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Acta Metall Sin  2025, Vol. 61 Issue (1): 109-116    DOI: 10.11900/0412.1961.2024.00255
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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.

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Abstract  

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.

Key words:  solidification      solid-state phase transformation      microstructure evolution      phase field method      integrated modeling     
Received:  14 August 2024     
ZTFLH:  TG111.4  
Fund: National Key Research and Development Program of China(2021YFC2202301)
Corresponding Authors:  WANG Jincheng, professor, Tel: (029)88460650, E-mail: jchwang@nwpu.edu.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00255     OR     https://www.ams.org.cn/EN/Y2025/V61/I1/109

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 d˜x and d˜y 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 (d˜x = d˜y = 1 nm)
Fig.3  Phase diagram of Au-Pt alloy (T—temperature)
ParameterVariableUnitValue
Liquid phase solute diffusivityDLm2·s-13.5 × 10-9 [23]
Solid phase solute diffusivityDSm2·s-10.5 × 10-12[23]
Solid-liquid interface energyσSLJ·m-20.5
Solid-solid interface energyσSSJ·m-21
Mole volumeVmm3·mol-19.8 × 10-6
Thickness of solid-liquid interfaceλLSμm5dx
Thickness of solid-solid interfaceλSSμm5dx
Anisotropy coefficient of interface energyγ4-0.02
Mean radius of initial nucleusrμm10dx
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
1 Kurz W, Fisher D J, Trivedi R. Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000[J]. Int. Mater. Rev., 2019, 64: 311
2 Kurz W, Rappaz M, Trivedi R. Progress in modelling solidification microstructures in metals and alloys. Part II: Dendrites from 2001 to 2018[J]. Int. Mater. Rev., 2021, 66: 30
3 Zhai W, Chang J, Geng D L, et al. Progress and prospect of solidification research for metallic materials[J]. Chin. J. Nonferrous Met., 2019, 29: 1953
翟 薇, 常 健, 耿德路 等. 金属材料凝固过程研究现状与未来展望[J]. 中国有色金属学报, 2019, 29: 1953
4 Liu F, Zhang X, Zhang Y B. Unified analysis of non-equilibrium solidification and solid-state phase transformations[J]. Acta Metall. Sin., 2018, 54: 701
doi: 10.11900/0412.1961.2018.00112
刘 峰, 张 旭, 张玉兵. 非平衡凝固与固态相变的一体化研究[J]. 金属学报, 2018, 54: 701
5 Ghosh S, Zollinger J, Zaloznik M, et al. Modeling of hierarchical solidification microstructures in metal additive manufacturing: challenges and opportunities[J]. Addit. Manuf., 2023, 78: 103845
6 Wang T M, Wei J J, Wang X D, et al. Progress and application of microstructure simulation of alloy solidification[J]. Acta Metall. Sin., 2018, 54: 193
doi: 10.11900/0412.1961.2017.00428
王同敏, 魏晶晶, 王旭东 等. 合金凝固组织微观模拟研究进展与应用[J]. 金属学报, 2018, 54: 193
doi: 10.11900/0412.1961.2017.00428
7 Wang J C, Guo C W, Li J J, et al. Recent progresses in competitive grain growth during directional solidification[J]. Acta Metall. Sin., 2018, 54: 657
doi: 10.11900/0412.1961.2017.00543
王锦程, 郭春文, 李俊杰 等. 定向凝固晶粒竞争生长的研究进展[J]. 金属学报, 2018, 54: 657
doi: 10.11900/0412.1961.2017.00543
8 Liu B C, Xu Q Y, Jing T, et al. Advances in multi-scale modeling of solidification and casting processes[J]. JOM, 2011, 63(4): 19
9 Warnken N, Larsson H, Reed R C. Coupled modelling of solidification and solution heat treatment of advanced single crystal nickel base superalloy[J]. Mater. Sci. Technol., 2009, 25: 179
