Core polarization ionic polarizabilities

Figure 2.8 Shell model of ionic polarizability (a) unpolarized ion (no displacement of shell) (b) polarized (displaced shell) (c) interactions 1, core-core 2, shell-shell 3, core-shell.

On the other hand, core polarization is easily treated by a fairly simple model due to Mayer and Mayer which reduces the I dependence of the energies of high-1 states to a few parameters. The essence of the model is that the electric field of the electron at the ionic core distorts the polarizable core leading to an energy shift. Explicitly the energy level is given by... 

Early we noted that if we could measure several A/ intervals we could parametrize all the higher A/ intervals in terms of the polarizability of the ionic core. As an example of the application of the static polarization model let us consider the Cs A/ intervals. It is clear that Eq. (4) may be recast in terms of the intervals between adjacent / states. Let us label the difference in the polarization enei ies of the / and / states, Wp i/ - Wpou- as A,/-. It is convenient to adopt the convention of Edlen and write An- in cm" and define for / the terms Pi = where R is the Rydberg constant and... 

The most popular model which takes into account both the ionic and electronic polarizabilities is the shell model of DICK and OVERHAUSER [4.12]. It is assumed that each ion consists of a spherical electronic shell which is isotropically coupled to its rigid ion-core by a spring. To begin with we consider a free ion which is polarized by a static field E. The spring constant is k, the displacement of the shell relative to its core is v and the charge of the shell is ye (Fig.4.7). In equilibrium, the electrostatric force yeE is equal to the elastic force kv yeE = kv. The induced dipole moment is d = yev = aE from which we obtain the free ion polarizability... 

The polarizability, a, is due to two contributions, atomic polarizability and displacement polarizability. The atomic polarizability is caused by the motion of the electron cloud in the material with respect to the ionic cores of the atoms on lattice sites. The displacement polarizability is similar but involves motions of charged atoms with respect to one another. Consequently, it requires that there be two or more types of atoms in the lattice having a net polarity or difference in electric charge (i.e. at least partial ionic bonding) and results from motion of the negative atoms with respect to the positive atoms. These two polarization responses are shown schematically in Figure 2.13. 

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