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Consistent Hydrodynamics for Phase Field Crystals.

V Heinonen1, C V Achim1, J M Kosterlitz2

  • 1COMP Centre of Excellence, Department of Applied Physics, Aalto University, School of Science, P.O. Box 11100, FI-00076 Aalto, Finland.

Physical Review Letters
|January 30, 2016
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Summary
This summary is machine-generated.

This study introduces a phase field crystal model coupling microscopic material structure to hydrodynamic fields. The model reproduces macroscopic theories and shows elastic excitations relax via phonon emission.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The phase field crystal (PFC) framework describes material microstructure.
  • Coupling microscopic fields to macroscopic hydrodynamics is challenging.
  • Understanding elastic excitation relaxation is crucial for material dynamics.

Purpose of the Study:

  • To develop a unified model linking microscopic material structure and hydrodynamic behavior.
  • To demonstrate the model's ability to recover established macroscopic theories.
  • To investigate the dynamics of elastic excitations and their relaxation mechanisms.

Main Methods:

  • Utilizing an amplitude expansion within the phase field crystal framework.
  • Coupling the phase field crystal order parameters to a hydrodynamic velocity field.
  • Deriving and analyzing the resulting coupled field equations.
  • Performing numerical simulations to validate theoretical predictions.

Main Results:

  • The proposed model successfully unifies microscopic and hydrodynamic descriptions.
  • In appropriate limits, the model reduces to compressible Navier-Stokes and wave equations.
  • The model predicts and numerically demonstrates long-wavelength phonon modes.
  • Elastic excitations within the system are shown to relax through phonon emission.

Conclusions:

  • The developed phase field crystal approach provides a robust framework for studying coupled micro-macro material dynamics.
  • The model's ability to recover known macroscopic theories highlights its validity.
  • Phonon emission is identified as a key mechanism for elastic excitation relaxation in this system.