Dielectric materials polarizability

In dielectric materials (oxides, semiconductors, halides, polymers, and he like), polarizability correlates with hardness. For metals, this is not the case. However, the frequencies of the collective polarizations known as plasmons are related to mechanical hardness. 

The ratio of permittivity with the dielectric to the permittivity in vacuum, e/eo, is called the relative permittivity, s, or dielectric constant. The dielectric constant is a material property. Some values of dielectric constants for common ceramic and glass insulators are given in Table 6.3. Since a polarizable material causes an increase in charge per unit area on the plates of a capacitor, the capacitance also increases, and it can be shown that the dielectric constant is related to the capacitance and displacement in vacuum and with the dielectric material as follows ... 

We can further describe the polarization, P, according to the different types of dipoles that either already exist or are induced in the dielectric material. The polarization of a dielectric material may be caused by four major types of polarization electronic polarization, ionic (atomic) polarization, orientation polarization, and space-charge (interfacial) polarization. Each type of polarization is shown schematically in Figure 6.24 and will be described in succession. In these descriptions, it will be useful to introduce a new term called the polarizability, a, which is simply a measure of the ability of a material to undergo the specific type of polarization. 

In this subsection, the connection is made between the molecular polarizability, a, and the macroscopic dielectric constant, e, or refractive index, n. This relationship, referred to as the Lorentz-Lorenz equation, is derived by considering the immersion of a dielectric material within an electric field, and calculating the resulting polarization from both a macroscopic and molecular point of view. Figure 7.1 shows the two equivalent problems that are analyzed. 

Therefore the dielectric constant is changed with temperature and the resonant frequency will change with temperature, and the microwave devices cannot respond at a specific frequency if the dielectric materials in microwave frequencies show a large TCK and thermal expansion coefficient a due to the thermal expansion of dielectric materials and the temperature dependence of polarizability. In general, the a of dielectric ceramics, which is well known as the slope of the Cockbain equation, is about 10 ppm/°C. Therefore control of TCP can be achieved by adequate manipulations of TCK. It is an important requirement for practical applications to control the stable TCP, nearly zero, which is available to temperature-stable microwave devices. 

To obtain low k, these three polarizations are kept as low as possible. An obvious way to have low polarizations is reduction of the density of the material N). The lower density will decrease the number of polarizable species in the films and thus results in a lower dielectric constant. This is done by incorporating low molecular weight molecules, space occupying molecules, inherently open structures, and, more significantly, introducing porosity. This entry presents an overview of nanoporous dielectric materials. This overview is not exhaustive because new materials are being developed as this entry is written. 

One example of a dielectric material in which ionic motion is important is barium titanate BaTiOj, which is ferroelectric (i.e., the induced polarization does not decay npon the removal of the electric field), hi these structures, titanium ion displacement within its octahedral sites canses extremely large polarizations (2,000-3,000) [14]. In nonferroelectric materials snch as titanium dioxide, ions will return to equilibrium position npon removal of field. Electronic polarizabihty is greater for materials containing more electrons (i.e., heavy atoms, greater polarizability). The frequency range for electronic motion is np to 10 Hz. In the case of materials for organic... 

Common polymers such as polystyrene (PS) and polymethylmethacrylate (PMMA) have been used as gate dielectric materials [7,20,46]. Their ready availability made them some of the early polymers investigated by researchers in the field [11,39,47]. However, the low capacitances of these films made them less attractive than other polymers. Poly(4-methylstyrene) has been explored as a possible polarizable gate insulator [48]. 

Debye equation - The relation between the relative permittivity (dielectric constant) polarizability a, and permanent dipole moment p in a dielectric material whose molecules are free to rotate. It takes the form... 

Following the discussion on ionic conductivity in section 12.1, and protonic conduction in section 12.1.2, it can definitely be seen that overall conduction in gum Arabica belongs to the aforementioned category. The nature of the mentioned conductivity is analyzed from a.c. conduction. In the microscopic level mechanism in the solid, there is a particular pair of states between which jumps take place which are influenced by the electric field. A dielectric material of natural type gum containing permanent dipole moment g, when sandwiched between two plane parallel electrodes of area A, separation d, the conductivity a and dielectric constant e are connected to conductance G and capacitance C by <7 = G (d/A) and = C (d/Eg A). In the absence of an external electric field, dipoles are oriented at random and possess only electronic polarizability in the field direction. 

Debye equation do- bI i- kwa-zhon. A relationship for the relative permittivity (8) of a dielectric material as a function of the electronics and atomic polarizability and the orientational polarizability terms. 

The first quantity, denoted d, is expressed in C.m V while the second quantity [a] is the absolute polarizability expressed in cubic meters (m ). The polarizability of a dielectric material, containing n atoms per unit volume (m" ) and having a relative dielectric permittivity , is given by the Clausius-Mosotti equation ... 

ERF dielectric response can be appropriately described by the classical Debye circuit model (Section 4-4). The model contains 1 pF/cm bulk base oil capacitance in parallel with Tohm range base oil resistance This combination results in a circuit with a time constant on the order of 10 seconds, typical of the impedance behavior of dielectric materials with very low ionic content. The presence of 10 to 50 percent polarizable particles results in the development of a parallel bulk-solution conduction mechanism through the particles. When compared to the ions that transport current by electrophoretic mobility, the ERF particles have larger sizes and lower mobility and are capable of becoming polarized and reoriented in the external electric field. This percolation type of conduction mechanism can be represented by a series of the particle resistance and the contact impedance between the particles (Figure 12-8). As the ionic content is essentially absent in the... 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

It has been shown that the polarizability of a substance containing no dipoles will indicate the strength o/any dispersive interactions that might take place with another molecule. In comparison, due to self-association or internal compensation that can take place with polar materials, the dipole moment determined from bulk dielectric constant measurements will often not give a true indication of the strength of any polar interaction that might take place with another molecule. An impression of a dipole-dipole interaction is depicted in Figure 11. 

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