19 March 2010 An examination of the structure and the gradient terms used in phase field modeling
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Abstract
Phase field modeling in ferroelectric materials is used to study the formation and evolution of domain structures. These domain structures evolve in a manner that reduces the free energy of the system. An important goal of phase field modeling is to develop computational techniques that can be used in the design of materials with improved properties. This requires accurate determination of each of the terms used in the Time-Dependent Ginzburg Landau equation. This work presents a discussion of the crystal structure and the gradient terms used in phase field models and proposes several modifications that will be implemented in the near future. This includes a discussion of why a constitutive law written in terms of quadratic electrostriction is appropriate and a suggestion that the Ginzburg term (energy proportional to the square of the gradient) has some overlap with the dipole-dipole interaction term.
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Wen Dong, Wen Dong, Christopher S. Lynch, Christopher S. Lynch, } "An examination of the structure and the gradient terms used in phase field modeling", Proc. SPIE 7644, Behavior and Mechanics of Multifunctional Materials and Composites 2010, 764405 (19 March 2010); doi: 10.1117/12.847776; https://doi.org/10.1117/12.847776
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