Paraelectric phase, ferroelectric crystals

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],... 

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... 

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... 

Now let us discuss the behavior recently observed in doped ferroelectric crystals in the paraelectric phase (see Section IV.C). Because process B was observed only in crystal 1 (see Fig. 18), it must be attributed to the presence of the Cu impurities embedded at random in the KTN crystal. The Arrhenius nature of the process at elevated temperatures above 354 K indicates normal relaxation of the independent Cu+ ions [179]. These ions are significantly smaller than the K+ sites in which they reside (the radii of the Cu+ and the K+ ions are 0.77 A and 1.52 A, respectively [250]), leading to off-center displacements. The Cu+ ions can therefore hop between the eight symmetrical minima of their potential wells. Indeed, the energy of activation of EBa = 0.37 eV corresponds to the activation energies for the hopping of transition metal ion impurities in KTa03 [251]. 

Thus, one may summarize the physical picture of the relaxation dynamics in KTN crystal-doped with Cu+ ions in the following way In the paraelectric phase, as the ferroelectric phase transition is approached, the Nb5+ ions form dipolar clusters around the randomly distributed Cu+ impurity ions. The interaction between these clusters gives rise to a cooperative behavior according to the AG theory of glass-forming liquids. At the ferroelectric phase transition the cooperative relaxation of the Cu+ ions is effectively frozen. ... 

Studying the temperature evolution of UV Raman spectra was demonstrated to be an effective approach to determine the ferroelectric phase transition temperature in ferroelectric ultrathin films and superlattices, which is a critical but challenging step for understanding ferroelectricity in nanoscale systems. The T. determination from Raman data is based on the above mentioned fact that perovskite-type crystals have no first order Raman active modes in paraelectric phase. Therefore, Raman intensities of the ferroelectric superlattice or thin film phonons decrease as the temperature approaches Tc from below and disappear upon ti ansition into paraelectric phase. Above Tc, the spectra contain only the second-order features, as expected from the symmetry selection rules. This method was applied to study phase transitions in BaTiOs/SrTiOs superlattices. Figure 21.3 shows the temperature evolution of Raman spectra for two BaTiOs/SrTiOa superlattices. From the shapes and positions of the BaTiOs lines it follows that the BaTiOs layers remain in ferroelectric tetragonal... 

Raman spectra as a function of temperature are shown in Fig. 21.6b for the C2B4S2 SL. Other superlattices exhibit similar temperature evolution of Raman spectra. These data were used to determine Tc using the same approach as described in the previous section, based on the fact that cubic centrosymmetric perovskite-type crystals have no first-order Raman active modes in the paraelectric phase. The temperature evolution of Raman spectra has indicated that all SLs remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below T. The Tc determination is illustrated in Fig. 21.7 for three of the SLs studied SIBICI, S2B4C2, and S1B3C1. Again, the normalized intensities of the TO2 and TO4 phonon peaks (marked by arrows in Fig. 21.6b) were used. In the three-component SLs studied, a structural asymmetry is introduced by the presence of the three different layers, BaTiOs, SrTiOs, and CaTiOs, in each period. Therefore, the phonon peaks should not disappear from the spectra completely upon transition to the paraelectric phase at T. Raman intensity should rather drop to some small but non-zero value. However, this inversion symmetry breakdown appears to have a small effect in terms of atomic displacement patterns associated with phonons, and this residual above-Tc Raman intensity appears too small to be detected. Therefore, the observed temperature evolution of Raman intensities shows a behavior similar to that of symmetric two-component superlattices. 

Figure 4.4. Crystal structure of (a) the ferroelectric and (b) the paraelectric phases of VF2-F3E copolymer. (From Tashiro Tadokoro, 1987.)...

Figure 9-3. A fragment of the KH2PO4 (KDP) crystal structure viewed along the (001) plane (horizontal in these drawings), and perpendicular to the [z] axis (vertical) (A) in the ferroelectric phase at 102 K (i.e. 20 K below the phase transition at 7 =122 K) and (B) in the paraelectric phase at 127 K (i.e. 5 K above T ). The non-H atoms are shown with thermal ellipsoids at the 50% probability level, and the sites of H atoms are represented as small circles of arbitrary size, half occupied in the paraelectric phase (B). The H bonds are indicated as dashed lines in drawing A...

A copolymer of vinylidene fluoride-trifluoroethylene (VDF/TrFE) copolymer is well known as the polymer for which a clear Curie point was found for the first time in an organic material. At this Curie point, the polymer undergoes a solid-to-solid phase transition from paraelectric to ferroelectric phases with decreasing temperature. Therefore, the changes in the physical properties such as crystal structure, electrical and thermal properties upon the ferroelectric phase transition have drawn many researchers interest. Here, the results concerning the ultrasomc spectroscopic mvestigation on acoustic and viscoelastic behaviour around the ferroelectric phase transition region of this copolymer are described [15]... 

Let us consider the system of electric dipoles and other defects randomly distributed in the film paraelectric phase. Similarly to the random field model for bulk relaxor ferroelectrics [83], this phase is called Burns reference phase. For example, the relaxor ferroelectric Pbo,92Lao,osZro,65Tio,3503 (PLZT) (where La ions are the main sources of random field) is known to have the Burns phase simply as the paraelectric phase of PbZro,65Tio,3s03 (PZT). Latter phase exists at T > Tj, Td is so-called Burns temperature and Td = 1), where Tc is transition temperature form paraelectric to ferroelectric phase in PZT. The indirect interaction of electric dipoles via soft phonon mode of a host crystal tends to order the system and so to generate the ferroelectric phase in it [84]. However, the direct interaction of dipoles and other defects like point charges, try to disorder a system, transforming it into relaxor ferroelectric. 

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