Total ionic polarizability

The terms in equation 1.166 represent total ionic polarizability, composed of electronic polarizability a plus an additional factor a , defined as a displacement term, due to the fact that the charges are not influenced by an oscillating electric field (as in the case of experimental optical measurements) but are in a static field (Lasaga, 1980) ... 

Finally, Shannon obtained 61 sets of ionic polarizabilities for 129 oxides and 25 fluorides using the Clausius-Mosotti equation and least square refinements, and suggested the periodic table of ionic polarizabilities. Therefore the dielectric constant of materials with compositional changes can be successfully predicted by Equation 22.17 and Equation 22.18. Erom another arrangement of Equation 22.16, the theoretical dielectric constant can be obtained from the total ionic polarizabilities in Equation 22.19. Erom Equation 22.17 through Equation 22.19, the theoretical values of dielectric constant and polarizabilities can be obtained as well as the measured values ... 

We recall from Chapter 1 that for ionic materials, ionic polarizability can be taken into account using the shell model of Dick and Overhauser (1958), which treats each ion as a core and shell, coupled by a harmonic spring. The ion charge is divided between the core and shell such that the sum of their charges is the total ion charge. The free ion polarizability, a, is related to the shell charge, Y, and spring constant, k, by ... 

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... 

The magnitude of the surface dipole. For the system hydrogen-nickel, formula (13) leads to a value of 0.66 D. The experimentally determined value 0.022 D. is therefore a factor of about 30 smaller. This is quite conceivable because (13) has been derived for a diatomic molecule. In our case one of the partners of the bond, the metal, has a very high polarizability, and hence the surface dipole will be quenched to a large extent. The value of the dipole moment calculated from (13), though larger than the experimental value, is still far smaller than that to be expected for a pure ionic bond (fora bond distance of 2 A. fj, = 10 D.). This is one of the reasons for us to think that the contribution of the ionic type M+X to the total bond... 

It is to be noted that with the C2h symmetry (Fig. 1), the cluster does not have a total dipole moment. However, an appreciable weight of the metallic or ionic structures (Fig.2), which is the case around an intermolecular separation of 1.7 A (Fig.3), will strongly contribute to the polarizability of the system. On the other hand, a small polarizability will arise if only the Kekule-type structures contribute to the ground state wave function. 

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... 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

In the absence of ionic specific adsorption, the properties of the inner layer are determined by those of the polarizable metal and of the solvent. Some small influence is also seen from the counter ion at the oHp. The latter effect is attributed to changes in the size of the counter ion, which results in a change in the total thickness of the inner layer. At potentials well removed from the PZC, the diffuse layer capacity is quite large, so that it gives only a minor contribution to the observed experimental capacity. 

A good and well investigated example of a non-polarizable interface is that between silver iodide and aqueous solutions. At this iriterface one may distinguish chaises of ionic concentrations in the aqueous layer and a certain excess or defect of one of the kinds of lattice ions. Experimentally one determines the total adsorption of certain ions (cf 2, p 116) and thus at a certain adsorption of Ag+-ions it remains uncertain whether this is an adsorption in the lattice or in the liquid layer ( 4 f. 2, p. 139). Usually, however, the concentration of Ag- or I ions in the aqueous solution is very low and the adsorption in the liquid layer may be neglected (or a small correction applied for it). 

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