Paraelectric phases, ferroelectrics

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],... 

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

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... 

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... 

In conclusion, it appears that microhardness yields information about paraelectric to ferroelectric phase changes in VF2/F3E copolymers which can be discussed in the light of the changes in the lattice spacings of the different phases and in variations of the crystallinity value. 

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. 

A primary focus of our work has been to understand the ferroelectric phase transition in thin epitaxial films of PbTiOs. It is expected that epitaxial strain effects are important in such films because of the large, anisotropic strain associated with the phase transition. Figure 8.3 shows the phase diagram for PbTiOs as a function of epitaxial strain and temperature calculated using Landau-Ginzburg-Devonshire (lgd) theory [9], Here epitaxial strain is defined as the in-plane strain imposed by the substrate, experienced by the cubic (paraelectric) phase of PbTiOs. The dashed line shows that a coherent PbTiOs film on a SrTiOs substrate experiences somewhat more than 1 % compressive epitaxial strain. Such compressive strain favors the ferroelectric PbTiOs phase having the c domain orientation, i.e. with the c (polar) axis normal to the film. From Figure 8.3 one can see that the paraelectric-ferroelectric transition temperature Tc for coherently-strained PbTiOs films on SrTiOs is predicted to be elevated by 260°C above that of... 

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