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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.

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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.