# Characterization of γ′ Precipitates in Cast Ni-Based Superalloy and Their Behaviour at High-Homologous Temperatures Studied by TEM and in Situ XRD

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## Abstract

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## 1. Introduction

_{3}, Ni

_{2}Al

_{3}, NiAl

_{9}and, the most important, Ni

_{3}Al) [1,2,3,4,5,6]. The γ matrix of superalloys is strengthened by coherent γ′ phase, possessing an ordered L1

_{2}structure. Taking into account operation at high temperature, the volume fraction, misfit, coarsening rate and antiphase boundary energy (related to the chemical composition) of the γ′ precipitates plays an important role [7,8,9]. Ordering of the γ′ phase is dependent on the strictly defined location of Al and Ni atoms in its crystal lattice, which influences further behaviour during high temperature exposure and deformation. Ni

_{3}Al is very rigid and impedes dislocation movement from the γ matrix, ensuring required strength under operation conditions. High degree of directional, covalent bonding (molecular bonds) leads to the accurate stoichiometric relation between the number of Al and Ni atoms in the unit cell. In Ni

_{3}Al crystal structure, Ni-Al, rather than Ni-Ni and Al-Al, chemical bonds are favoured [10]. Distance between Ni and Al atoms is calculated as $\sqrt{2}a$, therefore Al is preferentially substituted by large atoms. The alloying elements Ti, Ta, Nb and Pt are γ′ formers and dissolve in the γ′ phase. The second group is γ stabilisers, namely Co, Cr, Mo, Re, Ru and Ir [11]. The lattice misfit parameter and the volume fraction of the γ′ phase in the matrix are among the most important microstructural features, which have a strong effect on the dislocation density and evolution rate of dislocation networks, and consequently the creep life of superalloys [12,13,14,15,16,17,18]. The misfit parameter is usually defined as $\mathsf{\delta}=\frac{2({\mathrm{a}}_{{\mathsf{\gamma}}^{\prime}}-{\mathrm{a}}_{\mathsf{\gamma}})}{{\mathrm{a}}_{{\mathsf{\gamma}}^{\prime}}+{\mathrm{a}}_{\mathsf{\gamma}}}$, where a

_{γ}and a

_{γ′}are lattice parameter of the γ and γʹ phases, respectively [19,20].

_{L}) a lower lattice misfit reduces γ/γ′ interface energy, which maximises phase stability and decreases coarsening kinetics. Since the distance between the γ′ precipitates is usually less than 0.1 μm, the γ matrix never attains its strain-free (equilibrium) lattice parameter. So, the misfit measured for the standard heat treatment condition (solution + ageing), with a fully coherent γ′ phase, is not the equilibrium value, but a constrained value for the superalloy [23,24,25]. The start temperature of γ′ dissolution (T

_{sd}) for Inconel 738, determined by Zla [26] by differential thermal analysis, was reported to be between 914 and 957 °C, depending on the heating rate, and for Inconel 792, Strunz [27] showed T

_{sd}to be below 900 °C. In PM Astroloy, the start of dissolution occurred between 800 and 850 °C [28]. Sponseller [29] calculated γ′ solvus temperature (T

_{s}) for some superalloys to be between 1189 °C (equiaxed René 95) and 1307 °C (CMSX-2), and so the interval was also relatively wide. Critical temperatures are not constant and strongly dependent on the heating rate, as confirmed by Soucail [28]. The most outstanding feature concerns the large deviation for the solvus temperature. Under equilibrium conditions, it was 1140 °C, whereas heating at 300 °C s

^{−1}caused a displacement up to 1265 °C.

