Polarization spontaneous electric

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). 

Ferroelectric crystals exhibit spontaneous electric polarization and hysteresis effects in the relation between polarization and electric field, as shown in Figure 1. This behavior is usually observed in a limited temperature range, ie, usually below a transition temperature (10). 

In addition, some liquid-crystalline elastomers are ferroelectric (possess spontaneous electric polarization) [196,197], or piezoelectric (become electrically... 

There is considerable interest in developing new types of magnetic materials, with a particular hope that ferroelectric solids and polymers can be constructed— materials having spontaneous electric polarization that can be reversed by an electric field. Such materials could lead to new low-cost memory devices for computers. The fine control of dispersed magnetic nanostructures will take the storage and tunability of magnetic media to new levels, and novel tunneling microscopy approaches allow measurement of microscopic hysteresis effects in iron nanowires. 

Figure 8.16 Illustration of symmetry of Soto Bustamante-Blinov achiral antiferroelectric smectic LC with finite number of layers. Such systems can be studied using DRLM technique with thin freely suspended smectic films, (a) With even number of bilayers, film has local C2 symmetry, and therefore no net electric polarization, (b) With odd number of bilayers, film has local Cnv symmetry and is therefore polar, with net spontaneous electric polarization in plane of layers.

The soft mode concept can be extended to all distortive phase transitions (transitions with relatively small atomic displacements), even if they are only close to second order. In the case of a ferro-distortive transition, as for example in BaTiOs or KDP, the order parameter is proportional to the spontaneous electric polarization Fj. d F/ dp is not only proportional to co, but also to the dielectric susceptibility. This does not, however, mean that all components of the order parameter eigenvector must contribute to Ps. 

Piezoelectric materials are materials that exhibit a linear relationship between electric and mechanical variables. Electric polarization is proportional to mechanical stress. The direct piezoelectric effect can be described as the ability of materials to convert mechanical stress into an electric field, and the reverse, to convert an electric field into a mechanical stress. The use of the piezoelectric effect in sensors is based on the latter property. For materials to exhibit the piezoelectric effect, the materials must be anisotropic and electrically poled ie, there must be a spontaneous electric field maintained in a particular direction throughout the material. A key feature of a piezoelectric material involves this spontaneous electric field and its disappearance above the Curie point. Only solids without a center of symmetry show this piezoelectric effect, a third-rank tensor property (14,15). 

An ideal single crystal shows a P E) behavior as depicted in Figure 1.6. The non-ferroelectric dielectric ionic and electronic polarization contributions are clearly linear, and are suposed by the spontaneous polarization Ps (dashed curve in Figure 1.6). To reverse the polarization an electrical field with an amplitude E > Ec is required. In opposite to single crystals in polydomain ferroelectric ceramics, the remanent polarization Pr is smaller than the spontaneous one Ps due to backswitching even for opposite fields as shown in Figure 1.6. In that case Ps can be estimated by extrapolation of (non-switching) P-values to E — 0. 

However, the temperature, at which the maximum of the initial scattered light occurs, seems to be related to the scattering angle 9S and thus to the period Ag , respectively. Figure 9.14(b) shows the correspondence between the temperature Tm of maximum intensity Ig and the spatial period Agn. A spatial disorder of the smallest polar structures occurs at Tm = 45 °C, while the spatial orientation of the largest structures remains stable up to Tm = 60 °C. Such big dispersion of the thermal decay of polar structures over Agn unambiguously illustrates the relaxor behavior of sbn. At the same time it is a key point to understand the bandwidth in the determination of the phase transition temperature Tm in sbn from different methods. For example, in sbn doped with 0.66 mol% Cerium, Tm detected from the maximum of the dielectric permittivity e at 100 Hz (e-method) equals Tm = 67 °C [20], Determination of Tm from the inflection point of the spontaneous electric polarization P3... 

Ferroelectrics are a class of materials possessing a spontaneous electric polarization, which can be switched between crystallographically defined directions by... 

