Phase Field Modeling of Microstructure Evolution During Solidification and Subsequent Solid-State Phase Transformation of Au-Pt Alloys
YU Dong1, MA Weilong2, WANG Yali1, WANG Jincheng1()
1 State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China 2 College of Materials Science and Engineering, Xi'an University of Technology, Xi'an 710048, China
Cite this article:
YU Dong, MA Weilong, WANG Yali, WANG Jincheng. Phase Field Modeling of Microstructure Evolution During Solidification and Subsequent Solid-State Phase Transformation of Au-Pt Alloys. Acta Metall Sin, 2025, 61(1): 109-116.
The evolution of the microstructure during solidification and solid-state phase transformation is crucial for controlling the material microstructure and optimizing performance. Achieving an integrated numerical simulation of the microstructural evolution from solidification to solid-state phase transformation is a cutting-edge challenge in material-microstructure simulation. This study focuses on Au-Pt alloys, utilizing a multiphase field model combined with a microstructural information transfer algorithm to simulate and predict microstructural evolution during the solidification and solid-state phase transformation under different initial composition conditions. The study successfully realizes an integrated simulation prediction of the microstructural evolution across both processes, revealing the influence of microsegregation and grain boundaries during solidification on subsequent processes of decomposition and spinodal decomposition.
Fig.1 Schematics of interpolation between different scales (dx and dy are grid sizes for a large spatial scale used for modeling of solidification microstructure evolution, while and are grid sizes for a small spatial scale used for modeling of solid phase transformation; N is the number of fine grids in a certain dimension) (a) coarse and fine grids at different scales (b) bilinear interpolation algorithm
Fig.2 Schematics of interpolation process of solute field (a) simulated solidification microstructure with a domain of 15 μm × 15 μm and a coarse grid size (dx = dy = 10 nm; xPt—mole fraction of Pt) (b) microstructure extracted from Fig.2a with a small domain (1 μm × 1 μm) and a coarse grid size (dx = dy = 10 nm) (c) microstructure interpolated from Fig.2b with a much finer grid size ( = = 1 nm)
Fig.3 Phase diagram of Au-Pt alloy (T—temperature)
Parameter
Variable
Unit
Value
Liquid phase solute diffusivity
DL
m2·s-1
3.5 × 10-9 [23]
Solid phase solute diffusivity
DS
m2·s-1
0.5 × 10-12[23]
Solid-liquid interface energy
σSL
J·m-2
0.5
Solid-solid interface energy
σSS
J·m-2
1
Mole volume
Vm
m3·mol-1
9.8 × 10-6
Thickness of solid-liquid interface
λLS
μm
5dx
Thickness of solid-solid interface
λSS
μm
5dx
Anisotropy coefficient of interface energy
γ4
-
0.02
Mean radius of initial nucleus
r
μm
10dx
Table1 Physical property parameters of Au-Pt alloy and related modeling parameters
Fig.4 Evolutions of the concentration field during solification at t = 2 × 103Δt (a1, a2), 1 × 104Δt (b1, b2), and 5 × 104Δt (c1, c2); and the orientation fields at the late stage (d1, d2) of Au-Pt alloys with different initial compositions (Each color in Figs.4d1 and d2 represents grains with the same orientation; t—time, Δt—time step) (a1-d1) xPt = 0.3 (a2-d2) xPt = 0.6
Fig.5 Microstructure evolutions during subsequnet solid-state phase transformation at t = 0 (a1, a2), 1.2 × 103Δt (b1, b2), 8 × 103Δt (c1, c2), and 4 × 104Δt (d1, d2) when xPt = 0.3 with different initial microstructures as shown in the rectangle areas in Fig.4c1 (a1-d1) domain in grains (a2-d2) domain near grain boundaries
Fig.6 Microstructure evolutions during subsequnet solid state phase transformation at t = 0 (a1, a2), 1.2 × 103Δt (b1, b2), 8 × 103Δt (c1, c2), and 4 × 104Δt (d1, d2) when xPt = 0.6 with different initial microstructures as shown in the rectangle areas in Fig.4c2 (a1-d1) domain in grains (a2-d2) domain near grain boundaries
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