17 April 2007 Analytical model for the strain-field and polarization-field hysteresis curves for ferroic materials
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We present a generalized energy based analytical macroscopic model using distribution functions for the polarization and strain response to external electric field in electromechanical materials. Although the distributions are based on classical Boltzmann statistics, we show that they differ only by a factor of 2 in the exponential factor from Fermi-Dirac statistics in the two state system. The electric displacement-field D-E and strain-field S-E curves of antiferroelectric, ferroelectric, relaxor ferroelectric and linear piezoelectrics including hysteresis are described. The polarization model is based on a Weiss molecular field and assumes only net contributions to the polarizations need to be summed. No distinction between 90° and 180° domain contributions or domain dynamics is made. The strain field S-E curves are generated in all cases using the electrostriction relationship S=QD2. The model shows utility in modeling phase change between antiferroelectric ⇒ ferroelectric or ferroelectric ⇒ relaxor ferroelectric states. The hysteresis in the strain- field and electric displacement field curves is accounted for using the time derivative of the applied electric field. Although the model was developed for polarizable dielectric materials it is proposed that the same approach can be applied to magnetic, elastic or other ferroic materials.
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Stewart Sherrit, Stewart Sherrit, } "Analytical model for the strain-field and polarization-field hysteresis curves for ferroic materials", Proc. SPIE 6526, Behavior and Mechanics of Multifunctional and Composite Materials 2007, 652608 (17 April 2007); doi: 10.1117/12.715314; https://doi.org/10.1117/12.715314

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