Paraelectric phase state

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). 

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... 

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]. 

Tinte et al.54 have carried out molecular dynamic simulations of first-principles based effective Hamiltonian for PSN under pressure and of PMN at ambient pressure that clearly exhibit a relaxor state in the paraelectric phase. Analysis of the short-to-medium range polar order allows them to locate Burns temperature Tb. Burns temperature is identified as the temperature below which dynamic nanoscale polar clusters form. Below TB, the relaxor state characterized by enhanced short-to-medium range polar order (PNR) pinned to nanoscale chemically ordered regions. The calculated temperature-pressure phase diagram of PSN demonstrates that the stability of the relaxor state depends on a delicate balance between the energetics that stabilize normal ferroelectricity and the average strength of quenched "random" local fields. 

Thin pills and nanowires. To be specific, hereafter we put ai(T) = ar (T — Tc) and use typical (for screened ferroelectric thin pills) form of depolarization field Ef = ((P3) - P3)/(soSi), P3 is polarization directed along the pill symmetry axes (see inset to Fig. 4.25), where is so-called dielectric permittivity of the background [89] or reference state [90] unrelated to ferroelecfiic soft mode (typically Sb < 10). Linearized solution of Eq. (4.17a) gives the averaged value of susceptibility in paraelectric phase ... 

So at fixed radius R, superparaelectric (SPE) phase may appear only in the temperature range Tf(R) fixed temperature (e.g. at room one) SPE phase may appear only at nanoparticle radii RcAT) particle alignment is necessary for SPE appearance (see Fig. 4.35b). As we have already discussed for superparaelectric nanoparticles, the alignment due to the correlation effects is possible, when the particle radius R is less than the correlation radius Rc. On the other hand the particle radius must be higher than the critical radius R of size-driven ferroelectric-paraelectric phase transition. 

One of the solutions -P = 0- corresponds to the paraelectric phase. The state Ps = 0 is non-stable in the ferroelectric phase on the contrary. In this phase, the non-zero spontaneous polarization appears. 

G has a minimum for the order parameter of zero (P=0, corresponding to the paraelectric phase) for Torder parameter in thermodynamic equilibrium. A second order phase transition takes place at 7 = T. ... 

The ferroelectric state is therefore stable for temperatures less than T. Let us note that everything takes place as though there was an apparent stiffness In the paraelectric phase, the frequency of one of the vibration modes of the lattice, referred to as soft mode ... 

The phase transiton from a paraelectric to a ferroelectric state, most characteristic for the SbSI type compounds, has been extensively studied for SbSI, because of its importance with respect to the physical properties of this compound (e.g., J53, 173-177, 184, 257). The first-order transition is accompanied by a small shift of the atomic parameters and loss of the center of symmetry, and is most probably of a displacement nature. The true structure of Sb4S5Cl2 106), Bi4S5Cl2 194), and SbTel 108,403) is still unknown. In contrast to the sulfides and selenides of bismuth, BiTeBr 108) and BiTel (JOS, 390) exhibit a layer structure similar to that of the Cdl2 structure, if the difference between Te, Br, and I (see Fig. 36) is ignored. 

Measurements of NMR for Ti, Ti [33], and Sr [34,35] were carried out for STO 16 and STO 18-96. Ti and Sr nuclear magnetic resonance spectra provide direct evidence for Ti disorder even in the cubic phase and show that the ferroelectric transition at Tc = 25 K occurs in two steps. Below 70 K, rhomb ohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below Tc. This shows that the elusive ferroelectric transition in STO 18 is indeed connected with local symmetry lowering and impHes the existence of an order-disorder component in addition to the displacive soft mode [33-35]. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric... 

At high temperatures, ferroelectric materials transform to the paraelectric state (where dipoles are randomly oriented), ferromagnetic materials to the paramagnetic state, and ferroelastic materials to the twin-free normal state. The transitions are characterized through order parameters (Rao Rao, 1978). These order parameters are characteristic properties parametrized in such a way that the resulting quantity is unity for the ferroic state at a temperature sufficiently below the transition temperature, and is zero in the nonferroic phase beyond the transition temperature. Polarization, magnetization and strain are the proper order parameters for the ferroelectric. 

In some materials the antiferroelectric state is barely stable or metastable. In such materials, application of an electric field will convert the phase to ferroelectric, as described, but removal of the field leaves the phase in a ferroelectric state. This material then behaves like a typical ferroelectric and displays a conventional hysteresis loop. Heating the material to a high temperature so as to form the paraelectric structure, followed by cooling, can reform the original antiferroelectric state. 

Ceramic PLZT has a number of structures, depending upon composition, and can show both the Pockels (linear) electro-optic effect in the ferroelectric rhombohedral and tetragonal phases and the Kerr (quadratic) effect in the cubic paraelectric state. Because of the ceramic nature of the material, the non-cubic phases show no birefringence in the as-prepared state and must be poled to become useful electro-optically (Section 6.4.1). PMN-PT and PZN-PT are relaxor ferroelectrics. These have an isotropic structure in the absence of an electric field, but this is easily altered in an applied electric field to give a birefringent electro-optic material. All of these phases, with optimised compositions, have much higher electro-optic coefficients than LiNb03 and are actively studied for device application. 

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