8.2.1 Simulation of Materials with Uniaxial Anisotropy

Fig. 8.6 shows the different simulated down branches of the hysteresis when the orientation of the axis of a material with uniaxial anisotropy varies.

The absolute charge in the capacitor decreases with the angle and the coercive field increases. These effects can easily be understood by geometrical considerations. According to the Poisson equation, the contact charge is proportional to the component of the polarization which is perpendicular to the surface, and it will be reduced if the angle between the polarization and the vector perpendicular to the surface increases.

A similar effect causes the increase of the coercive field. In this case the component of the electric field in the direction of the anisotropy axis is decisive for the resulting polarization. Obviously, if the electric field is not parallel to the anisotropy axis, it has to be increased in order to raise a field of the same strength in the axis direction.

The nonlinearity of the material leads to a complex field distribution. Due to Poisson's equation, the displacement (Fig. 8.7) and, as a consequence of the monotonic $D/E$ characteristics, the electric field (Fig. 8.8) decrease near the charge free boundary to the insulating material.

Figure 8.6: Hysteresis curves for different angles of the anisotropy axis

Figure 8.7: Distribution of the polarization field, angle = $45^\circ$

Figure 8.8: Distribution of the electric field, angle = $45^\circ$

Figure 8.9: Distribution of the potential, angle = $45^\circ$