## 2. Experimental Procedure

^{2}). Each image was subjected to binarisation and a despeckle filter, which removed noise without blurring edges. The area (A) and perimeter (P) of each precipitate in a range of 0.06–5.0 μm

^{2}were measured. Based on these values, the equivalent length of the square’s side of precipitates (square root of precipitates’ area) and shape factor $(\mathsf{\xi}=\frac{4\mathsf{\pi}\mathrm{A}}{{\mathrm{P}}^{2}}$) were determined. Specimens for transmission electron microscopy were firstly ground mechanically to a thickness of about 0.05 mm, and then 3 mm discs were punched and dimpled on each side. The last step was thinning by Ar

^{+}ion beam (PIPS of Gatan). The probe Cs-corrected FEI Titan

^{3}G2 60-300 with a ChemiSTEM system (Thermo Fisher Scientific) was used to obtain nanostructure and chemical composition of the γ matrix and γ′ precipitates. Based on TEM images, the stereological parameters of nanoprecipitates of γ′ in the thin channel matrix were determined. High resolution images were subjected to fast Fourier transformation (FFT), to reveal the position of diffraction peaks. Segregation coefficient of alloying elements between matrix and γ′ was calculated according to the equation ${\mathrm{k}}_{\mathsf{\gamma}\prime}^{\mathrm{i}}=\frac{{\mathrm{C}}_{\mathsf{\gamma}\prime}^{\mathrm{i}}}{{\mathrm{C}}_{\mathsf{\gamma}}^{\mathrm{i}}}$ (concentration of alloying element in the γ′ precipitates divided by concentration in channels of matrix). X-ray diffraction experiments were carried out on a Philips X’Pert Pro MRD diffractometer, (Philips, Amsterdam, Netherlands) using Cu K

_{α}radiation in Bragg-Brentano geometry. High temperature measurements were realised on samples placed on the platinum strip in the heating chamber (Anton Paar HTK16). The samples were wire cut from the blade holder part into rods with a diameter of 6 mm and subsequently sliced and polished into discs with a thickness of 30 μm. Specimens were heated at a rate 100 °C/min, held for 30 s in order to homogenise the temperature in the sample volume, and then the diffraction measurement was started. The in situ study was realised for four temperatures: 1100 °C, 1150 °C, 1200 °C and 1250 °C. To record the high temperature time-resolved processes, samples were measured repeatedly at a narrow interval of 2ϴ between 41.5° and 46.5° to capture the (111) peak from the superalloy and the (200) peak from the Pt plate. Collected data were fitted by well-known procedures using the pseudo-Voigt profile function to determine the structure parameters. The angles were read off from the positions of the peaks on a diffractogram and the interplanar spacings d

_{khl}were calculated using the Bragg-Wulff equation (Equation (1)). Based on the computed lattice parameter of matrix a

_{γ}and precipitates a

_{γ′}(Equation (2)), the misfit parameter was determined. The thermodynamic simulations using Thermo-Calc software (version 2020a, Thermo-Calc software, Solna, Sweden) (database TCNI6:Ni-Alloys) were carried out, in order to calculate the maximum solubility of γ′ formers in the Ni matrix with an increase of the test temperature.

## 3. Results and Discussion

#### 3.1. Characterisation of γ and γ′ Phases Structure in the Initial Condition

^{2}(±0.82 μm

^{2}) and their perimeter 3.51 μm (±3.42 μm). The size of precipitates expressed as equivalent length of the square’s side was 0.61 μm (±0.44 μm). All the calculated values were presented as a histogram with fitted curves (Figure 3). Three classes of precipitates are shown, large secondary γ′ (the mean size 1.0 μm-pink curve), fine secondary γ′ with near-cubic morphology (the mean size 0.4 μm-green curve) and also the largest amount of tertiary γ′ precipitates in wide channels (the mean size 0.22 μm-blue curve). The stereological parameters of tertiary γ′ nanoprecipitates were investigated on TEM images. In accordance with the shape factor equation $(\mathsf{\xi}=\frac{4\mathsf{\pi}\mathrm{A}}{{\mathrm{P}}^{2}}$), the precipitates with a perfectly cubic shape have a coefficient of ζ 0.785, while the ideal sphere exhibits ζ of 1.0. The shape factor of γ′ precipitates was 0.51, indicating a much more complex geometry than a perfect cube. The standard deviations of the parameters were relatively high, due to the large diversity in particle area, which is typical for many equiaxed superalloys, in contrast to the single crystal variant [1,2]. It is related to the various chemical compositions, period of formation and also interfacial stresses.

