Polarization, spontaneous

The value of spontaneous polarization depends on the molecular characteristics of an FLC substance itself and the achiral dopant introduced into the matrix, and can vary from 1 to more than 200 nC/cm [11]. Spontaneous polarization Pg could be expressed via FLC molecular parameters [4, 5, 11] 

FIGURE 7.3. Dependence of spontaneous polarization Ps on tilt angle 0, The upper curve was measured for DOBAMBC [4], (left) scale lower ciurve was measured for a high polarization mixtm e [5]. 

The spontaneous polarization of FLCs can be measured by the pyroelectric technique using the temperature dependence of the pyroelectric coefficient 7 = dPsfdT [27], and by the conventional capacity Sawyer-Tower method [28] or by integrating the time dependence of the repolarization current ip (5 is the electrode area) [175, 176] 

Although there are important exceptions, a characteristic feature of the crystalline state is that compositions are stoichiometric, i.e. the various types of ion are present in numbers which bear simple ratios one to the other. In contrast, glass compositions are not thus restricted, the only requirement being overall electrical neutrality. 

Vitreous materials do not have the planes of easy cleavage which are a feature of crystals, and they do not have well-defined melting points because of the variable bond strengths that result from lack of long-range order. 

In general, because the value of a crystal property depends on the direction of measurement, the crystal is described as anisotropic with respect to that property. There are exceptions for example, crystals having cubic symmetry are optically isotropic although they are anisotropic with respect to elasticity. For these reasons, a description of the physical behaviour of a material has to be based on a knowledge of crystal structure. Full descriptions of crystal systems are available in many texts and here we shall note only those aspects of particular 

For the present purpose it is only necessary to distinguish polar crystals, i.e. those that are spontaneously polarized and so possess a unique polar axis, from the non-polar variety. Of the 32 crystal classes, 11 are centrosymmetric and consequently, non-piezoelectric. Of the remaining 21 non-centrosymmetric classes, 20 are piezoelectric and of these 10 are polar. An idea of the distinction between polar and non-polar structures can be gained from Fig. 2.3 and Eqs (2.70) and (2.71). 

The piezoelectric crystals are those that become polarized or undergo a change in polarization when they are stressed conversely, when an electric field is applied they become strained. The 10 polar crystal types are pyroelectric as well as piezoelectric because of the polarization inherent in their structure. In a pyroelectric crystal a change in temperature produces a change in polarization. 

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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) ... 

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

Tbe purpose of tbe bydroxyl group is to acbieve some hydrogen bonding with the nearby carbonyl group and therefore hinder the motion of the chiral center. Another way to achieve the chiral smectic Cphase is to add a chiral dopant to a smectic Chquid crystal. In order to achieve a material with fast switching times, a chiral compound with high spontaneous polarization is sometimes added to a mixture of low viscosity achiral smectic C compounds. These dopants sometimes possess Hquid crystal phases in pure form and sometimes do not. 

Pyroelectrics. Pyroelectric ceramics are materials that possess a uoique polar axis and are spontaneously polarized ia the abseace of an electric field. Pyroelectrics are also a subset of piezoelectric materials. Ten of the 20 crystal classes of materials that display the piezoelectric effect also possess a unique polar axis, and thus exhibit pyroelectricity. In addition to the iaduced charge resultiag from the direct pyroelectric effect, a change ia temperature also iaduces a surface charge (polarizatioa) from the piezoelectric aature of the material, and the strain resultiag from thermal expansioa. 

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. 

When all of the atomic displacement vectors are parallel to a polar axis of the crystal structure, the compound belongs to the one-dimensional category. In this case, linkage manner of octahedrons, MeX6, is of fundamental significance of spontaneous polarization appearance. Typical examples of compounds that belong to the one-dimensional category include perovskites,... 

The variation in the repolarization character causes systematic changes in the properties of the materials. Particularly, the transition from onedimensional structure compounds to three-dimensional structure compounds is accompanied by a decrease in the spontaneous polarization value and in the compound s Curie temperature, and a change in the character of the compound s chemical bonds [390]. 

A rich variety of complex oxyfluoride compounds containing tungsten, molybdenum, and titanium and displaying spontaneous polarization was discovered and described in [396 - 399]. 

Spontaneous polarization and non-linear optical effect in niobium and tantalum fluoride compounds... 

A very simple equation exists that relates spontaneous polarization to the intensity of the second harmonic signal. Spontaneous polarization is conceived as the sum of the products of each of the charges in a dielectric material by each of their displacements from the centrosymmetric positions. Hence, the relationship between spontaneous polarization and the second harmonic signal value can be presented as follows ... 

In order to avoid defining the constant, relative measurements are usually applied for at least two materials, A and B, one of which is used as an etalon. In this case, if material A is an etalon, the spontaneous polarization of material B can be calculated using the following equation ... 

The appearance of spontaneous polarization in the case of LuTaO is related to volumetric irregularities and ordering of the Li+ - Ta5+ dipoles, as is in the case of the similar niobium-containing compound Li4Nb04F. It can be assumed that the main difference between the two compounds is that the irregularities and the Li+ - Ta5+ dipoles are thermally more stable compared to the niobium-containing system. This increased stability of the dipoles leads to the reversible phase transition at 660°C. 

Thus, in cubic oxyfluorides of niobium and tantalum with rock-salt (NaCl) crystal structures, the formation and extinction of spontaneous polarization occurs due to polar ordering or disordering of Li+ - Nb5+(Ta5+) dipoles. 

It seems that structural irregularities that cause spontaneous polarization are a relatively common property of niobium and tantalum oxyfluoride crystals. Fig. 100 shows the temperature dependence of SHG signals for several compounds that form island-type and chain-type structures. 

The crystal structure of MsM OF compounds, where M = NH4, K, Rb, is made up of infinite chains of oxyfluoroniobate octahedrons that are similar to MNbOF4 chain-type compounds. Infinite chains are separated by isolated complexes NbFy2, whose structure is similar to that found in the island-type compound K2NbF7. The structure of the M5Nb30Fi8 compounds was described and discussed in Chapter 3.2. Due to the separation of the chains, the displacement of the niobium ion is in the same direction in all chains. The above displacement leads to a spontaneous polarization value that is as high as 4-5 pC/cm2. 

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