Paraelectric-to-ferroelectric phase transition

Smith M6, Page K, Siegrist Th (2008) Crystal structure and the paraelectric-to-ferroelectric phase transition of nanoscale EaTrOs. J Am Chem Soc 130 6955-6963... 

Lynch and Shelby (1984) examined the reasons for the high dielectric properties of lead titanate glass-ceramics. They defined the matrix phase around the ferroelectric crystals. They also determined a special effect they called clamping. This phenomenon occurs when the glass matrix contracts and produces compressive stress within the ferroelectric particles, causing paraelectric-to-ferroelectric phase transition. As a result, the crystal size must be controlled for electro-optic applications. The crj tals should preferably be smaller than 0.1 pm. 

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]... 

Detailed calculations in Ref. [70] had shown, that latter criterion implies the transition from paraelectric to ferroelectric phase for sufficiently thin antiferroelectric film. For such film, the ratio 8/ < 0, while at 8/ > 0 the transition PE AEE can be realized. Therefore, the signs of the coefficients before different types of polarization gradients (see Eq. 3.56) essentially influence the form of antiferroelectric films phase diagram. 

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. 

We emphasize, that the quantity dtEo(h)/kB is indeed a Burns temperature Td [90] of the film. We recollect that Td is a temperature of transition from paraelectric to ferroelectric phase under the condition of random fields absence. It is seen, that Td depends on the film thickness, which reflects the size effect in relaxor ferroelectric films. 

The dielectric susceptibility is also temperature dependent. According to the Ciuie-Weiss law (Eq. (5.19)), the dielectric susceptibility is divergent at the temperature 0 when going throngh the phase transition point from the paraelectric to ferroelectric phase. Therefore, the expansion coefficient g2 mnst go through zero value at the same temperature 0... 

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. 

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]. 

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. 

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... 

An independent assessment of the validity of the A G interpretation to the Cu+-induced relaxation (process B) was provided by direct estimation of the configurational entropy at the ferroelectric phase transition. The phase transition is dominated by a shift in the position of the Nb5+ ion in relation to the lattice. The coupling between the Cu+ ions and the Nb5+ polar clusters, evident in the paraelectric phase, will further contribute to the configuational entropy of the phase transition. 

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. ... 

On the other hand, the proton potential of the 5-bromo compound is exactly symmetrical with reference to the reaction coordinate of the tautomerization. Consequently, the proton transfer can proceed through the tunnelling mechanism. This is the reason why the paraelectric behaviour is maintained even at 4 K. The suppression of the antiferroelectric phase transition may be derived from a quantum tunnelling effect. Such paraelectric behaviour can be regarded as quantum paraelectricity , which is a notion to designate the phenomenon that (anti)ferroelectric phase transitions are suppressed even at cryogenic temperatures due to some quantum-mechanical stabilization, proton tunnelling in this case. 

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... 

Initially, it appeared that the phase transitions are purely of the order-disorder type [24]. However, it soon became apparent that atomic displacements also contribute to these phase transitions. These displacements are easy to identify, when one compares the molecular arrangements in the ordered -OH 0= bonds in Fig. 1, with the arrangement of these molecules linked by the disordered bond in Fig. 2. The hydrogen-bonded molecules/ions must rotate before the two H-sites become symmetry-equivalent in the paraelectric phase above Tc- These rotations, usually of few degrees, can be termed as angular displacements. In other words, these angular displacements measure the distortions of the ferroelectric structure where the H-atom ordered from the paraelectric structure where the H-atom is dynamically disordered in two equivalent sites. 

In order to understand the origin of the paraelectric to ferroelectric transition and the accompanying structural phase transitions it is important to understand how the local field is affected by the polarization of the lattice. Equation (14A.3), which relates the local field Eioc to the applied field , and the polarization P can be generalized to read... 

The results of specific heat measurements were reported earlier in the Sect. 2.2.1.4 (Chap. 2) for nanogranular BaTiOj ceramics. As in this case the ferroelectric phase transition is of the first kind, the Td R) in Eq. (3.85) is a boundary of paraelectric phase stability, while the real transition temperature is shifted from it by some R-independent value [93]. With respect to this statement it is possible to write specific heat Cp on the base of Eq. (3.85) with the only /(-dependent free energy coefficient Ar T). Since Cp = -7 (d /dr )(4> is a free energy) one can find, that the difference between specific heat in ferroelectric and paraelectric phases reads ... 

The divergences of correlation radius could be achieved only for T = Tcr R,/aa) or at R = Rcr, corresponding to the paraelectric-ferroelectric phase transition point as one can see from Eq. (4.24). One can see from Fig. 4.28, that these conditions can be met at fixed radius R for arbitrary f A or for arbitrary R at given temperature T. Since the same fixed values of R or f A correspond to the divergence (or maxima for finite electric field value) of dielectric permittivity x (because R y/guJ.) these values of the radius and flexoelectric coefficient... 

As we have seen, locally the smectic C layers are polar, belonging to pyroelectric class C2. Macroscopically SmC either forms a helical structore or does not. So, we can discuss a structure without helicity. In a sense, the formation of a helix is equivalent to formation of ferroelectric domains which would reduce overall macroscopic polarisation. Thus we can consider the (1) (very important) and (2) (additional) requirements fulfilled. As to the phase transition (3), we know that in the smectic A phase, even chiral, there is no polar axis, therefore that phase can be considered as a paraelectric phase. The two-component order parameter of the A -C transition is the same as the parameter of the A-C transition in an achiral substance, namely 9exp (i(p), where we recognise the tilt 9 and azimuth (p angles. The spontaneous... 

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