_{2}structure of the γ′ phase, the {100}, {110} and {010} superlattice reflections are also present. It confirmed that a distinct cube-cube orientation relationship exists between the γ′ precipitates and γ matrix. Crystallographic relationship can be represented by: {100} γ//{100} γ′; <010> γ//<010> γ′, which is referred to as the cube-cube orientation relationship.

^{2}(±0.005 μm

^{2}) and mean perimeter 0.359 μm (±0.101 μm). The size of the precipitates, defined as the equivalent length of the square’s side of γ′ precipitates, was 0.095 μm (±0.026 μm). Shape coefficient factor ζ indicated that this value is much closer to unity namely, 0.877 (±0.069). Distribution maps revealed strong segregation of alloying elements, therefore, they can be clearly divided into γ′ formers and γ strengtheners. In order to get more accurate statistics about difference in chemical composition of precipitates and matrix, a quantitative analysis in several regions of the superalloy was carried out. The concentration of alloying elements in secondary γ′ precipitates in the dendritic regions and interdendritic spaces, primary γ′ precipitates and the γ matrix was determined by STEM-EDX (Figure 7a). No results from tertiary γ′ nanoparticles are presented, due to the overlapping from precipitates and matrix.

^{i}

_{γ′}values lower than 1, hence, they enriched the γ matrix channels. Chromium was the most segregated between the two phases, while values close to 1 were found for W and Ni, which indicates a relatively even distribution in the volume. The atomic radius of Ni is 1.49 Å, while for the strengtheners, the radii are bigger: for Co, the atomic radius is 1.52 Å, for Cr: 1.66 Å, for Mo: 1.90 Å, and for W: 1.93 Å [36]. The solid solution elements Cr, W and Mo strengthen the γ phase by increasing the solidus temperature and decreasing the stacking fault energy, which, in turn, influences the thermodynamic stability and the resistance towards dislocation movement [1]. The intermetallic γ′ phase was enriched in elements characterised by the k

^{i}

_{γ}factor above 1, namely Ta, Ti, Al and Hf, for which mean k

^{i}

_{γ}strongly exceeded unity, being 3.64–8.09. Alloying elements in the γʹ phase alter the formation energies of antiphase boundaries, superlattice intrinsic stacking faults and complex stacking faults, and may also directly influence the strength and plasticity of the γʹ phase [37,38].

#### 3.2. Dissolution of γ′ Precipitates Studied by in Situ X-Ray Diffractometry

_{γ}and a

_{γ′}are lattice parameters of the γ and γʹ phases, respectively. The dependence of the misfit parameter on the time of temperature exposure has an increasing trend at the studied temperatures (Figure 9d). Then, the γ′ phase lattice parameter changed only slightly with time, whereas the lattice parameter of the matrix increased with temperature and rapidly with exposure time. An exception was at 1100 °C, when the lattice parameter of the matrix grew quite slowly, and the relative change at the beginning and after last measurement ∆a

_{γ}was 2.50 × 10

^{−4}nm. For the temperatures 1150 °C, 1200 °C and 1250 °C ∆a

_{γ}was 4.35 × 10

^{−4}, 7.81 × 10

^{−4}and 12.90 × 10

^{−4}nm, respectively. Increase in the misfit parameters was closely related to the dissolution of the precipitates, change of chemical composition and probably the loss of a coherent interface. Too high misfit value also has a negative effect on the mechanical properties, because it increases the coarsening rate of the γ′ precipitates [8].

