Paraelectric phase

Historically, materials based on doped barium titanate were used to achieve dielectric constants as high as 2,000 to 10,000. The high dielectric constants result from ionic polarization and the stress enhancement of k associated with the fine-grain size of the material. The specific dielectric properties are obtained through compositional modifications, ie, the inclusion of various additives at different doping levels. For example, additions of strontium titanate to barium titanate shift the Curie point, the temperature at which the ferroelectric to paraelectric phase transition occurs and the maximum dielectric constant is typically observed, to lower temperature as shown in Figure 1 (2). 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

Figure 2 shows the schematic structure in the paraelectric (T > Tn) and an-tiferroelectric (T < Tn) phases, hi the paraelectric phase the time-averaged position of the H atoms hes in the middle of an O - H...0 bond, whereas in the antiferroelectric phase, the protons locahze close to one or the other O atom. Prior to the recent NMR work [20-25], the largely accepted model of the phase transition was that the phase transition involved only the ordering of the H atoms in the O - H...0 bonds, and no changes in the electronic structure of the C4 moieties were considered to take place. The NMR results show that, in addition to the order/disorder motion of the H atoms, the transition also involves a change in the electronic charge distribution and symmetry of the C4 squares. 

Figures 15 and 16 show the temperature dependence of the chemical shift for 80% deuterated KD2PO4 and RbH2P04. Obviously, iso varies significantly with temperature in the paraelectric phase and shows a clear break at Tc of 202 K for DKDP and 147 K for RbH2P04, respectively. The shift exhibits a distinct discontinuity at Tc while the line width shows an abrupt increase below Tc, in agreement with the (close to) first-order nature of the phase transition, and an anticipated pronounced distortion in the PO4 moiety. The cause of the line width increase below Tc has yet to be explained, but is at least partly due to a lack of the increased spinning speed to average out the enhanced chemical shift anisotropy below Tc.

Fig.l Ti positions in the cubic luiit cell in the paraelectric phase according to the displacive (left) and order-disorder (right) scenarios... 

The results show that in the paraelectric phase near Tc all Ti ions are disordered between several off-center sites. This agrees with the early view of Slater of a ratthng Ti ion in BaTiOs as well as with the original interpretation of the diffuse X-ray scattering [16]. 

In the calculation of the angular dependence of the second moment M2 of the Ti and Ti satelhte background in the paraelectric phase of BaTiOs, we have assumed that the Ti off-center shifts are static. The results are however also valid if we have biased exchange among the off-center sites, and... 

Figure 14 shows the result of a Brillouin scattering experiment in the vicinity of Tc [11]. Closed circles and open circles below Tc indicate the modes split from the doubly degenerated ferroelectric soft mode. The closed circles above Tc denote the frequency of the doubly degenerated soft u mode in the paraelectric phase. The results clearly show a softening of the soft mode toward zero frequency at Tc following the Curie-Weiss law. The soft mode remains underdamped even at Tc. Generally, a soft mode is heavily damped in the vicinity of Tc, e.g., as for PbTiOs, which are typical displacive-type... 

It should be noted that the Raman-inactive soft mode is observed in the temperature region above Tc. A spectral shape completely different from that of the Lorentz-type peak function indicates the defect-induced Raman scattering (DIRS) in the paraelectric phase of ST018. When centrosymmetry is locally broken in the paraelectric phase, the nominally Raman-inactive soft mode is optically activated locally to induce DIRS in the soft mode. 

Ferroelectric-paraelectric transitions can be understood on the basis of the Landau-Devonshire theory using polarization as an order parameter (Rao Rao, 1978). Xhe ordered ferroelectric phase has a lower symmetry, belonging to one of the subgroups of the high-symmetry disordered paraelectric phase. Xhe exact structure to which the paraelectric phase transforms is, however, determined by energy considerations. 

Ferroelectricity has also been found in certain copolymer compositions of VF2 with trifluoroethylene, F3E, [6-11] and tetrafluoroethylene, F4E, [12-15] and in nylon 11 [16]. Specifically, copolymers of vinylidene fluoride and trifluoroethylene (VF2/F3E) are materials of great interest because of their outstanding ferroelectricity [9,17-18], together with a parallel strong piezo- [7] and pyroelectricity [19]. These copolymers exhibit, in addition, an important aspect of ferroelectricity that so far has not been demonstrated in PVF2 the existence of a Curie temperature at which the crystals undergo reversibly a ferroelectric to a paraelectric phase transition in a wide range of compositions [9, 17-18],... 

