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Classical nucleation theory in the phase-field crystal model.

Paul Jreidini1, Gabriel Kocher1, Nikolas Provatas1

  • 1Department of Physics, and Centre for the Physics of Materials, McGill University, Montreal, Quebec, Canada H3A 2T8.

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|May 16, 2018
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Summary

The phase-field crystal (PFC) model simulates material nucleation, bridging atomic and mesoscale simulations. This study numerically calculates nucleation rates, finding qualitative agreement with classical nucleation theory (CNT) but also revealing discrepancies that suggest a multivariable approach for PFC models.

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Physical Chemistry

Background:

  • Understanding polycrystalline materials necessitates studying nucleation, a critical phase transition occurring at atomistic scales.
  • Traditional numerical methods like phase-field and molecular dynamics face limitations in bridging atomic and mesoscale simulation regimes for nucleation and growth.
  • The phase-field crystal (PFC) model offers a potential solution by integrating atomic and mesoscale characteristics for microstructure simulations.

Purpose of the Study:

  • To numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times using the simplest version of the PFC model.
  • To assess the qualitative and quantitative agreement of the PFC model with classical nucleation theory (CNT).
  • To investigate the early development of lattice structures in nucleating grains within the PFC model.

Main Methods:

  • Numerical calculation of homogeneous liquid-to-solid nucleation rates and incubation times.
  • Simulation using the phase-field crystal (PFC) model across various parameter choices.
  • Comparison of PFC model results with predictions from classical nucleation theory (CNT).

Main Results:

  • The PFC model demonstrates qualitative agreement with classical nucleation theory (CNT) predictions for nucleation rates and incubation times.
  • Discrepancies were observed regarding the early appearance of lattice structure in nucleating grains, challenging some fundamental assumptions of CNT.
  • The study indicates that a multivariable theory is likely required for quantitatively accurate nucleation predictions within the PFC model.

Conclusions:

  • The phase-field crystal (PFC) model provides a valuable framework for simulating nucleation processes across different scales.
  • While qualitatively aligning with CNT, the PFC model highlights the need for refinements to classical nucleation theories, particularly concerning lattice formation.
  • Extending classical nucleation theory (CNT) to a multivariable approach is proposed as a necessary step for quantitatively accurate modeling in the PFC framework.