Ferroelectrics phase transitions

The PTC materials already mentioned depend directly on the ferroelectric phase transition in solid solutions based on BaTi03, suitably doped to render them semiconducting. This is a typical example of the interrelations between different electrical phenomena in ceramics. 

The concept of quantum ferroelectricity was first proposed by Schneider and coworkers [1,2] and Opperman and Thomas [3]. Shortly thereafter, quantum paraelectricity was confirmed by researchers in Switzerland [4], The real part of the dielectric susceptibihty of KTO and STO, which are known as incipient ferroelectric compounds, increases when temperature decreases and becomes saturated at low temperature. Both of these materials are known to have ferroelectric soft modes. However, the ferroelectric phase transition is impeded due to the lattice s zero point vibration. These materials are therefore called quantum paraelectrics, or quantum ferroelectrics if quantum paraelectrics are turned into ferroelectrics by an external field or elemental substitution. It is well known that commercially available single crystal contains many defects, which can include a dipolar center in the crystal. These dipolar entities can play a certain role in STO. The polar nanoregion (PNR originally called the polar microregion) may originate from the coupling of the dipolar entities with the lattice [5-7]. When STO is uniaxially pressed, it turns into ferroelectrics [7]. 

According to the concept of the displacive-type ferroelectric phase transition [10], an increase in the dielectric constant corresponds directly to the softening of the IR-active transverse phonon. When the crystal can be regarded as an assembly of the vibrators of normal coordinates, the soft phonon... 

It has been widely recognized that the Ught scattering technique yields essential information on a dynamic mechanism of ferroelectric phase transition because it clearly resolves the dynamics of the ferroelectric soft mode that drives the phase transition. Quantum paraelectricity is caused by the non-freezing of the soft mode. Therefore, the isotope-exchange effect on the soft mode is the key to elucidating the scenario of isotopically induced ferroelectricity. 

Static dielectric measurements [8] show that all crystals in the family exhibit a very large quantum effect of isotope replacement H D on the critical temperature. This effect can be exemphfied by the fact that Tc = 122 K in KDP and Tc = 229 K in KD2PO4 or DKDP. KDP exhibits a weak first-order phase transition, whereas the first-order character of phase transition in DKDP is more pronounced. The effect of isotope replacement is also observed for the saturated (near T = 0 K) spontaneous polarization, Pg, which has the value Ps = 5.0 xC cm in KDP and Ps = 6.2 xC cm in DKDP. As can be expected for a ferroelectric phase transition, a decrease in the temperature toward Tc in the PE phase causes a critical increase in longitudinal dielectric constant (along the c-axis) in KDP and DKDP. This increase follows the Curie-Weiss law. Sc = C/(T - Ti), and an isotope effect is observed not only for the Curie-Weiss temperature, Ti Tc, but also for the Curie constant C (C = 3000 K in KDP and C = 4000 K in DKDP). Isotope effects on the quantities Tc, P, and C were successfully explained within the proton-tunneling model as a consequence of different tunneling frequencies of H and D atoms. However, this model can hardly reproduce the Curie-Weiss law for Sc-... 

Determination of the critical temperature after equation (1), T0 = En/Syl, is considered in the cooperative JT and PJT effects [2,3,8,9]. In particular, the origin of structural ferroelectric phase transitions as due to the PJT effect (the vibronic theory of ferroelectricity) was suggested first in the sixties [10] (see also Ref. [9]). JT structural phase transitions are reviewed in Ref. [8]. 

Tc a phase transition to a state with spontaneous polarization takes place (ferroelectric phase transition). The mechanism becomes clearer considering Figure 1.11 (b). At the zone center (k = 0) the wavelength of the to mode is infinite (A —> oo), i.e the region of homogeneous polarization becomes infinite. In the case of the softening of the to mode the transverse frequency becomes zero and no vibration exists anymore ( frozen in ). 

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... 

Chaotic Behavior near the Ferroelectric Phase Transition... 

The ferroelectric phase transition of second-order in tgs at 0C = 49° C can be described in the framework of the Landau-theory (e.g. [4]) by the thermodynamical potential... 

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