Ferroelectricity of piezoelectric ceramic crystals

The polarization of some dielectrics is very special. In a certain temperature range, their dielectric constants are not constant, but vary with field strength, and after removing the external electric field, these dielectrics are not neutral. There is residual polarization. In order to be analogous to the fact that ferromagnetic materials can remain magnetized, this property of piezo ceramic transducer is often referred to as ferroelectricity. A ferroelectric dielectric is called a ferroelectric. Among them, barium titanate ceramics (BaTiO3), sodium potassium tartrate single crystal (NaKC4H4O6⋅H2O) and the like are most prominent.Ferroelectrics will exhibit hysteresis during the electrodeposition process. The hysteresis loop shows that the polarization between the ferroelectric body and the applied electric field is nonlinear, and the polarization is reversed as the external electric field is reversed. The polarization inversion is the result of domain inversion, so the hysteresis loop indicates the presence of domains in the ferroelectric. The so-called domains are small regions in which the spontaneous polarization directions in the ferroelectrics are uniform, and the domains. The boundary between them is called the domain wall. Ferroelectric crystals of piezoelectric ceramic products are usually multi-domains, the spontaneous polarization in each domain has the same direction, and the spontaneous polarization in the different domains is strong.

For polycrystalline ferroelectrics, there is no regularity between the relative orientations of spontaneous polarization in the different domains for the entire polycrystal due to the complete arbitrariness of the orientation of the crystal axes between the grains.
Ferroelectrics generally do not spontaneously form single domains, but multidomain crystals can be monodomainized under a strong external electric field. Under the action of a strong external electric field, the domain volume of the spontaneous polarization in the multi-domain crystal parallel or close to the external field direction will rapidly expand due to the formation of new domain nuclei and the movement of the domain walls, and the domain volume in other directions will decrease rapidly. Small disappears,which is turning the entire crystal into a single domain. Under the action of external electric field, the dynamic process of new domain nucleus and domain wall motion is called the domain reversal process. This reversal has some hysteresis characteristics, so the ferroelectric exhibits the aforementioned hysteresis loop.

Considering a single piezo crystal is assuming that the orientation of spontaneous polarization has only two possibilities.it is positive and negative along a certain crystal axis; the direction of the external electric field is parallel to the polarization axis. When the external electric field is zero, the polarization of adjacent domains in the crystal is opposite, and the total electric moment of the crystal is zero. When the external electric field is gradually increased, the domain volume of the spontaneous polarization direction opposite to the direction of the electric field will gradually decrease due to the inversion of the domain, and those domains are having the same direction as the electric field will gradually expand, so that the crystal is in the direction of the external field. The intensity increases with the increasing of the electric field. When the electric field of piezoelectric disc element increases enough to reverse all the reverse domains in the crystal to the external field, the crystal becomes a single domain, the polarization of the crystal reaches saturation, and then the electric field increases. The polarization will increase linearly with the electric field (same as the polarization of a typical dielectric) and reach a maximum value Pmax, which is a function of the highest polarization electric field. 

When the linear portion is extrapolated to zero electric field, the resulting intercept Ps on the vertical axis is called the saturated polarization, which is actually the spontaneous polarization of each domain.When the electric field begins to decrease from C, the polarization will gradually decrease along the C-B curve. When the electric field of piezoelectric ceramic component is reduced to zero, the polarization decreases to a certain value Pr, which is called the residual polarization of the ferroelectric. When the electric field changes direction and increases to Ec in the negative direction, the polarization decreases to zero, the reverse electric field continues to increase, and the polarization is reversed. Ec is called the coercive field strength of the ferroelectric. As the reverse electric field continues to increase, the polarization continues to increase in the negative gradient direction and reaches a saturation value (-Pr) in the negative direction, and the ultrasonic piezoelectric transducer becomes a single domain crystal which is having a negative polarization. If the electric field changes continuously from a high negative value to a high positive value, the positive domain begins to form and grow again until the entire crystal becomes a single domain crystal with forward polarization again. During this process, the polarization is returned to point C along the FGH portion of the return line. Thus, under the action of a large alternating electric field, the electric field changes by one week, and the above process is repeated once, showing the hysteresis loop shown. The area enclosed by the return line is the energy required to