One-dimensional switching model for major and minor hysteresis loops in ferroelectric materials

The one-dimensional phase transformation model of shape memory alloys [Ikeda et al., Smart Materials and Structures, 13, 916-925 (2004)] is applied to expressing the major and minor hysteresis loops in ferroelectric materials. An analogy between the phase transformation in the shape memory alloys and the switching in the ferroelectric materials is involved. The one-dimensional phase transformation model has the following two features. (i) A specimen is assumed to be comprised of grains with infinitesimal sizes, and the order of the energy required for the transformation of the grains is unchanged independently of the transformation directions. Accordingly, the phase transformation occurs onedimensionally. (ii) The required transformation energy is approximated as a sum of two exponential functions of phase volume fraction. To express the ferroelectric behavior, four phases (variants) are considered, namely, the 0° variant, 90° variant, 180° variant, and initial mixed variant. Electro-mechanical behavior of a ferroelectric material is simulated numerically. The result shows the model can approximately duplicate the electro-mechanical behavior observed in the ferroelectric material.

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