Dielectric permittivity/properties

The dielectric permittivity properties, summarized for the shell in the coefficient A44(s), are considered for the beam by integration over the cross-section ... 

Tantalum and niobium are added, in the form of carbides, to cemented carbide compositions used in the production of cutting tools. Pure oxides are widely used in the optical industiy as additives and deposits, and in organic synthesis processes as catalysts and promoters [12, 13]. Binary and more complex oxide compounds based on tantalum and niobium form a huge family of ferroelectric materials that have high Curie temperatures, high dielectric permittivity, and piezoelectric, pyroelectric and non-linear optical properties [14-17]. Compounds of this class are used in the production of energy transformers, quantum electronics, piezoelectrics, acoustics, and so on. Two of... 

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 compounds K5Nb3OFi8 and Rb5Nb3OFi8 display promising properties for their application in electronics and optics. The compounds can be used as piezoelectric and pyroelectric elements due to sufficient piezo- and pyroelectric coefficients coupled with very low dielectric permittivity. In addition, the materials can successfully be applied in optic and optoelectronic systems due to their wide transparency range. High transparency in the ultraviolet region enables use of the materials as multipliers of laser radiation frequencies up to the second, and even fourth optical harmonic generation. 

In contrast with Eq. (5), Eq. (11) gives the frequency behavior in relation to the microscopic properties of the studied medium (polarizability, dipole moment, temperature, frequency of the field, etc). Thus for a given change of relaxation time with temperature we can determine the change with frequency and temperature of the dielectric properties - the real and imaginary parts of the dielectric permittivity. 

The fourth term is a polarisation term. Here E(z) = di/z/dz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of erA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value... 

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... 

The last 20 years have seen enormous progress in the development of high-performance fluoropolymers. Fluorine-containing polyimides stand out as one of the few types of materials that simultaneously possess outstanding thermal stability and mechanical properties, low dielectric permittivity, and thin-film processability. This combination of properties makes them ideal for use as high-performance insulators in electronic devices. 

IR spectra measurements as well as variation of the film thickness, shrinkage, and refractive index demonstrated substantial differences in the mechanisms of thermal decomposition of films prepared from the exclusively metal alkoxide precursor and from the metal alkoxides modified by 2-ethylhexanoic acid. These differences affect the evolution of film microstructure and thus determine the different dielectric properties of the obtained films. The dielectric permittivity of the films prepared from metal alkoxide solutions was relatively low (about 100) and showed weak dependence ofthe bias field. This fact may be explained by the early formation of metal-oxide network (mostly in the... 

In order to calculate the Hamaker constant the dielectric properties of all three materials need to be known. For frequencies starting in the visible range the dielectric permittivity can be described by... 

The Hamaker constant is determined by the dielectric permittivities and the optical properties of the interacting media. 

The standard method for making measurements of dielectric properties is to place a sample between closely spaced parallel conducting plates, and to monitor the AC equivalent capacitance and dissipation factor of the resulting capacitor. The capacitance is proportional to the dielectric permittivity (e ) at the measurement frequency, and the dissipation factor in combination with the value can be used to extract the dielectric loss factor (e"). ... 

In spite of numerous studies, the properties of liquid water are still far from been understood at a molecular level. For instance, large isotope effects are seen in some properties, such as the temperature of maximum density, which occur at 277.2 K in liquid H20 and 284.4 K in D20. The isotope shift 7.4 K will be used below with the purpose to employ the Liebe et. al. formula [17] for calculation of the low-frequency dielectric permittivity of D20 in analogous way as it used for H20. 

Most of the physical properties of the polymer (heat capacity, expansion coefficient, storage modulus, gas permeability, refractive index, etc.) undergo a discontinuous variation at the glass transition. The most frequently used methods to determine Tg are differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical thermal analysis (DMTA). But several other techniques may be also employed, such as the measurement of the complex dielectric permittivity as a function of temperature. The shape of variation of corresponding properties is shown in Fig. 4.1. 

Figure 4.1 Variation of physical properties vs temperature, used to determine the glass transition (a) volume (V) or enthalpy (H) (b) expansion coefficient (a) or heat capacity (cp) (c) storage modulus (E ) (d) dissipation modulus (E") and dumping factor (tan 8) (e) real part of the complex dielectric permittivity (s ) (f) imaginary part of the complex dielectric permittivity (e").

The effective medium theory consists in considering the real medium, which is quite complex, as a fictitious model medium (the effective medium) of identical properties. Bruggeman [29] had proposed a relation linking the dielectric permittivity of the medium to the volumetric proportions of each component of the medium, including the air through the porosity of the powder mixture. This formula has been rearranged under a symmetrical form by Landauer (see Eq. (8), where e, is the permittivity of powder / at a dense state, em is the permittivity of the mixture and Pi the volumetric proportion of powder / ) and cited by Guillot [30] as one of the most powerful model. 

The compositions of most dielectric materials used for ceramic capacitors are based on ferroelectric barium titanate. As discussed in detail in Pragraph 1.3 the permittivity of ferroelectric perovskites shows marked changes with temperature, particularly close to the phase transition. From the device point of view a high dielectric permittivity with stable properties over a wide temperature range is required. There are various specifications which have to be fulfilled (e.g. X7R AC/C(T = 25°C) < 0.15 in a range between -55°C and 125°C). 

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