Ferroelectrics temperature dependence

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

Fig. 11. Fundamental characteristics of relaxor materials compared to BaTiO. Temperature dependence for the relaxor ferroelectric 0.93...

Figure 3.8 Anomalous temperature dependence of relative dielectric constant of ferroelectric crystals at the transition temperature (Curie point).

Fig. 106. Temperature dependence of vs(NbO) and vs(NbF) wave numbers for a single crystal of RbsNbsOF/s- Reproduced from [442], A. I. Agulyansky, J. Ravez, R. Cavagnat, M. Couzi, Ferroelectrics 152 (1993) 373, Copyright 1993, with permission of Taylor Francis, Inc., http //www.routledge-ny.com.

Figure 12. Temperature dependence of the inverse dielectric susceptibility (xr ) of DNP along the principal axis for polymerization. (Reproduced with permission from Ref. 16. Copyright 1980, Ferroelectric. ...

The introduction of a polymer network into an FLC dramatically changes phase and electro-optic behavior. Upon addition of monomer to the FLC, the phase transitions decrease and after polymerization return to values close to that observed in the neat FLC. The phase behavior is similar for the amorphous monomers, HDD A and PPDA. The electro-optic properties, on the other hand, are highly dependent on the monomer used to form the polymer/FLC composite. The ferroelectric polarization decreases for both HDDA and PPDA/FLC systems, but the values for each show extremely different temperature dependence. Further evidence illustrating the different effects of each of the two polymers is found upon examining the polarization as both the temperature and LC phase of polymerization are changed. In PPDA systems the polarization remains fairly independent of the polymerization temperature. On the other hand, the polarization increases steadily as the polymerization temperature of HDDA systems is increased in the ordered LC phases. 

Il is interesting to discuss, next, the available e data for the various compositions in the light of the classical theory of ferroelectricity. According to this theory [100] for T > Tc the temperature dependence of e can be written as... 

The origin of the pyroelectric effect, particularly in crystalline materials, is due to the relative motions of oppositely charged ions in the unit cell of the crystal as the temperature is varied. The phase transformation of the crystal from a ferroelectric state to a paraelectrlc state involves what is called a "soft phonon" mode (9 1). In effect, the excursions of the ions in the unit cell increase as the temperature of the material approaches the phase transition temperature or Curie temperature, T. The Curie temperature for the material used here, LiTaO, is 618 C (95). The properties of a large number of different pyroelectric materials is available through reference 87. For the types of studies envisaged here, it is preferable to use a pyroelectric material whose pyroelectric coefficient, p(T), is as weakly temperature dependent as possible. The reason for this is that if p(T) is independent of temperature, then the induced current in the associated electronic circuit will be independent of ambient temperature and will be a function only of the time rate of change of the pyroelectric element temperature. To see this, suppose p(T) is replaced by pQ. Then Equation U becomes... 

Piezoelectric coefficients are also temperature dependent quantities. This is true for both the intrinsic and the extrinsic contributions. Typically, the piezoelectric response of a ferroelectric material increases as the transition temperature is approached from below (See Figure 2.3) [3], Where appropriate thermodynamic data are available, the increase in intrinsic dijk coefficients can be calculated on the basis of phenomenology, and reflects the higher polarizability of the lattice near the transition temperature. The extrinsic contributions are also temperature dependent because domain wall motion is a thermally activated process. Thus, extrinsic contributions are lost as the temperature approaches OK [4], As a note, while the temperature dependence of the intrinsic piezoelectric response can be calculated on the basis of phenomenology, there is currently no complete model describing the temperature dependence of the extrinsic contribution to the piezoelectric coefficients. 

It should be noted that in practice, the piezoelectric response will typically not continue to rise all the way to the transition temperature, as elevated temperatures induce depoling of the ferroelectric, unless appropriate care is taken to insure that the material remains polarized (e. g. by application of a bias electric field). Depoling of this type is often important at temperatures of 1/2 of the Curie temperature, making high transition temperature materials interesting both for the decreased temperature dependence in the response, and the wider use range that can be achieved. 

From the lattice dynamics viewpoint a transition to the ferroelectric state is seen as a limiting case of a transverse optical mode, the frequency of which is temperature dependent. If, as the temperature falls, the force constant controlling a transverse optical mode decreases, a temperature may be reached when the frequency of the mode approaches zero. The transition to the ferroelectric state occurs at the temperature at which the frequency is zero. Such a vibrational mode is referred to as a soft mode . 

The perovskite structure is, of course, of special significance in the electroceramics context since the ferroelectric perovskites are dominant in the ceramic capacitor, PTC thermistor and electromechanical transducer industries. The structure favours the existence of soft modes (low frequency phonons) as evidenced by its tendency to instability, for example the ferroelectric-paraelectric transition. Instability is evident in the case of the T23 compound which exhibits a tetragonal-orthorhombic transition in the region of 700 °C (the exact temperature depends on the oxygen content). Extensive twinning, very reminiscent of ferroelectric domain structures, is observed. 

In ferroelectric sodium nitrite the resonance disappears when the temperature is increased to the vicinity of the ferro-paraelectric transition and the nitrite ions start to rotate. Moreover, the frequency exhibits a strong temperature dependence that cannot be explained by the Bayer theory. 

Finally we can conclude that confinement could be responsible for nonmonotonic relaxation kinetics and could provide a specific saddle-like temperature dependence of the relaxation time. The experimental examples discussed show that this type of kinetics may be inherent in systems of completely different natures confined liquids, ferroelectric crystals, and it was even demonstrated recently macromolecular folding kinetics [78]. In each case, the specific interpretation of the parameters of model (129) depends on the discussed experimental situation. We are far from the opinion that confinement is the only reason for nonmonotonic relaxation kinetics. However, for all the examples discussed in this paper, the nonmonotonic dependence of the relaxation time on temperature has the same origin, that is, confinement either in real or configurational space. 

---