Dielectric polarizability of ions and the corresponding effective number of electrons

In a previous paper it was shown that in-crystal ion polarizabilities derived from low-frequency precision measurements of the dielectric constants of single-crystal oxides can be given a quantitative interpretation using a quantum mechanically based result for a single, completely filled, electron subshell. In this paper, by exploiting the fact that the radii of related subshells differ only slightly, we propose an equation amended to include the possibility of contributions from incomplete or several subshells. Using the new result, effective electron numbers are derived for all the ions for which experimental polarizabilities have recently been published. It is shown that there is generally a good correspondence between these numbers and the known electronic configurations of the ions concerned. The new calculations show that the concept of a polarizability determined by the contribution of a single electron subshell is certainly valid with ions corresponding to elements of low atomic number, but that in the case of transition and rare earth ions there is probably more than one contributing electron subshell.