24 July 1998 Modeling time-dependent behavior in relaxor ferroelectrics
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A time-dependent, constitutive model is proposed for electrostrictive, relaxor ferroelectric materials. The model is based on Ising spin theory, and simulates stress, electric field and temperature dependent phase transformations in a ceramic material. The resulting model is consistent with Devonshire's theory for temperature induced phase transformations, however it captures the non- linear saturation response characteristic of ferroelectrics driven by high fields. Electric hysteresis occurs when bifurcations cause the solution state to jump between stable branches. The model shows that these bifurcations depend on electric field, stress and temperature. This bifurcation approach differs significantly from phenomenological models based on phase switching. A 1D version of the constitutive model is used to predict the induced strain and polarization as a non-linear function of applied field for a Lead Magnesium Niobate-Lead Titanate-Barium Titanate ceramic. The results are compared with experiments at various temperatures.
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Craig L. Hom, Craig L. Hom, Natarajan Shankar, Natarajan Shankar, "Modeling time-dependent behavior in relaxor ferroelectrics", Proc. SPIE 3323, Smart Structures and Materials 1998: Mathematics and Control in Smart Structures, (24 July 1998); doi: 10.1117/12.316310; https://doi.org/10.1117/12.316310

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