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Correlation-space description of the percolation transition in composite microstructures.
Megan E Frary1, Christopher A Schuh
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
|November 13, 2007
Summary
Introducing short-range correlations in binary composites shifts the percolation threshold. This study develops methods to map this threshold, enabling predictions for various correlation states.
Area of Science:
- Materials Science
- Statistical Physics
- Network Theory
Background:
- Percolation theory describes the formation of connected clusters in random systems.
- Understanding how correlations affect percolation is crucial for designing composite materials.
- Previous models often simplified or ignored the impact of short-range order.
Purpose of the Study:
- To investigate the influence of short-range correlations on the percolation threshold in binary composites.
- To develop quantitative methods for describing and predicting percolation behavior in correlated systems.
- To establish a framework for analyzing percolation in systems with varying degrees of short-range order.
Main Methods:
- Developed two complementary representations for short-range correlations: phase bond distributions and short-range order parameters.
- Systematically explored the correlation space across different lattice structures (2D/3D site lattices, 2D hexagonal bond network).
- Analyzed systems with two-body and three-body correlations.
Main Results:
- Identified a distinct boundary separating percolating from non-percolating structures within the correlation space.
- Derived empirical equations to accurately predict the percolation threshold for diverse short-range correlation states.
- Demonstrated the method's applicability to various lattice types and correlation orders.
Conclusions:
- Short-range correlations significantly alter the percolation threshold in binary composites.
- The developed framework provides a generalizable approach to predict percolation in complex, correlated systems.
- This work offers a pathway to tailor material properties by controlling short-range order.
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