linear / non linear approximation

Hysteresis

As with the case of ferromagnetism, the ferroelectric materials have a hysteretic behavior connected with the existence of a structure in domains of the matter. As for the ferromagnetic materials, we can speak of «hard» or «soft» ferroelectric materials, depending on the shape of the D(E) dependence. A D(E) hysteresis cycle is mainly characterized by a residual polarization, a polarization of saturation and a coercive electric field.

Modeling of the hysteresis

The modeling of the hysteresis is a sensitive problem that is not currently treated in Flux.

Modeling the hysteresis correctly is difficult, as shown in the graph of the previous figure there is infinity of possible curves as a function of the values that have passed on the fields.

… in Flux

In Flux, the relation D(E) is a univocal relation : only one value of D corresponds to each value of E and this is mutual.

Linear / non linear approximation

For a «soft» ferroelectric material, it is possible to visualize one linear or nonlinear approximation functioning in the working zone (this is presented in the graph below).

Linear approximation (weak electric field)	Non linear approximation (anhysteretic curve)