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Electrochemical systems provide a fascinating insight into the dynamic interplay of charged species within various phases. One notable example is the interaction between a membrane permeable to K⁺ ions but not to Cl⁻ ions, separating an aqueous KCl solution from pure water. As K⁺ ions diffuse through the membrane, they generate net charges on each phase, leading to a potential difference between them.Similarly, when a piece of Zn is immersed in an aqueous ZnSO₄ solution, the Zn metal, composed...

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Related Experiment Video

Updated: Jun 3, 2026

Evolution of Staircase Structures in Diffusive Convection

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

Percolation of diffusionally evolved two-phase systems.

Victor E Brunini¹, Christopher A Schuh, W Craig Carter

¹Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 17, 2011

Summary

This summary is machine-generated.

This study computes percolation thresholds and critical exponents for microstructures formed by phase transformations. Results show distinct thresholds for nucleation and growth versus spinodal decomposition, aligning with universal scaling laws.

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Area of Science:

Materials Science
Statistical Physics
Computational Modeling

Background:

Understanding microstructural evolution is crucial for material properties.
Phase transformations dictate microstructure formation, influencing material performance.
Percolation theory provides a framework for analyzing connectivity in disordered systems.

Purpose of the Study:

To compute percolation thresholds and critical exponents for 2D microstructures from phase transformations.
To compare these values with established models like random disk placement and spinodal decomposition.
To analyze the time evolution of microstructural length scales.

Main Methods:

Utilizing computational methods to simulate phase-transformation processes in two dimensions.
Applying percolation theory to analyze the connectivity and scaling behavior of generated microstructures.
Calculating critical exponents and characteristic microstructural lengths over time.

Main Results:

Percolation threshold for nucleation and growth (p(c)≈0.6612) found to be higher than spinodal decomposition (p(c)≈0.4987).
Computed critical exponents closely match universal values, indicating scale invariance.
Time evolution analysis revealed power-law growth for spinodal decomposition and complex transitions for nucleation and growth.

Conclusions:

Microstructural evolution via phase transformations exhibits distinct percolation behaviors.
The computed exponents support the universality of scaling laws in these systems.
Observed growth law transitions in nucleation and growth may stem from competing coalescence and coarsening effects.