Effect of Interactions Among Elements on Diffusion Process Associated with γ′ Coarsening in a Ni-Based Single-Crystal Superalloy

doi:10.1007/s40195-020-01009-z

Abstract

Abstract:

Coarsening of cuboidal γ′ precipitates and relevant diffusion process in Ni-based single-crystal superalloy CMSX-4 were investigated at 1000, 1020 and 1040 °C for specific times. The γ′ coarsening kinetics followed a cubic rate law with time and was presumably controlled by bulk diffusion of elements in γ matrix. The associated diffusion activation energy was experimentally determined to be about 300 kJ/mol when it is considered the temperature-dependent thermo-physical parameters in modified Lifshitz-Slyozov-Wagner theory. The influence of temperature on γ/γ′ microstructure is briefly discussed based on pseudo-binary [Ni]-[Al] phase diagram. Interactions among elements can effectively raise the local vacancy formation and vacancy-atom exchange barriers close to γ- and γ′-partitioning elements, respectively. Thus, it can significantly reduce the inter-coupling migrations of atoms during the macroscopic cross-diffusion process associated with γ′ coarsening of Ni-based superalloys.

Key words: Ni-based superalloy, Coarsening kinetics, Diffusion activation energy, Elemental interaction

Guang-Lei Wang, Dong-Qing Qi, Ji-De Liu, Jin-Lai Liu, Yi-Zhou Zhou, Xu-Dong Sun, Hai-Feng Zhang, Xiao-Feng Sun. Effect of Interactions Among Elements on Diffusion Process Associated with γ′ Coarsening in a Ni-Based Single-Crystal Superalloy[J]. Acta Metallurgica Sinica (English Letters), 2020, 33(7): 1013-1020.

Figures/Tables 10

Table 1 Isothermal exposure experiments of CMSX-4 alloy

Temperature (°C)	Time (h)
1000	260	284	304	352
1020	210	234	260	304
1040	170	194	210	260

Fig. 1 SEM micrographs of γ/γ′ microstructure: a, d, g, j 1000 °C; b, e, h, k 1020 °C; c, f, i, l 1040 °C

Fig. 2 Evolutions of γ′ precipitates with temperature and time: volume fraction a and average size b

Fig. 3 Comparisons between square a and cubic b rate laws of γ′ coarsening

Table 2 Fitting parameters of cubic and square rate laws

Temperature (°C)	Square rate law	Cube rate law
1000	0.9639	0.9739
1020	0.9645	0.9807
1040	0.9887	0.9970

Table 3 A(Vγ′), σ, Nα and Vm at various temperatures [17, 29, 39, 40]

Temperature (°C)	A(V_γ′)	σ (mJ/m²)	N_α	V_m (cm³/mol)
850	19.42	84.51	0.4555	7.21
900	18.96	82.84	0.4460	7.23
925	18.67	82.00	0.4415	7.25
950	18.35	81.19	0.4370	7.26
1000	17.28*	79.51	0.4274	7.28
1020	16.85*	78.83	0.4237	7.29
1040	16.20*	78.16	0.4199	7.30

Fig. 4 Comparison of Da, D0b, Qeffc values finely estimated from this paper and Ref. [16], D values of Re in Ni included in d [41]

Table 4 Values of r, D0 and Q of solute in Ni [40,41,42]

Solute	r (nm)	D₀ (m²/s)	Q (kJ/mol)
Cr	0.128	2.42 × 10^-4**	280**
Co	0.126	3.30 × 10^-4**	294**
Al	0.143	1.69 × 10^-4**	257**
Ti	0.146	1.10 × 10^-4**	259**
Ta	0.147	2.19 × 10^-5; 7.05 × 10^-5*	251; 267*
Hf	0.159	1.91 × 10^-4**	252**
Mo	0.140	2.01 × 10^-4**	282**
W	0.141	8.0 × 10^-6; 6.77 × 10^-5*	264; 288*
Re	0.138	8.2 × 10^-7; 8.67 × 10^-6*	255; 285*
Ni	0.125	5.64 × 10^-8**	265**

Fig. 5 Schematic drawing of pseudo-binary [Ni]-[Al] phase diagram

Fig. 6 Schematic drawing of microscopically directional migration of Al a, b and Re c, d atoms in terms of probability

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