Total polarizability

There have been a few recent studies of the corrections due to nuclear motion to the electronic diagonal polarizability (a ) of LiH. Bishop et al. [92] calculated vibrational and rotational contributions to the polarizability. They found for the ground state (v = 0, the state studied here) that the vibrational contribution is 0.923 a.u. Papadopoulos et al. [88] use the perturbation method to find a corrected value of 28.93 a.u. including a vibrational component of 1.7 a.u. Jonsson et al. [91] used cubic response functions to find a corrected value for of 28.26 a.u., including a vibrational contribution of 1.37 a.u. In all cases, the vibrational contribution is approximately 3% of the total polarizability. 

Although the wave functions employed to compute polarizability at separate internuclear distances are of very high accuracy the presence of the singularities in the integration domain lowers significantly the precision of the final results. Nevertheless, the present computation reveals that the total polarizability of the... 

There are two types of charging currents and condenser charges, which may be described as rapidly forming or instantaneous polarizations and slowly forming or absorptive polarizations. The total polarizability of the dielectric is the sum of contributions due to several types of charge displacement in the materials caused by the applied field. The relaxation time is the time required for polarization to form or disappear. The magnitude of the polarizability, k, of a dielectric is related to the dielectric constant, s, as follows ... 

With appropriate substitution of the expressions for the various types of polarization, it is easy to show that the total polarizability, a, is also the sum of the various types of polarizabihty ... 

Figure 6.25 Frequency dependence of (a) total polarizability and (b) power loss. From K. M. RaUs, T. FI. Conrtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Whey Sons, Inc.

It can be shown that for some ionic crystals, such as LiF, both ionic and electronic polarization can contribute to the overall dielectric constant, s. In such cases, Eq. (6.81) is not entirely correct, and the electronic contribution to the polarizability, oie, is given by Eq. (6.82), since the refractive index affects only the frequencies in the electronic range, and the number of ions per unit cell, in this case two, must be included in the denominator. The total polarizability, a = oie + at, h then given by... 

Person 2 Calculate the electronic contribution to the total polarizability. 

Thus, fluorine substitution in polyimides can affect the total polarizability in different directions. It is the combined changes to the orientational and electronic polarizations, at a given frequency of interest, that must be considered. Since the orientation polarization can either go up or remain unchanged and the electronic polarization is always decreased, the net dielectric constant can go in either direction upon fluorination. However, it is more often observed that the net dielectric constant is decreased with fluorination. 

To the permanent-dipole response aperm add the coefficient aind for a dipole induced by the electric field on a polarizable particle for a total polarizability aperm + cnnd- The interaction of molecules in a gas can then be written immediately from the general form ... 

In Eq. (4), the atomic polarizability is generally so small comparing to the electronic polarizability. That it can be neglected [62], that is, ao = ae. Therefore, the total polarizability, a, of the molecule may be ascribed by the sum of two contributions of polarizability (so-called Debye-Langevin equation), such as... 

Induction (or Debye) and Orientation (or Keesom) force 0°+K which are the specific (or polar) properties of the van der Waals attraction exist in the presence of the dipole moment and (total) polarizability, resulting in specific (or polar) intermolecular attraction. 

An understanding of gas-solid interaction as a physical origin begins with an appreciation of (total) polarizability of molecules which was described as being related to both the deformation polarizability and dipole moment (or orien- tational polarizability) properties of two different substances at an interface. 

Even for the case of isotropic polarizabilities, where ap = aq = a, it follows from Eq. (3-36) that the total polarizability will be anisotropic. If we want to define effective polarizabilities from Eq. (3-37) for the members, we must (arbitrarily ) distribute the interaction term. For ap = aq equipartitioning could work, leading to local anisotropy with a// (local)>a and a (local)[Pg.53]

The same formula applies if the electron polarizability is replaced by the total polarizability, and the optical dielectric constant is replaced by the static dielectric constant, provided attention is then restricted to nonpolar materials. 

Polarizability (of a molecule) — There are numerous different mechanisms that contribute to the total polarizability of a molecule. The three most important of these are termed electron polarizability, molecular-distortion polarizability, and orientation polarizability. All these parameters are measured as statistical averages over large numbers of molecules present in the bulk phase. (1) -> Electron polarizability a is a measure of the ease with which electrons tend to be displaced from their zero-field positions by the applied -> electric field. Thus, the electron polarizability of a molecule is defined as the ratio of induced dipole moment pincj (coulomb meters) to the inducing electric field E (volts per meter) ... 

In a recent publication, J. H. Simons and J. B. Hickman, J. Phys. Chem., 56 (1952) 420, an empirical linear relation is postulated for non-ionic, non-asso-ciated liquids between the energy of vaporization (A /298 o ) and the total polarizability. Such a type of relationship lacks, however, as we have seen, a sound basis... 

Here B is an optical constant, or is the total polarizability of the particle, and n is the number of components in each particle. The indexes i and j refer to components of the same particle. If the assumption of independent particles was not made, then the indexes could refer to components of any two particles, and the autocorrelation expression could not be written as a simple sum of contributions from individual particles. The spatial vector r(r) refers to the center of mass of the particle. R(r). In the case of a nonspherical particle (arbitrary shape), Eq. (I0) would describe the coupled motion of the center of mass and the relative arrangement of the components of the particle. For spherical particles, translational and rotational motion arc uncoupled and we have a simplified expression for the electric field time correlation function ... 

Table 4 Total polarizabilities and calculated dielectric constants of materials with large deviations from the additivity rule...

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