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Corners in phase-field theory.

Thomas Philippe1

  • 1Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique, CNRS, IP Paris, 91128 Palaiseau, France.

Physical Review. E
|April 17, 2021
PubMed
Summary
This summary is machine-generated.

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Phase-field models with small corner sizes exhibit distinct equilibrium corner shapes compared to sharp-interface models. Despite this, the interface phase transition properties remain consistent with classical theories.

Area of Science:

  • Materials Science
  • Mathematical Modeling
  • Surface Physics

Background:

  • Phase-field models require regularization for anisotropic surface energy to address ill-posed dynamic equations.
  • Regularization introduces a 'corner size' or 'bending length' as a critical length scale.
  • Convergence to sharp-interface theory occurs for large corner sizes relative to interface thickness.

Purpose of the Study:

  • Investigate the behavior of phase-field models in the limit of small corner sizes (smaller than interface width).
  • Determine if equilibrium corner shapes in this regime differ from sharp-interface predictions.
  • Analyze the impact of small corner sizes on interface phase transition properties.

Main Methods:

  • Analysis of phase-field models with anisotropic surface energy.

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  • Focus on the mathematical limit where corner size is smaller than interface thickness.
  • Comparison of equilibrium states with sharp-interface theory predictions.

    • Main Results:

    • Equilibrium corner shapes in the small corner size limit deviate from the sharp-interface picture.
    • The phase transition at the interface is preserved in this regime.
    • The properties of the interface phase transition remain consistent with classical problems.

    Conclusions:

    • The study reveals unique equilibrium corner morphologies in phase-field models with small corner sizes.
    • Despite morphological differences, fundamental phase transition characteristics are maintained.
    • Findings highlight the importance of the corner size parameter in phase-field modeling of anisotropic systems.