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Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification

Munekazu Ohno1, Tomohiro Takaki2, Yasushi Shibuta3

  • 1Division of Materials Science and Engineering, Faculty of Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan.

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Summary

This study introduces a new quantitative phase-field model for alloy solidification, incorporating tensor diffusivity and cross-coupling terms for improved accuracy. The model shows excellent convergence in simulations of dendritic growth.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Chemical Engineering

Background:

  • Quantitative phase-field models are crucial for simulating alloy solidification.
  • Accurate modeling requires accounting for diffusion in the solid phase and interface phenomena.
  • Existing models may lack the necessary coupling for complex solidification behaviors.

Purpose of the Study:

  • To develop a variational formulation of a quantitative phase-field model for binary dilute alloy solidification.
  • To incorporate tensor diffusivity and cross-coupling terms, including the antitrapping current.
  • To validate the model's accuracy and numerical performance against free-boundary problems and simulations.

Main Methods:

  • Variational formulation of a phase-field model.
  • Inclusion of tensor diffusivity and cross-coupling terms in evolution equations.
  • Asymptotic analysis in the thin-interface limit.
  • Two-dimensional simulations of free dendritic growth.

Main Results:

  • Cross-coupling terms and tensor diffusivity naturally arise in the time evolution equations.
  • Successful mapping to a free-boundary problem in the thin-interface limit.
  • Nonvariational models with tensor diffusivity demonstrate excellent convergence with respect to interface thickness.

Conclusions:

  • The proposed variational phase-field model accurately captures alloy solidification phenomena.
  • Tensor diffusivity and cross-coupling terms are essential for precise modeling.
  • The model offers a robust framework for simulating complex solidification processes.