Ferroelectric spontaneous polarization

Ferroelectric Spontaneous polarization Electric field BaTiOj... 

Ferroelectrics Spontaneous polarization Electric field BaTiOs... 

Barium strontilun titanate - (Ba, Sr)Ti03 Ferroelectrics spontaneous polarization that can be switched with an electric field. They have a structural phase transition at a temperatiu-e (Curie temperature (TJ) at which permittivity has a strong anomaly. For example, lead zirconate titanate - Pb(Zr, Ti)Os, barium titanate - BaTiOs... 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

The most important materials among nonlinear dielectrics are ferroelectrics which can exhibit a spontaneous polarization PI in the absence of an external electric field and which can spHt into spontaneously polarized regions known as domains (5). It is evident that in the ferroelectric the domain states differ in orientation of spontaneous electric polarization, which are in equiUbrium thermodynamically, and that the ferroelectric character is estabUshed when one domain state can be transformed to another by a suitably directed external electric field (6). It is the reorientabiUty of the domain state polarizations that distinguishes ferroelectrics as a subgroup of materials from the 10-polar-point symmetry group of pyroelectric crystals (7—9). 

Both the Spontaneous polarization PI and the remanent polarization P/ are strong functions of temperature, particularly near the transition temperature T in ferroelectrics (7) ... 

Ferroelectrics. Ferroelectrics, materials that display a spontaneous polarization ia the abseace of an appHed electric field, also display pyroelectric and piezoelectric behavior. The distinguishing characteristic of ferroelectrics, however, is that the spontaneous polarization must be re-orientable with the appHcation of an electric field of a magnitude lower than the dielectric breakdown strength of the material. 

Since niobates and tantalates belong to the octahedral ferroelectric family, fluorine-oxygen substitution has a particular importance in managing ferroelectric properties. Thus, the variation in the Curie temperature of such compounds with the fluorine-oxygen substitution rate depends strongly on the crystalline network, the ferroelectric type and the mutual orientation of the spontaneous polarization vector, metal displacement direction and covalent bond orientation [47]. Hence, complex tantalum and niobium fluoride compounds seem to have potential also as new materials for modem electronic and optical applications. 

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],... 

The main source of spontaneous polarization in crystals is the relative freedom of cations that fit loosely into the crystal s octahedral cavities. The number of degrees of freedom of the octahedrons affects the spontaneous polarization value and hence influences the crystal s ferroelectric properties. Abrahams and Keve [389] classified ferroelectric materials into three structural categories according to their atomic displacement mechanisms onedimensional, two-dimensional and three-dimensional. 

A similar chiral chlorogold(I) compound [AuCl(CNC6H4C00C6H40C H-MeC6Hi3)j has been described, displaying ferroelectric SmC (152 °C), and SmA (185 °C) mesophases before decomposition occurs at the clearing temperature (285 °C). However, the spontaneous polarization could not be measured with precision due to the inherent conductivity of the compound [12]. 

Hysteresis curve of a ferroelectric crystal, v = initial (virginal) curve, Pr = remanent polarization, Ps = spontaneous polarization, Ec = coercive field... 

Using this method, the M6R8/PM6R8 blend showed precisely the behavior expected for the achiral SmAPA structure. Specifically, the optical properties of the films were consistent with a biaxial smectic structure (i.e., two different refractive indices in the layer plane). The thickness of the films was quantized in units of one bilayer. Upon application of an electric field, it was seen that films with an even number of bilayers behaved in a nonpolar way, while films with an odd number of bilayers responded strongly to the field, showing that they must possess net spontaneous polarization. Note that the electric fields in this experiment are not strong enough to switch an antiferroelectric to a ferroelectric state. Reorientation of the polarization field (and director structure) of the polar film in the presence of a field can easily be seen, however. 

This volume of Topics in Stereochemistry could not be complete without hearing about ferroelectric liquid crystals, where chirality is the essential element behind the wide interest in this mesogenic state. In Chapter 8, Walba, a pioneering contributor to this area, provides a historical overview of the earlier key developments in this field and leads us to the discovery of the unique banana phases. This discussion is followed by a view of the most recent results, which involve, among others, the directed design of chiral ferroelectric banana phases, which display spontaneous polar symmetry breaking in a smectic liquid crystal. 

Note 7 When the tilt direction alternates from layer to layer, the smectic mesophase is antiferroelectric such mesophases do not possess spontaneous polarization. They can be turned into ferroelectric structures through the application of an electric field. 

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-... 

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