Ions, polarizability

Free-ion polarizability calculations have been proposed by various authors, based on the values of molecular refraction of incident light according to... 

Free-ion polarizabilities, arranged in isoelectronic series, are listed in table 1.7. A semilogarithmic plot of the listed values (figure 1.6) reveals a functional dependence on atomic number. This dependence, quite marked, allows us to estimate the free-ion polarizability for ions for which there are no precise experimental data (values in parentheses in table 1.7 estimates according to Viellard, 1982). 

Figure 1,6 Free-ion polarizability as a function of atomic number. Curves are drawn for isoelectronic series. Reprinted from Viellard (1982), Sciences Geologiques, Memoir n°69, Universite Louis Pasteur, with kind permission of the Director of Publication.

The dipole-dipole ( / /+ ) and dipole-quadrupole dq+ ) coefficients can be derived from free-ion polarizability a and the mean excitation E by applying... 

Because the effective charge may also be related to free ion polarizability a ... 

The concept of dipole moment and its relationship to ion polarizability were discussed in section 1.8. Section 1.19 introduced the concept of dielectric constant of a crystalline solid and its relationship with the polarizability of its constituting ions (see eq. 1.168). The dielectric constant of a liquid solvent such as water represents the capacity of the solvent s molecules to shield the charges of ion... 

Table 1.7 Free-Ion polarizability (o ) arranged in isoelectronic series. Data in A. N = number of electrons (adapted from Viellard, 1982).

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

In the model, the smaller ion gives the stronger ion binding. However, it seems that in most cases other factors, e.g., ion hydration and ion polarizability, dominate over the ion size effect, particularly for anions, (cf. Sect. 4). 

Molecular polarizabilities of complex substances can also be broken up into ion polarizabilities according to... 

Observed and calculated polarizabilities from oxide polarizabilities Observed and calculated dielectric constants from ion polarizabilities ... 

Using the C-M equation and oxide polarizabilities from Table 1. Using the C-M equation and ion polarizabilities from column 2 of Table 3. 

For nonstoichiometric phases the stabilization of extended defects depends on the ion polarizability. The formation of extended defects is associated with a drastic decrease in the ionic conductivity, as for instance in calcia-stabilized zirconia (Section 3.2.1). 

The numerical calculations are based on a classical model for the ion-molecule collision. The potential energy, of course, includes both ion-dipole and ion-polarizability terms. It is necessary to use definite values of all physical constants in order to make a calculation. In all studies values of the... 

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 ... 

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