Temperature Dependence of Ferroelectricity

The temperature dependence of the relative permittivity of many ferroelectric crystals in the paraelectric state can be desaibed fairly accurately by the Curie-Weiss law  

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Figure 6.10 Temperature dependence of ferroelectricity (a) first-order and second-order transitions to the high-temperature paraelectric state (b) the variation of relative permittivity across the Curie temperature...

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... 

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. ...

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... 

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. 

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. 

The high-frequency dielectric response of ferroelectrics seems so far to be fitted quite well by rather simple, mechanical models, at fixed temperature, and for that reason not to be very informative about the internal mechanism. Information about the temperature dependence of the medianical parameters has to be supplemented by measurements of magnetic resonance and of A -ray and neutron scattering. ... 

Vinylidene fluoride-trifluoroethylene (VF2-F3E) copolymers exhibit a ferroelectric-paraelectric phase transition, the first such case found for a synthetic polymer. In this transition, the electric polarization and piezoelectric constant of the film disappear above the Curie point (Tcurie)- The temperature dependence of the dielectric constant, , obeys the so called Curie-Weiss law ... 

Figure 4.18. Temperature dependence of the microhardness (a) during heating and (b) during cooling of the 60/40 (O), 70/30 (A), 80/20 ( ) VF2-F3E copolymers. The filled symbols denote the Curie transition region between ferroelectric (low T) and paraelectric (high T) and paraelectric (high T) behaviour. (From Balta Calleja, Santa Cruz et al, 1992.)...

Ferroelectric properties are exhibited by all three low-temperature modifications. The temperature dependence of the permittivity shows a distinct peak at the Curie temperature (cf. Fig. 194). 

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