Permittivity dielectric

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

Also use constant dielectric Tor MM+aiul OPLS ciilciilatimis. Use the (lislance-flepeiident dielecinc for AMBER and BlO+to mimic the screening effects of solvation when no explicit solvent molecules are present. The scale factor for the dielectric permittivity, n. can vary from 1 to H(l. IlyperChem sets tt to 1. .5 for MM-r. Use 1.0 for AMBER and OPLS. and 1.0-2..5 for BlO-r. 

The first modification is to simply scale the dielectric permittivity of free space (T( ) by a scale factorD to rn ediate or dam pen thelong range electrostatic interactions. Its value was often set to be between 1.0 and 7H.0, the macroscopic value for water. A value of D=2..5, so that u=2..5Ug, wasoften used in early CIIARMM calculation s. 

Dielectric films Dielectric fluids Dielectric insulators Dielectric masking Dielectric materials Dielectric permittivity Dielectrics... 

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

Principles in Processing Materials. In most practical apphcations of microwave power, the material to be processed is adequately specified in terms of its dielectric permittivity and conductivity. The permittivity is generally taken as complex to reflect loss mechanisms of the dielectric polarization process the conductivity may be specified separately to designate free carriers. Eor simplicity, it is common to lump ah. loss or absorption processes under one constitutive parameter (20) which can be alternatively labeled a conductivity, <7, or an imaginary part of the complex dielectric constant, S, as expressed in the foUowing equations for complex permittivity ... 

The internal field is that microwave field which is generally the object for solution when MaxweU s equations are appUed to an object of arbitrary geometry and placed in a certain electromagnetic environment. The is to be distinguished from the local field seen by a single molecule which is not necessarily the same (22). The dielectric permittivity as a function of frequency can be described by theoretical models (23) and measured by weU-developed techniques for uniform (homogeneous) materials (24). 

The dielectric permittivity as a function of frequency may show resonance behavior in the case of gas molecules as studied in microwave spectroscopy (25) or more likely relaxation phenomena in soUds associated with the dissipative processes of polarization of molecules, be they nonpolar, dipolar, etc. There are exceptional circumstances of ferromagnetic resonance, electron magnetic resonance, or nmr. In most microwave treatments, the power dissipation or absorption process is described phenomenologically by equation 5, whatever the detailed molecular processes. 

The apphcation of microwave power to gaseous plasmas is also of interest (see Plasma technology). The basic microwave engineering procedure is first to calculate the microwave fields internal to the plasma and then calculate the internal power absorption given the externally appHed fields. The constitutive dielectric parameters are useful in such calculations. In the absence of d-c magnetic fields, the dielectric permittivity, S, of a plasma is given by equation 10 ... 

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... 

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

Liquids The rate of dissipation of charges in a liquid, assuming that its conductivity and dielectric permittivity are constant, can be expressed as ... 

Atomic charges (q ) Dipole moments [57] QM, dielectric permittivity, Stark effect, microwave... 

Fig. 4.7. The dielectric permittivity of impact-loaded dielectrics can be determined from current pulse measurements on disks biased with a voltage V. The magnitudes of the normalized current pulse values shown for two crystallographic orientations of sapphire are linear change with applied strain (after Graham and Ingram [68G05]).

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],... 

Among the alkali metal hexafluorometalates, potassium hexafluoronibate (KNbF6) was investigated in detail. An anomaly in the dependence of temperature on dielectric permittivity was observed at 240-265°K [401]. 

Fig. 107. Temperature dependence of the dielectric permittivity r determined at various frequencies for a ceramic sample ofRbsNb3OF,H.

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. 

Maxima observed on the plot of the temperature dependences of the dielectric permittivity confirm a phase transition at a temperature of about 480-500K. 

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 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. 

Here, cv is the dielectric permittivity of the semiconductor. The charge density is given by... 

For simple salts the influence of parameters (1)—(3) can be studied separately by the investigation of series of salts with a common anion or cation in a solvent of high dielectric permittivity. Flowever, high solvent permittivity is only a necessary, but not a sufficient, condition for complete dissociation. High permittivity of the solvents does not prevent ions from associating, if these ions interact specifically... 

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