Polarization-voltage hysteresis

Cellular PP is biaxially stretched PP and has porous voids inside as shown in Fig. 8. It becomes electret through dielectric barrier discharging in the micro voids and exhibits ferroelectric-Uke behavior such as polarization-voltage hysteresis. This is due to the electrical dipole and may also be expressed as ferroelectrets or piezoelectrets distinct fi om piezoelectric materials. 

Here, Rs, and denote the area, the electrical resistance, and the capacitance of the sample. By considering the capacitive component and, in case of highly conductive samples, the conduction current, the polarization current can be isolated to construct the true ip(E) curve. A representative example showing the current-voltage hysteresis curve obtained for PVDF is displayed in Fig. 10b. 

Several important aspects of the SHG experiments are not described in a straight forward way by the model. These are the residual SHG prior to field perturbation and asymmetric response to fields of different polarity. These effects may be due to the fact that the dipoles within the stacks as formed are subjected to remnant fields from surrounding stacks. The asymmetry may be associated with structural asymmetry within the stacks or some higher ordering or arrangement which does not allow for a symmetric hysteresis about zero voltage. A distribution of nonidentical stacks is also possible. 

Based on these assumptions the measurement of the large signal ferroelectric hysteresis with additional measurements of the small signal capacitance at different bias voltages are interpreted in terms of reversible and irreversible parts of the polarization. As shown for ferroelectric thin films in Figure 1.24, the separation is done by substracting from the total polarization the reversible part, i. e. the integrated C(V)-curve [18]. 

To obtain the dynamic hysteresis loop of a ferroelectric capacitor the polarization is measured versus the applied voltage. Since the hysteresis is neither a linear nor a time invariant property, the hysteresis loop is dependent on the sample history and on the measurement method. To have a standardized and comparable hysteresis loop, certain parameters are commonly fixed. One is the absolute position of the loop on the polarization axis, since the initial (virgin) state of the polarization is unknown in almost all cases, the hysteresis loop is balanced to a reference value. Most commonly the positive and negative saturation polarization are set to... 

The third loop establishes the sample into the positive remanent polarization state without sampling data. The fourth loop now starts in the positive relaxed remanent polarization state (Prrei+), turns into the negative saturation (Pmax-), then crosses the polarization axis at zero volts excitation signal in the negative remanent polarization state (Pr ). Afterwards the sample is driven into the positive saturation (Pmax+) and ends up in the positive remanent polarization state (Pr+) when the voltage is zero again. Subsequently, the hysteresis loop is balanced respectively to the values P(+Vmax) and P(-Vmax). From the data of the second loop the parameters Vc-, Pr, Prrei- are determined and from the data of the fourth loop the parameters Vc+, Pr+, Prrei+ The closed hysteresis loop (continuous loop) can be calculated from the second half of the second loop and the second half of the fourth loop. 

The ferroelectric sample is pre-polarized by measuring a complete hysteresis. The excitation voltage is then kept constant for the relaxation time at a particular voltage. The relaxed... 

After cycling once again through a complete hysteresis to ensure the same initial condition the excitation signal is stopped at the next voltage for the relaxation time. The relaxed polarization is again determined as described above. The whole procedure is repeated for each point until a complete quasi static hysteresis loop has been recorded. 

Furthermore, the remanent polarization values Pr and Prrei also change due to the shift of the loop. A correlation between voltage shift and polarization change can be given with the static hysteresis loop (see Section 3.3.4). 

Figure 3.19 Failure mechanism related to the voltage shift in the hysteresis loop. Pthres is used as the threshold polarization to detect the stored information.

The vertical plates are attached to a linear capacitor in series with the ferroelectric crystal. Since the voltage generated across the linear capacitor is proportional to the polarization of the ferroelectric, the oscilloscope will display the hysteresis loop. 

The hydrogen over-voltage on lead at a given current density depends on the time of polarization and the nature of the anions in the solution [28]. Figure 2.14 shows the 77 vs Ig I c relationship at two different polarization rates. It can be seen that the Tafel curve displays hysteresis phenomena which depend on the speed with which the polarization is changed [28]. The observed hysteresis has been attributed (a) to adsorption of anions on the Pb surface which alter both the distribution of the surface charges and the surface H concentration [28,29] or (b) to dissolution of a certain amount of hydrogen in the Pb [30,31]. 

The polarization curves in Figure 3.10 show a hysteresis loop, where the steady state current and voltage depend on the direction of approach. It was possible to go around the hysteresis loop shown in Figure 3.10 reproducibly many times. When the load resistance was between 5 and 110, the steady state current and voltage were dependent on the direction of approach. These multi-valued steady states were stable the current and voltage at any point on the steady state polarization curve was steady for periods of >24 h. 

The piezoelectric hysteresis loops have been studied additionally to above dielectric hysteresis. This kind of loop is shown on Fig. 2.17. It has been recorded on PZT nanotube with outer diameter 700 and 90 nm wall thickness with the help of piezoatomic force microscopy (see Refs. [42, 43]). The obtained loop is the direct evidence of ferroelectric properties of the nanotube. Square form of the loop speaks about sharp polarization switching at coercive voltage 2 V. The residual (at zero voltage) piezoelectric coefficient d ff is of the same order as for the thin PZT film. 

Fig. 13.24 Tri-stable switching of an antifenoelectric liquid crystal. Typical hysteresis-type dependence [34] of the total polarization P as a function of the external field (a) and optical transmission-voltage curves [35] measured at three different Imiperatures (Tj > T2 > T ) in the...

Achiral smectic materials with anticUnic molecular packing are very rare [40] and their antiferroelectric properties have unequivocally been demonstrated only in 1996 [41]. The antiferroelectilc properties have been observed in mixtures of two achiral components, although no one of the two manifested this behaviour. In different mixtures of a rod like mesogenic compound (monomer) with the polymer comprised by chemically same rod-like mesogenic molecules a characteristic antiferroelectric hysteresis of the pyroelectric coefficient proportional to the spontaneous polarization value has been observed for an example see Fig. 13.27a. Upon application of a low voltage the response is linear, at a higher field a field-induced AF-F transition occurs. 

Fig. 13.27 Achiral antiferroelectric. Voltage dependence of pyroelectric coefficient describing the double hysteresis loop (a) and dependence of the field-induced polarization on the content of a monomer in the polymer-monomer mixtures (b)...

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