A ferroelectric crystal shows a spontaneous electric polarization that can be reoriented between multiple equilibrium directions by application of an electric field The materials known as ferroelectric ceramics have attained a high level of importance". ... 

Electrostrictive polymers have a spontaneous electric polarization. Electrostriction results from the change in dipole density of the material. These polymers contain molecular or nanocrystaUine polarizations that align with an applied electric field. PVDF copolymers with nano-sized crystalline domains, electrostrictive graft copolymers, and liquid crystal elastomers fall under this category. 

The orientation of liquid crystals can be influenced by an electric field. This property makes LCPs attractive for LCDs. Some liquid crystals undergo a spontaneous electric polarization even in the absence of an external electric field. This phenomenon is referred to as a ferroelectricity. 

Surfactant molecules are made up of two moieties that have antagonistic properties, a polar or electrically charged hydrophilic moiety and a hydrophobic moiety, most often an alkyl chain. In aqueous solution, most surfactants self-assemble and form micelles when their concentration becomes larger than the so-called critical micellization concentration (CMC). In micelles (fromthe Creek mica, which means "grain "), the alkyl chains are in contact and form an oily core that is coated by the polar head groups. The outer layer that contains head groups, counterions (in the case of ionic surfactants), water and the first methylene group of the alkyl chain is called the palisade layer. The formation o/micelles is a cooperative process that is spontaneous and reversible. Micelles are thermodynamically stable species that are in chemical equilibrium with free surfactants. 

Barium titanate is cubic with a perovskite structure. However, at room temperature (actually below the Curie temperature of 120°C) it is tetragonal with a spontaneous electric polarization in the direction of the c-axis (only the higher temperatures form is shown in Figure 7.2). In this ferroelectric condition a crystal of BaTiOs has a domain structure. 

The pyroelectric effect is used in pyroelectric energy harvesting, and the electrocaloric effect is currently being explored for refrigeration. Perovskite aystals that show the pyroelectric effect contain a unique polar axis and a spontaneous electric polarisation, P, directed along this axis. As all ferroelectrics are also pyroelectrics (Chapter 6),... 

It is known that the crystal symmetry defines point symmetry group of any macroscopic physical property, and this symmetry cannot be lower than corresponding point symmetry of a whole crystal. The simplest example is the spontaneous electric polarization that cannot exist in centrosymmetric lattice as the symmetry elements of polarization vector have no operation of inversion. We remind that inversion operation means that a system remains intact when coordinates x, y, z are substituted by —x, —y, —z. If the inversion center is lost under the phase transition in a ferroic at T < 7), Tc is the temperature of ferroelectric phase transition or, equivalently, the Curie temperature), the appearance of spontaneous electrical polarization is allowed. Spontaneous polarization P named order parameter appears smoothly... 

All above means that the ferroics can be regarded as a general notation for the materials, where at T < (so-called low-temperature phase) some reorientable physical quantities (order parameters) spontaneously appear. Latter order parameters can be of vector (spontaneous electric polarization, spontaneous magnetization) or tensor (second order tensor like spontaneous deformation or higher order tensors like elastic moduli and piezoelectric coefficients) nature. In low-temperature phase ferroics can usually split into domains, their switching being possible by the external fields. 

Lebeugle, D., Colson, D., Forget, A., and Viret, M. (2007) Very large spontaneous electric polarization in BiFeOr single crystals at room temperature and its evolution under cycling fields. Appl. Phys. Lett., 91, 022907. 

A ferroelectric crystal is defined as a crystal which belongs to the pyroelectric family (i. e. shows a spontaneous electric polarization) and whose direction of spontaneous polarization can be reversed by an electric... 

The point group C2 is a polar point group with the C2-axis being a polar axis allowing a nonzero spontaneous electric polarization Pg. In a molecular picture, this means that the transverse dipole moments are not canceled due to the lack of the mirror plane. In consequence, a spontaneous electric polarization Pg occurs along the polar C2-axis and thus perpendicular to the plane spaimed by n and k ... 

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