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Patterning in systems driven by nonlocal external forces
L Luneville1, K Mallick2, V Pontikis3
1DEN-Service dÉtudes et de Recherche en Mathématique Appliquée, LRC CARMEN CEA-CNRS-ECP/SPMS, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France.
Physical Review. E
|December 15, 2016
Summary
We developed a new method to describe domain patterns in systems with competing dynamics. This approach helps engineer material microstructures by controlling external forces and temperature.
Area of Science:
- Physics
- Materials Science
- Chemistry
Background:
- Systems with competing internal and external dynamics often exhibit complex domain patterns.
- Existing methods for analyzing long-range order interactions do not fully account for external nonlocal forces.
Purpose of the Study:
- To introduce a novel Lyapunov functional for describing steady states in systems under external forces.
- To extend existing methodologies to incorporate external nonlocal forces.
- To investigate domain patterning in chemical and binary mixtures.
Main Methods:
- Introduction of a Lyapunov functional with nonlocal terms added to the Landau-Ginzburg free energy.
- Computation of the phase diagram by analyzing the quadratic term of the Lyapunov functional.
- Investigation of patterning in reactive and irradiated binary mixtures.
Main Results:
- The study computes the phase diagram as a function of temperature and external field.
- All possible modulated phases (domain patterns) are determined based on external forces and temperature.
- Irradiated binary mixtures show potential for micro-structural engineering.
Conclusions:
- The developed Lyapunov functional effectively describes steady states and domain patterns in complex systems.
- The findings provide a framework for understanding and predicting domain formation.
- The research opens new avenues for micro-structural engineering of materials through controlled irradiation.
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