A simple model of the evolution of ferroelectric microstructure in single crystals is developed by using variational methods to minimize a functional based on free energy and dissipation. The thermodynamic variables in this formulation correspond to the positions of a set of domain walls within a single ferroelectric crystal. The total dissipation rate is taken to be a function of the velocities of the individual domain walls. With only two-degrees of freedom, a model of this type has sufficient richness to reproduce many of the observed features found in the single crystal response of a tetragonal ferroelectric. This includes the dielectric hysteresis, butterfly hysteresis, and the variation of the hysteresis loops under uniaxial compressive stress. Additional degrees of freedom can be used to capture multi-axiality. The model also highlights the marked differences in response that should occur when a single crystal is subjected to different boundary conditions.
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A Variational Model of Ferroelectric Microstructure
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Huber, JE, & Cocks, ACF. "A Variational Model of Ferroelectric Microstructure." Proceedings of the ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Smart Materials, Adaptive Structures and Intelligent Systems, Volume 1. Ellicott City, Maryland, USA. October 28–30, 2008. pp. 225-230. ASME. https://doi.org/10.1115/SMASIS2008-360
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