## 4. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Inhomogeneous microstructure of René 108 superalloy: (

**a**) dendritic structure; (

**b**) precipitates in dendritic regions; (

**c**) precipitates in interdendritic spaces.

**Figure 2.**Microstructure of γ′ precipitates in dendritic region: (

**a**) distribution of large secondary γ′ precipitates; (

**b**) tertiary γ′ precipitates in channels of γ matrix.

**Figure 4.**Morphology of γ′ precipitates: (

**a**) interdendritic spaces; (

**b**) detailed morphology of primary γ′ precipitates in interdendritic spaces.

**Figure 5.**Interface γ/γ′: (

**a**) γ and γ′ phases structure in atomic scale resolution, zone axis [001]; (

**b**), (

**c**) diffraction peaks of γ and γ′ calculated by fast Fourier transformation (FFT).

**Figure 6.**STEM-EDX mapping comprising both dendritic regions and interdendritic spaces: (

**a**) selected region for the STEM-EDX mapping; (

**b**–

**f**) distribution of selected alloying elements in the γ matrix and γ′ precipitates.

**Figure 7.**Results of quantitative STEM-EDX analysis of γ′ precipitates and γ matrix: (

**a**) chemical composition of the γ′ precipitates and γ matrix; (

**b**) segregation coefficient k

^{i}

_{γ′}: the calculation based on the concentration of alloying elements.

**Figure 8.**Normalised (111) peak shape evolution during exposure at: (

**a**) 1100 °C; (

**b**) 1150 °C; (

**c**) 1200 °C; (

**d**) 1250 °C.

**Figure 9.**Influence of exposure time and temperature on: (

**a**) time-temperature-transformation diagram; (

**b**) lattice parameter of γ phase; (

**c**) lattice parameter of γ′ phase; (

**d**) misfit parameter (δ).

**Table 1.**Change of equilibrium solubility of selected γ′ formers in Ni matrix with increasing temperature calculated by Thermo-Calc software.

Element | 1100 °C | 1150 °C | 1200 °C | 1250 °C | ||||
---|---|---|---|---|---|---|---|---|

wt.% | at.% | wt.% | at.% | wt.% | at.% | wt.% | at.% | |

Al | 8.57 | 16.94 | 9.0 | 17.71 | 9.38 | 18.38 | 9.85 | 19.20 |

Ti | 10.79 | 12.92 | 11.38 | 13.60 | 11.98 | 14.30 | 12.65 | 15.08 |

Ta | 17.08 | 6.27 | 18.52 | 6.87 | 20.19 | 7.58 | 22.28 | 8.51 |

Hf | 2.58 | 0.86 | 3.24 | 1.09 | 3.67 | 1.24 | 2.98 | 1.00 |

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**MDPI and ACS Style**

Rakoczy, Ł.; Milkovič, O.; Rutkowski, B.; Cygan, R.; Grudzień-Rakoczy, M.; Kromka, F.; Zielińska-Lipiec, A. Characterization of γ′ Precipitates in Cast Ni-Based Superalloy and Their Behaviour at High-Homologous Temperatures Studied by TEM and in Situ XRD. *Materials* **2020**, *13*, 2397.
https://doi.org/10.3390/ma13102397

**AMA Style**

Rakoczy Ł, Milkovič O, Rutkowski B, Cygan R, Grudzień-Rakoczy M, Kromka F, Zielińska-Lipiec A. Characterization of γ′ Precipitates in Cast Ni-Based Superalloy and Their Behaviour at High-Homologous Temperatures Studied by TEM and in Situ XRD. *Materials*. 2020; 13(10):2397.
https://doi.org/10.3390/ma13102397

**Chicago/Turabian Style**

Rakoczy, Łukasz, Ondrej Milkovič, Bogdan Rutkowski, Rafał Cygan, Małgorzata Grudzień-Rakoczy, František Kromka, and Anna Zielińska-Lipiec. 2020. "Characterization of γ′ Precipitates in Cast Ni-Based Superalloy and Their Behaviour at High-Homologous Temperatures Studied by TEM and in Situ XRD" *Materials* 13, no. 10: 2397.
https://doi.org/10.3390/ma13102397