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Phase field model for dendritic growth with impurities

Author

Listed:
  • F. L. O. Rodrigues

    (Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil)

  • M. P. Almeida

    (Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil)

  • Raimundo N. Costa Filho

    (Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil)

Abstract

A phase field model is used to study dendritic growth in a media with impurities. The model consists of a square lattice where a parameter ψ can take values between 0 and 1 at each site. A site is in the solid phase for ψ>1, in the liquid phase for ψ=0, and the solid-liquid interface is expressed by 0<ψ<1. A fraction of the sites are considered impurities that cannot be solidified, i.e. ψ is fixed and taken as zero. These impurities are distributed randomly. As the probability p of impure sites in the lattice increases, the growth loses its dendritic characteristic. It is shown that the perimeter of the growing solid goes from quadratic to a linear function with time. It was also found that as the probability of impurities reaches p=0.004, the solid undergoes a transition from anisotropic to isotropic growth.

Suggested Citation

  • F. L. O. Rodrigues & M. P. Almeida & Raimundo N. Costa Filho, 2017. "Phase field model for dendritic growth with impurities," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(08), pages 1-8, August.
    • Handle: RePEc:wsi:ijmpcx:v:28:y:2017:i:08:n:s0129183117501054
    DOI: 10.1142/S0129183117501054
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