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Phase Field Method

Locally coupled ferromagnetic (FM), ferroelectric (FE), and ferroelastic (FL) domains in a heterostructureThe phase field method has emerged as a powerful and flexible tool for quantitative modeling of the coevolution of microstructure and physical properties at the mesoscale. In the phase field method, the microstructure is described by a system of continuous variables, where the microstructure interfaces have a finite width over which the variables transition between values. The evolution of the microstructure is defined in terms of the free energy of the system, and can be coupled to other physics to provide a complete view of the material behavior. Phase field simulations range from hundreds of nanometers to hundreds of microns and evolve at diffusive time scales. Common applications of the phase field method include:

  • Grain boundary migration and grain growth
  • Solidification
  • Phase transformation
  • Irradiation damage
  • Domain evolution in ferro-electric and ferro-magnetic materials

Reference: General Phase Field Modeling:
Chen, Long-Qing. "Phase-field models for microstructure evolution." Annual review of materials research 32, no. 1 (2002): 113-140.

Reference: Phase Field Modeling for Ferroelectric Materials
Chen, Long‐Qing. "Phase‐Field Method of Phase Transitions/Domain Structures in Ferroelectric Thin Films: A Review." Journal of the American Ceramic Society 91, no. 6 (2008): 1835-1844.

Ferroelectric domains in hexagonal YMnO3 from (left) phase-field simulations and (right)Domain structures and switching in ferroelectric, ferromagnetic, ferroelastic and multiferroic thin films and devices

Phase Field Figure Animation

design of high-performance MeRAM