Coarsening kinetics of γ′ precipitates in a Re-containing Ni-based single crystal superalloy during long-term aging

doi:10.1016/j.jmst.2020.05.034

Abstract

Abstract:

The morphological evolution and coarsening kinetics of γ′ precipitates in a Re-containing Ni-based single crystal superalloy were investigated during isothermal aging at 900, 950 and 1000 °C. After heat treatment, well-defined cuboidal γ′ precipitates with low misfit was obtained within the experimental alloy. Then coarsening rate constants and particle size distribution (PSD) of γ′ phases were calculated and specified based on the measured precipitate sizes for varying periods of aging times from 100 to 2000 h. After aging for 2000 h, γ′ precipitates maintained cubical shape at 900 °C, while exhibited sphere at 950 and 1000 °C. Coarsening models based on diffusion-controlled process with a functional relationship of r³ vs. t (classic Lifshitz-Slyozov-Wagner coarsening model) and interface-controlled model with a function of r² vs. t (trans-interface diffusion-controlled coarsening model) were investigated to fit between the experimental results and theoretical analysis. It was found that Re as the slowest diffusing solute in the alloy constituted the rate-limited step for coarsening based on LSW model, while the process limiting coarsening as governed by an interface diffusion process could possibly be related to the Al diffusion through the γ/γ′ interface. The PSDs and coarsening exponent were discussed by comparing the experimental data with predictions of LSW and TIDC models. Finally, coarsening mechanism could be divided into four regimes: (i) coarsening by diffusion-controlled; (ii) coarsening by diffusion and interface co-controlled; (iii) coarsening by interface-controlled; (iv) coarsening by interface-controlled accompanied with γ′ coalescence.

Key words: Precipitate coarsening, Three-dimensional atom probe (3DAP), Interfacial energy, Diffusion, Particle size distribution, Ni-base single crystal superalloys

Jiachen Zhang, Lin Liu, Taiwen Huang, Jia Chen, Kaili Cao, Xinxin Liu, Jun Zhang, Hengzhi Fu. Coarsening kinetics of γ′ precipitates in a Re-containing Ni-based single crystal superalloy during long-term aging[J]. J. Mater. Sci. Technol., 2021, 62: 1-10.

Figures/Tables 15

Fig. 1. (a) The typical microstructure revealed by TEM with an inset selected-area electron diffraction pattern taken along the [100] zone axis. (b) The X-ray diffraction peak (asymmetric (400) plane reflection) revealing two overlapping peaks corresponding to γ and γ′ phases. (c) The normalised PSD for γ′ precipitates is in comparation with the predictions of the LSW model (black solid line) and the TIDC model (red dashed line).

Fig. 2. (a) APT reconstruction of the tip from the alloy sample after heat treatment. (b) The compositional profile across the γ/γ′ interface for the solutes Mo, Ti, Cr, Al, W, Ta, Co, Re. The compositional width of the interface, measured according to Cr concentration distribution, has been marked.

Table 1 Elemental concentration distribution in γ/γ′ phases of the alloy (atomic fraction, at.%).

	Cr	Co	Mo	Re	Al	Ti	Ta	W	Ni
γ	24.47	14.15	0.86	1.8	2.94	0.63	0.21	2.03	52.91
γ′	2.42	4.12	0.38	0.11	14.58	4.68	2.27	1.92	69.5

Fig. 3. γ′ microstructure evolution in the alloy subjects to isothermal aging periods of 100, 200, 500, 1000 and 2000 h at 900, 950 and 1000 °C. γ′ precipitates coalescence is labelled by green dotted circle.

Fig. 4. The temporal changes of: (a) average size of γ′ precipitates and (b) volume fraction of γ′ precipitates.

Fig. 5. The evolution of scaled PSDs for γ′ precipitates compared with the prediction of the LSW model (black solid line) and the TIDC model (red dashed line).

Table 2 Measured lattice misfit magnitude, |δ| at 900 °C, 950 °C and 1000 °C by high resolution XRD, the X-ray diffraction peaks are not shown here.

T (°C)	HT (%)	2000 h (%)
900	0.146	0.139
950	0.178	0.152
1000	0.221	0.181

Fig. 6. Plot showing linear fit of average precipitate size (r3, in nm3) vs aging time (t, in s) during isothermal aging at 900, 950 and 1000 °C. The corresponding LSW rate constant (K, in nm3·s-1) and coefficient of determination (R2) are also labelled.

Table 3 Coarsening rate K calculated by coarsening exponent, parameters from Al and Re. The diffusivity of Al and Re at corresponding temperatures (°C) are also calculated according to equations from Janssen [13] and Karunaratne [33].

T (°C)	K (nm³ s^-1)	D_Al (m² s^-1)	K_Al (nm³ s^-1)	D_Re (m² s^-1)	K_Re (nm³ s^-1)
900	3.18	7.6×10^-16	28.64	3.6×10^-18	4.33
950	12.76	2.3×10^-15	63.47	1.1×10^-17	10.92
1000	42.57	6.8×10^-15	112.63	2.8×10^-17	21.5

Fig. 7. Plot showing linear fit of average precipitate size (r2, nm2) vs aging time (t, s) during isothermal aging at 900, 950 and 1000 °C. The corresponding TIDC rate constant (k, in nm2·s-1) and coefficient of determination (R2) are also labelled.

Table 4 Values of the “effective” diffusion coefficient $\tilde D$, calculated by the Eq. (12), compared with diffusion coefficient of Al in Ni and Ni3Al calculated by the equations from Janssen [13] and Ikeda [12], respectively.

T (°C)	$\tilde D$ (m² s^-1)	D in Ni (m² s^-1)	D in Ni₃Al (m² s^-1)
900	8.85×10^-17	7.61×10^-16	6.47×10^-17
950	3.73×10^-16	2.38×10^-15	2.33×10^-16
1000	1.34×10^-15	6.81×10^-15	7.56×10^-16

Fig. 8. PSDs for Ni-Al-Cr-Re aged for 0 h (a) and 264 h (b) at 800 °C [40], PSDs for investigated alloy for HT state (c) and aged for 500 h, 1000 h, 2000 h at 950 °C.

Table 5 Duration of each stage at different temperatures, determined by PSDs evolution.

T (°C)	Stage i (h)	Stage ii (h)	Stage iii (h)	Stage iv (h)
900	Before HT	0-1000	1000-2000	-
950	Before HT	0-500	500-1000	1000-2000
1000	Before HT	0-200	200-500	500-2000

Fig. 9. Plot of log(rt/r0) vs. log(t) for aging at 950 °C of experimental alloy, the inverse of the temporal growth exponents is also marked.

Fig. 10. (a) SEM images for experimental alloy after homogenized at 1300 °C for 24 h followed by water quench, (b) the corresponding PSD for experimental alloy before HT stage.

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