Permittivity crystals

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],... 

In the case of single crystals of K5Nb3OF 8, a maximum in the dielectric permittivity 33 was observed at about 400K. Fig. 108 shows the temperature dependence of b at different frequencies. 

Fig. 108. Temperature dependence of dielectric permittivity r determined at various frequencies for a single crystal of KsNbsOFis along the c axis. Reproduced from [443], A. I. Agulyansky, J. Ravez, R Von Der Muhll, A. Simon, Ferroelectrics 158 (1994) 139, Copyright 1994, with permission of Taylor Francis, Inc., http //www.routledge-ny.com.

The idea is that X must govern in some way all properties of the interface, including the permittivity. The latter includes an electronic and a molecular term, which have been tentatively separated7 on the basis of model approaches. In this chapter, only the correlation of the capacitance with X is relevant. The correlation between 11C and tX has been demonstrated for eight metals in aqueous solution. It has been shown26,34 that the correlation derived from sp-metals is fit also by single-crystal faces of sd-metals. In particular, the capacitance of Ag increases in the sequence... 

In order to allow for the crystal structure itself, which will modify the interaction energy, it is possible, as a first approximation, to assume that the force of attraction is diluted in the crystal by an amount equal to its relative permittivity. The modified formula is then... 

The first (exponential) term represents repulsion between electron orbitals on the atoms. The second term can be seen to be opposite in sign to the first and so represents an attraction—the weak van der Waals interaction between the electron orbitals on approaching atoms. The adjustable parameters can sometimes be calculated using quantum mechanics, but in other systems they are derived empirically by comparing the measured physical properties of a crystal, relative permittivity, elastic constants, and so on, with those calculated with varying parameters until the best fit is obtained. Some parameters obtained in this way, relevant to the calculation of the stability of phases in the system SrO-SrTiC>3, are given in Table 2.3. 

Photonic band gap crystals can be dehned as long-range ordered structures whose relative permittivity varies as a spatially periodic function. These three-dimensional periodic structnres have a feature size comparable to or shorter than the wavelength of visible light. 

Let us consider a sphere composed of a material described by the constitutive relation (5.46). We assume that the principal axes of the real and imaginary parts of the permittivity tensor coincide this condition is not necessarily satisfied except for crystals with at least orthorhombic symmetry (Born and Wolf, 1965, p. 708). If we take as coordinate axes the principal axes of the permittivity tensor, the constitutive relation (5.46) in the sphere is... 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

Fig. 35. Modulation function of the polyimide modulator with thickness of the liquid crystal in pm 20 (/), 15 (2), 10 (3), 3 (4). Anisotropy of the dielectric permittivity of 12 (2,2,3) 0.05 (4). Polyimide thickness - 2 pm. Pulse regime [14]...

The dielectric permittivity ofBST films (measured at the frequency of 1 MHz at 20°C without application of bias electric field) as a function of the strontium content in the films is shown in Fig. 102. The maximum value of dielectric permittivity is observed for the films with Ba/(Ba+Sr) = 0.3 in accordance with single-crystal behavior. The values of dielectric permittivity increase with the increase of annealing temperature of the films (from 700 to 800°C), as well as with the increase of film thickness. 

Dispersions of nanoparticles in ferroelectric liquid crystals (FLCs) predominantly focused on induced or altered electro-optic effects, but also on the alignment of FLCs. Raina and co-workers reported on a gradual decrease of the dielectric permittivity, e, by doping with SiC>2 nanoparticles at frequencies up to 1 kHz and a rather minor increase of as well as an increase in optical transmission at frequencies above 2 kHz [279]. Liang et al. used BaTiC>3 nanoparticles (31 nm in diameter after grinding commercially available 90 nm nanoparticles Aldrich) and showed, perhaps expectably, a twofold increase in the spontaneous polarization... 

Obtain the permittivity matrix i for orthorhombic and monoclinic crystals. What differences arise in the monoclinic case for a T(2) that is not symmetric ... 

In comparison to ordinary dielectrics, the permittivities of the so-called ferroelectric materials are about 103 times larger. The ferroelectric material can be transformed into a new type of material called piezoelectric material by heating the ferroelectric above its Curie temperature and then cooling it in a powerful electric field. A piezoelectric crystal changes its polarization once subjected to a mechanical strain. As a result, it can deform mechanically under an electric field or produce electric impulses as a result of mechanical impulses. Currently, piezoelectric materials are widely used as force or pressure transducers with fast response times and very sensitive output. Permittivities of common dielectric and ferroelectric materials are given in Table 1.9. 

The quantity eoo represents the optical permittivity, which is determined by the electronic polarizability. The second term represents the ionic crystal lattice as a sum of N classical harmonic oscillators with eigenfrequencies ujj, damping constants Tj and oscillators strengths Sj. In order to fit Equation (5.7) to the observed far infrared spectra, these parameters are used... 

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