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The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
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Related Experiment Video

Updated: May 2, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Multicomponent phase-field model for extremely large partition coefficients.

Michael J Welland1, Dieter Wolf1, Jonathan E Guyer2

  • 1Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 4, 2014
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Summary

This study introduces a robust phase-field model for simulating extreme concentration changes across interfaces, accurately capturing solute trapping and diffusion behavior in materials science.

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Chemical Engineering

Background:

  • Simulating extreme concentration gradients across material interfaces is challenging.
  • Accurate modeling is crucial for understanding phase transformations and material properties.

Purpose of the Study:

  • To develop a multicomponent phase-field model capable of robustly simulating large concentration variations across interfaces.
  • To investigate the behavior of species with partition coefficients exceeding 10^23.
  • To compare interface composition models in the context of large partitioning.

Main Methods:

  • Developed a multicomponent phase-field model incorporating substitutional and interstitial diffusion.
  • Implemented interface composition models from Kim, Kim, and Suzuki (1999) and Wheeler, Boettinger, and McFadden (1992).
  • Validated the model against analytical solutions for binary diffusion couples and solute trapping.

Main Results:

  • The model successfully simulates concentration variations from molar to atomic magnitudes.
  • Demonstrated robust performance for species with partition coefficients greater than 10^23.
  • Accurately reproduced analytical solutions for binary diffusion and solute trapping.

Conclusions:

  • The developed phase-field model provides a robust framework for simulating extreme partitioning phenomena.
  • This model is valuable for predicting material behavior under conditions of high solute insolubility.
  • The findings advance the understanding of diffusion and phase segregation in multicomponent systems.