Random copolymers of VF2/F3E when crystallized from the molten state above the Curie temperature show a microstructure in the form of very thin needle-like morphological units which are probably semicrystalline. Figure 5a illustrates the needle-like microstructure of the copolymer 80/20 melt crystallized in the paraelectric phase observed at 140 °C. After codling at room temperature the microstructure of the ferroelectric crystals is such that what appear in the optical microscope as radial fibers are, in fact, stacks of thin platelet-like morphological units (see Fig. 5b). 

Fig. 5. a. Needle-like microstructure of the 80/20 copolymer. Sample cast from dimethyl formamide molten at 180 °C and recrystallized at 140 °C in the paraelectric phase, b. Stacks of thin platelet-like crystals of the same copolymer after cooling the sample at room temperature in the ferroelectric phase. Scale bars, 25 pm... 

A schematic phase diagram summarizing the three temperature regions (Ff, Fnf and melt) is shown in Fig. 9. For VF2 compositions below 82%, at room temperature, one observes the predominant ferroelectric phase. With increasing temperature, the paraelectric phase appears and at higher temperatures one obtains the molten state of the paraelectric crystallites. The Tm values of the copolymers are considerable lower than those of both homopolymers and show... 

Fig. 16a-c. Schematic model of the lamellar structure of the copolymer in the, a. high temperature range (paraelectric phase) b. Curie transition region and c. low temperature region L and I denote respectively the long period and the average crystal thickness comprising a mixture of non ferroelectric and ferroelectric domains... 

T = 140 °C. Here, during solidification, the H increase from 140 °C down to about 100 °C is the result of a double contribution of (a) the crystallization of the fraction of molten crystals and (b) the thermal contraction of the nonpolar phase crystals. The hysteresis behavior is also found in other mechanical properties (dynamic modulus) derived from micromechanical spectroscopy [66, 67], where it is shown that the hysteresis cycle shifts to lower temperatures if the samples are irradiated with electrons. It has also been pointed out that the samples remain in the paraelectric phase, when cooling, if the irradiation dose is larger than 100 Mrad. 

Fig. 30. Quasielastic broadening of the neutron scattering peak observed in the paraelectric phase for the copolymer 60/40. The points represented the experimental results with their statistical error bar. The solid line is the Lorentzian function obtained after the deconvolution process described in the text...

Fig. 31. HWHM of the Lorentzian function versus the momentum transfer Q at several temperatures in the paraelectric phase...

The analysis of the real and imaginary part of the complex dielectric permittivity allows one to distinguish between the two main relaxation processes (a and P). The a-process is correlated to the transition from the ferro to the paraelectric phase and the p-process is attributed to segmental motions in the amorphous phase. 

Microhardness (MH), has been shown to be a convenient additional technique to detect accurately the ferro to paraelectric phase changes in these copolymers. The increase of MH as a function of VF2 polar sequences observed at room temperature is correlated with the contraction of the p-all-trans unit cell On the other hand, the fast exponential decrease of MH with increasing temperature, observed above Tc, is similar to that obtained for glassy polymers above Tg and suggests the existence of a liquid crystalline state in the high temperature paraelectric phase. This phase is characterized by a disordered sequence of conformational isomers (tg-, tg+, tt) as discussed for Condis crystals [109]. 

In the article by Balta Calleja et al., the latest results of investigations into the structure of poly(vinylidenefluoride)and its copolymers withpoly(trifluoroethylene) are summarized and extensively dicussed. These polymers are the most important ferroelectric materials. Special emphasis is placed on the relation between the change of structure and the transition from the ferroelectric into the paraelectric phase. 

It is useful to check whether this kind of relations is valid for other systems like ferromagnetics and ferroelectrics too. Here the order parameters are the magnetization M and the polarization P, respectively. At high temperatures (T > Tc), and zero external field these values are M = 0 (paramagnetic phase) and P = 0 (paraelectric phase) respectively. At lower temperatures close to the phase transition point, however, spontaneous magnetization and polarization arise following both the algebraic law M, P oc (Tc - Tf. 

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