中国物理B ›› 2024, Vol. 33 ›› Issue (9): 96103-096103.doi: 10.1088/1674-1056/ad57ac

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Dendritic tip selection during solidification of alloys: Insights from phase-field simulations

Qingjie Zhang(张清杰)1, Hui Xing(邢辉)1,2,†, Lingjie Wang(王灵杰)1, and Wei Zhai(翟薇)1   

  1. 1 School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China;
    2 Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518063, China
  • 收稿日期:2024-03-15 修回日期:2024-05-20 接受日期:2024-06-13 发布日期:2024-08-15
  • 通讯作者: Hui Xing E-mail:huixing@nwpu.edu.cn
  • 基金资助:
    Project supported by the National Key Research and Development Program of China (Grant No. 2021YFB3502600) and Shenzhen Science and Technology Program (Grant No. JCYJ20220530161813029).

Dendritic tip selection during solidification of alloys: Insights from phase-field simulations

Qingjie Zhang(张清杰)1, Hui Xing(邢辉)1,2,†, Lingjie Wang(王灵杰)1, and Wei Zhai(翟薇)1   

  1. 1 School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China;
    2 Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518063, China
  • Received:2024-03-15 Revised:2024-05-20 Accepted:2024-06-13 Published:2024-08-15
  • Contact: Hui Xing E-mail:huixing@nwpu.edu.cn
  • Supported by:
    Project supported by the National Key Research and Development Program of China (Grant No. 2021YFB3502600) and Shenzhen Science and Technology Program (Grant No. JCYJ20220530161813029).

摘要: The effect of undercooling $\Delta T$ and the interface energy anisotropy parameter $\varepsilon_{4} $ on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys. It was found that the tip radius $\rho $ increases and the tip shape amplitude coefficient $A_{4} $ decreases with the increase of the fitting range for all cases. The dendrite tip shape selection parameter $\sigma^{\ast }$ decreases and then stabilizes with the increase of the fitting range, and $\sigma^{\ast }$ increases with the increase of $\varepsilon_{4} $. The relationship between $\sigma^{\ast }$ and $\varepsilon_{4}$ follows a power-law function $\sigma^{\ast }\propto \varepsilon_{4}^{\alpha } $, and $\alpha $ is independent of $\Delta T$ but dependent on the fitting range. Numerical results demonstrate that the predicted $\sigma^{\ast }$ is consistent with the curve of microscopic solvability theory (MST) for $\varepsilon_{4} <0.02$, and $\sigma ^{\ast }$ obtained from our phase-field simulations is sensitive to the undercooling when $\varepsilon_{4} $ is fixed.

关键词: phase-field simulations, dendritic structure, interface energy anisotropy, tip shape selection parameter

Abstract: The effect of undercooling $\Delta T$ and the interface energy anisotropy parameter $\varepsilon_{4} $ on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys. It was found that the tip radius $\rho $ increases and the tip shape amplitude coefficient $A_{4} $ decreases with the increase of the fitting range for all cases. The dendrite tip shape selection parameter $\sigma^{\ast }$ decreases and then stabilizes with the increase of the fitting range, and $\sigma^{\ast }$ increases with the increase of $\varepsilon_{4} $. The relationship between $\sigma^{\ast }$ and $\varepsilon_{4}$ follows a power-law function $\sigma^{\ast }\propto \varepsilon_{4}^{\alpha } $, and $\alpha $ is independent of $\Delta T$ but dependent on the fitting range. Numerical results demonstrate that the predicted $\sigma^{\ast }$ is consistent with the curve of microscopic solvability theory (MST) for $\varepsilon_{4} <0.02$, and $\sigma ^{\ast }$ obtained from our phase-field simulations is sensitive to the undercooling when $\varepsilon_{4} $ is fixed.

Key words: phase-field simulations, dendritic structure, interface energy anisotropy, tip shape selection parameter

中图分类号:  (Theory of crystal structure, crystal symmetry; calculations and modeling)

  • 61.50.Ah
81.10.Aj (Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation) 02.70.-c (Computational techniques; simulations) 61.72.-y (Defects and impurities in crystals; microstructure)