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# Ferroelectric material simulation in COMSOL Multiphysics

#### What are Ferroelectric Materials?

Materials that demonstrate ferroelectricity are referred to as ferroelectric materials. Ferroelectricity refers to a material's capacity to exhibit spontaneous electric polarisation, and it may be a useful property. By applying an external electric field in the opposite direction, it is possible to invert this polarisation.

#### Polarization and Hysteresis Loop

First, a dielectric substance is taken into consideration, and a peripheral electric field is established. As seen in figure 2, we can observe that the polarisation will always be exactly proportional to the applied field.

Next, when we polarise a paraelectric material, we get a nonlinear polarization. However, it is a function of the field, as shown in figure 3

Next, an electric field is applied to a ferroelectric material. A nonlinear polarisation results. Additionally, it displays spontaneous polarisation that is nonzero without a peripheral field. We can also observe that the polarisation direction may be modified or reversed by flipping the direction of the applied electrical field. As a result, we may state that the polarisation will rely on the electric field's prior and current states. Figure 4 shows how to generate the hysteresis loop.

Source courtesy: www.electrical4u.com

#### COMSOL Multiphysics simulation - ferroelectric material

At high applied electric fields, ferroelectric materials display nonlinear polarisation phenomena including hysteresis and saturation. There are several ferroelectric piezoelectric materials. In this model, an applied electric field is used to examine a straightforward actuator built of a PZT piezoelectric ceramic material. The material shows spontaneous polarisation in its ferroelectric phase, resulting in domains with nonzero polarization even at zero applied field. The domains may be rearranged by the introduction of an electric field, which will cause the material to become net polarised. Due to the alignment of all ferroelectric domains in the material along the direction of the applied field, at extremely high electric fields, the polarisation saturates. The polarisation may exhibit strong hysteresis as a result of domain wall interactions. In COMSOL Multiphysics, you may find the Jiles-Atherton hysteresis model for ferroelectric materials. It assumes that the sum of the reversible and irreversible components may be used to describe the overall polarisation.

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