSX series, DD series, and so on.
• Analyzing how alloying elements affect the creep resistance, microstructure, oxidation resistance, castability, density, and cost of superalloys is essential in alloy design to narrow down the vast combination space to a few optimal compositions.
• In order to obtain better high-temperature performance, the content of refractory elements (Ta + Re + W + Mo) increased gradually during the composition evolution of nickel-based SC superalloys. Ru was added into the fourth-generation nickel-based SC superalloy to inhibit the formation of the TCP phase and maintain the stability of the microstructures [35,156]. In addition, the content of Cr decreased significantly and the content of Co gradually increased to further improve the structural stability of high-generation SC superalloys.
• The optimization process of alloy composition has focused more on the presence of antioxidant elements (Al, Cr, Ta) to enhance oxidation resistance while balancing mechanical properties. In the process of alloy design, the influence of Ta, Mo, Re, and W content on castability also needs to be considered. Considering the cost and density of SC superalloys, the content of refractory elements needs to be appropriately reduced in the alloy’s design without affecting the key properties.

4.2. Outlook and Perspective

In addition to composition, the factors that need to be considered in the design of alloys are very complex. Although the relationship between the composition, process, structure, and mechanical properties of superalloys has been deeply studied, there is no mature theory to describe their interaction, and there is no complete theory to explain the influence of elements on the physical and metallurgical properties of superalloys.

With the development of the aviation industry, especially the continuous improvement of thrust and thrust–weight ratio requirements for advanced aero engines, the turbine inlet temperature is forced to rise, which puts forward higher requirements for the temperature bearing capacity of superalloys. Researchers urgently need to apply new alloy design methods to design more excellent properties of superalloys and remove much of the traditional reliance placed on empiricism and testing, which is based on trial and error. Therefore, the focus of future research is to strengthen theoretical research on the microstructure of alloys on the basis of experiments and to study the physical and chemical behavior of the interaction between various alloy elements and its influence on the mechanical properties of alloys at high temperatures with the help of advanced computer technology.