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Interphase anisotropy effects on lamellar eutectics: a numerical study.

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Summary
This summary is machine-generated.

Directional solidification of binary eutectics shows tilted lamellar growth patterns. Numerical simulations confirm theories predicting tilt angles based on crystal anisotropy, with BI simulations capturing bistable behavior not seen in PF models.

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Area of Science:

  • Materials Science
  • Crystallography
  • Computational Materials Science

Background:

  • Directional solidification of binary eutectics often results in two-phase lamellar growth patterns tilted relative to the temperature gradient.
  • This tilt angle is a crystallographic effect dependent on the orientation of the α and β crystal phases.
  • An approximate theory links lamellar tilt to the anisotropy of the solid(α)-solid(β) interphase boundary free energy.

Purpose of the Study:

  • To numerically simulate lamellar growth patterns in binary eutectics using phase field (PF) and dynamic boundary integral (BI) methods.
  • To validate a theory predicting lamellar tilt angles based on interphase boundary free energy anisotropy.
  • To investigate the influence of unstable interphase boundary orientations on tilt behavior and compare PF and BI simulation capabilities.

Main Methods:

  • Two-dimensional simulations of steady periodic patterns using phase field (PF) and dynamic boundary integral (BI) numerical methods.
  • Systematic variation of the angle θ(R) between the temperature gradient and a reference crystallographic axis.
  • Analysis of Wulff plots representing interphase boundary free energy anisotropy.

Main Results:

  • Both PF and BI methods agreed well for Wulff plots without unstable orientations, confirming the approximate theory.
  • Crystallographic locking of lamellae onto facet planes was accurately reproduced by both simulation methods.
  • BI simulations reproduced the experimentally observed bistable tilt angle behavior in the presence of unstable orientations, a phenomenon not captured by the PF model.

Conclusions:

  • The study validates a theory linking lamellar tilt angles to interphase boundary free energy anisotropy in directional solidification.
  • The dynamic boundary integral method is more capable of simulating complex phenomena like bistable tilt behavior compared to the phase field model.
  • Discrepancies between PF and BI models in simulating bistable behavior warrant further investigation into the underlying physical mechanisms.