Phase-field simulation of early-stage kinetics evolution of γ' phase in medium supersaturation Co-Al-W alloy

doi:10.1016/j.jmst.2020.02.038

Abstract

Abstract:

The early precipitation of γ'-Co₃(Al, W) phase affects the spatial distribution and kinetic evolution of precipitates for the morphology transmission effect, but the nucleation and concomitant growth are not studied still by aging experiments due to the expeditious precipitation of γ' phase in Co-Al-W alloy. By using the phase-field simulation with sublattice free energy, the early-stage kinetics evolution of γ'-Co₃(Al, W) phase in a medium supersaturation Co-9Al-8W (at.%) alloy aged from 1023 K to 1173 K is investigated. The influences of aging temperature on the evolution of morphology and composition of γ' phase, and the kinetics of nucleation and growth to coarsening are clarified. It is found that the rates of composition evolution of W in γ phase are two or three times that of γ' phase, and the W compositions in γ and γ' phases show a linear relationship with time t^-1/3, which means that the coarsening takes place earlier at high temperature. In addition, the equilibrium partitioning ratios indicate Al and W partition into the γ' phase and the ratios decrease with elevated temperature. The compositional variations across the γ/γ' phase interfaces suggest that low aging temperature makes the stoichiometric ratio closer to 3:1. Moreover, the precipitation evolutions from early nucleation to growth and coarsening in Co-Al-W alloy are distinguished, and the rate constants of square and cube of average particles radius increase with temperature. In later growth stage, the relationship of the square of average particles radius and time is obeyed, while the steady-state coarsening stage follows the cube law. The time exponents of particles number density at the coarsening stage are close to -1 of Kuehmann-Voorhees (KV) theory. The study demonstrates that the early-stage evolution of γ' phase which is undiscovered in the experiment can be captured by the phase-field simulation, and the resultant kinetics laws agree well with the experimental and theoretical results.

Key words: Early precipitation, Kinetics, Co-Al-W, Phase-field

Shujing Shi, Zhengwei Yan, Yongsheng Li, Suleman Muhammad, Dong Wang, Shi Chen, Shengshun Jin. Phase-field simulation of early-stage kinetics evolution of γ' phase in medium supersaturation Co-Al-W alloy[J]. J. Mater. Sci. Technol., 2020, 53: 1-12.

Figures/Tables 13

Fig. 1. Morphology evolution of γ' phase with aging time at different temperatures: (a-d) 1023 K; (e-h) 1073 K; (i-l) 1123 K; (m-p) 1173 K.

Fig. 2. The early composition evolution of elements (a) Co, (b) Al and (c) W with aging time in the vicinity of the γ/γ' phase interfaces at 1123 K, x* = 125-135, y* = 212.

Table 1 Solute depletion (-) or retention (+) in the matrix near the γ/γ' phase interfaces at 1123 K (at.%).

Element	0.05 h	0.08 h	0.17 h	0.25 h	0.27 h
Co	+ 0.51	+ 0.65	+ 0.82	+ 0.58	+ 0.08
Al	- 0.18	- 0.21	- 0.25	- 0.16	- 0.02
W	- 0.33	- 0.44	- 0.57	- 0.42	- 0.06

Fig. 3. The composition evolutions of W in γ and γ' phases at (a, b) 1023 K, (c, d) 1073 K, (e, f) 1123 K and (g, h) 1173 K.

Fig. 4. Concentrations of Al, W and order parameter profiles throughout the γ' phases with coordinates and temperatures: (a) x* = 109, y* = 153-178 at 1023 K; (b) x* = 215-237, y* = 135 at 1073 K; (c) x* = 215-240, y* = 87 at 1123 K; (d) x* = 82-99, y* = 46 at 1173 K, t = 6.67 h.

Table 2 The equilibrium partitioning ratios $K_{\gamma '/\gamma}^{\text{eq}}$ of Co, Al and W in Co-9Al-8W (at.%) alloy at different temperatures.

Element	1023 K	1073 K	1123 K	1173 K
Co	0.84	0.86	0.88	0.91
Al	1.50	1.39	1.33	1.24
W	3.67	3.21	2.58	2.06

Fig. 5. Equilibrium compositions of (a) Co, (b) Al and (c) W through γ/γ' phase interfaces at t = 6.67 h, x* = 115, y* = 210-226 at 1023 K; x* = 104-120, y* = 140 at 1073 K; x* = 48-64, y* = 21 at 1123 K and x* = 201-217, y* = 205 at 1173 K. The green solid point represents the inflection point with W concentration.

Fig. 6. Evolution of the particles number density of γ' phase with aging time in Co-9Al-8W (at.%) alloy aged at (a) 1023 K, (b) 1073 K, (c) 1123 K and (d) 1173 K.

Fig. 7. Variations of $<r>$, $<r{{>}^{2}}$ and $<r{{>}^{3}}$ of γ' phase with aging time in Co-9Al-8W (at.%) alloy aged at 1023 K, 1073 K, 1123 K and 1173 K.

Table 3 Rate constants $k_{i}^{\text{T}}$ of $<r{{>}^{2}}$ for TIDC model (nm2 h-1) and $k_{i}^{\text{L}}$ of $<r{{>}^{3}}$ for LSW model (nm3 h-1) in different precipitation stages.

T	$k_{\text{I}}^{\text{T}}$	$k_{\text{II}}^{\text{T}}$	$k_{\text{III}}^{\text{T}}$	$k_{\text{I}}^{\text{L}}$	$k_{\text{II}}^{\text{L}}$	$k_{\text{III}}^{\text{L}}$
1023 K	5.39 ± 0.68	21.30 ± 1.20	12.21 ± 0.70	21.54 ± 2.49	143.01 ± 12.24	147.49 ± 6.38
1073 K	16.93 ± 1.24	39.09 ± 0.74	15.57 ± 0.94	78.40 ± 6.18	355.58 ± 16.85	238.91 ± 8.73
1123 K	534.22 ± 76.32	812.27 ± 26.32	353.05 ± 25.54	4016.49 ± 838.98	13813.17 ± 265.48	8598.51 ± 519.58
1173 K	683.16 ± 88.23	1720.32 ± 49.24	733.13 ± 65.14	5760.09 ± 1128.20	38086.24 ± 1901.80	24705.25 ± 1991.93

Table 4 Determinable coefficients $R_{i\text{T}}^{2}$ of $<r{{>}^{2}}$ for TIDC model and $R_{i\text{L}}^{2}$ of $<r{{>}^{3}}$ for LSW model in different precipitation stages.

T	$R_{\text{IT}}^{2}$	$R_{\text{IIT}}^{2}$	$R_{\text{IIIT}}^{2}$	$R_{\text{IL}}^{2}$	$R_{\text{IIL}}^{2}$	$R_{\text{IIIL}}^{2}$
1023 K	0.838	0.972	0.980	0.860	0.938	0.989
1073 K	0.939	0.997	0.979	0.930	0.980	0.992
1123 K	0.906	0.991	0.969	0.814	0.997	0.978
1173 K	0.922	0.993	0.954	0.834	0.978	0.962

Fig. 8. Volume fraction of γ' phase calculated from lever rule in two-phase region aging for 6.67 h in Co-9Al-8W at.% alloy at 1023 K, 1073 K, 1123 K and 1173 K.

Fig. 9. Variation of the particle size distributions of γ' phase with time for different aging temperatures.

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