Special Properties of Ferroelectrics

The ferroelectric domain structure in the crystal is a reason of the non-linear behavior of the polarization as a function of an electric field. Dielectric hysteresis appears in the alternating electric fields. The dielectric hysteresis loop is one of the most important features of ferroelectric materials (Fig. 5.6). Hysteresis loop or domain structure observation could serve as a proof of ferroelectricity in the material. Due to the presence of domain wall structure, the remanent polarization Pr is always smaller than the spontaneous polarization Ps. 

Temperature range close to the phase transition temperature is the temperature region where some of the material properties exhibit anomalous behavior. Among 

Other properties, also the strong piezoelectric effect could be observed. Paraelectric phase transfers to the ferroelectrie phase by rising up the spontaneous polarization. Similarly, reverse transition from ferroelectric to paraelectric phase might take place. Phase transition will be treated in more details in one of the next paragraphs. 

When the temperature is lowered in the paraelectric phase close to the phase transition temperature, significant temperature dependence of permittivity is observed. Omitting tensorial coefficients of permittivity, such temperature dependence could be described by the Curie-Weiss law 

Immediately below the phase transition temperature in the ferroelectric phase, similar approximation holds 

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