10 Meng X N, Gao X H, Huang S, et al. Cross-scale modeling of MnS precipitation for steel solidification[J]. Metals, 2018, 8: 529
11 Shi R P, Khairallah S, Heo T W, et al. Integrated simulation framework for additively manufactured Ti-6Al-4V: Melt pool dynamics, microstructure, solid-state phase transformation, and microelastic response[J]. JOM, 2019, 71: 3640
12 Liu P W, Wang Z, Xiao Y H, et al. Integration of phase-field model and crystal plasticity for the prediction of process-structure-property relation of additively manufactured metallic materials[J]. Int. J. Plast., 2020, 128: 102670
13 Zhang Q, Wang J C, Zhang Y C, et al. Simulation of multi-grain solidification and subsequent spinodal decomposition by using phase field crystal model[J]. Acta Phys. Sin., 2011, 60: 088104
张 琪, 王锦程, 张亚丛 等. 多晶凝固及后续调幅分解过程的晶体相场法模拟[J]. 物理学报, 2011, 60: 088104
14 Kodama T, Nakai R, Goto K, et al. Preparation of an Au-Pt alloy free from artifacts in magnetic resonance imaging[J]. Magn. Reson. Imaging, 2017, 44: 38
doi: S0730-725X(17)30124-8 pmid: 28700894
15 Silvestri Z, Davis R S, Genevès G, et al. Volume magnetic susceptibility of gold-platinum alloys: Possible materials to make mass standards for the watt balance experiment[J]. Metrologia, 2003, 40: 172
16 Liu M W, Weissmüller J. Phase decomposition in nanoporous Au-Pt[J]. Acta Mater., 2022, 241: 118419
17 Celik F A, Özel S. A simulation study on the orientational phase transformation behavior of Au-Pt alloy for different concentration of Pt[J]. Solid State Commun., 2020, 316-317: 113940
18 Vidano S, Novara C, Pagone M, et al. The LISA DFACS: Model Predictive Control design for the test mass release phase[J]. Acta Astron., 2022, 193: 731
19 Kim S G. A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties[J]. Acta Mater., 2007, 55: 4391
20 Steinbach I, Pezzolla F. A generalized field method for multiphase transformations using interface fields[J]. Physica, 1999, 134D: 385
21 Xu X N, Qin G W, Ren Y P, et al. Experimental study of the miscibility gap and calculation of the spinodal curves of the Au-Pt system[J]. Scr. Mater., 2009, 61: 859
22 Grolier V, Schmid-Fetzer R. Experimental study of Au-Pt-Sn phase equilibria and thermodynamic assessment of the Au-Pt and Au-Pt-Sn systems[J]. J. Electron. Mater., 2008, 37: 264
23 Liu Y J, Wang J, Du Y, et al. Phase boundary migration, Kirkendall marker shift and atomic mobilities in fcc Au-Pt alloys[J]. Calphad, 2012, 36: 94
24 Rappaz M, Gandin C A. Probabilistic modelling of microstructure formation in solidification processes[J]. Acta Metall. Mater., 1993, 41: 345
25 Ye W C, Kou H H, Liu Q Z, et al. Electrochemical deposition of Au-Pt alloy particles with cauliflower-like microstructures for electrocatalytic methanol oxidation[J]. Int. J. Hydrogen Energy, 2012, 37: 4088
26 Ramanarayan H, Abinandanan T A. Spinodal decomposition in polycrystalline alloys[J]. Physica, 2003, 318A: 213
27 Li L L, Li Z M, da Silva A K, et al. Segregation-driven grain boundary spinodal decomposition as a pathway for phase nucleation in a high-entropy alloy[J]. Acta Mater., 2019, 178: 1
28 Guo C, Zhao Y P, Deng Y Y, et al. A phase-field study on interaction process of moving grain boundary and spinodal decomposition[J]. Acta Phys. Sin., 2022, 71: 078101
郭 灿, 赵玉平, 邓英远 等. 运动晶界与调幅分解相互作用过程的相场法研究[J]. 物理学报, 2022, 71: 078101
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