Electronic Polarizabilities of Ions in Crystals

Abstract

A set of electronic polarizabilities has been obtained from a least-squares fit of experimental refraction data using simple additivity and a Lorentz factor of $\frac{4\ensuremath{\pi}}{3}$. Except for the fluorides, the electronic polarizability values of the alkali-halide crystals calculated from this set agree with the experimental data within 3 percent. Similar least-squares fits were attempted with various values of the Lorentz factor, the best fit being obtained for $\frac{4\ensuremath{\pi}}{3}$. On the basis of $\frac{4\ensuremath{\pi}}{3}$, the additivity assumption and the alkali-halide set, polarizabilities have been obtained for other ions. The best values for the sodium $D$ line in ${\mathrm{A}}^{3}$ are ${\mathrm{Li}}^{+}$ 0.03, ${\mathrm{Na}}^{+}$ 0.41, ${\mathrm{K}}^{+}$ 1.33, ${\mathrm{Rb}}^{+}$ 1.98, ${\mathrm{Cs}}^{+}$ 3.34, ${\mathrm{F}}^{\ensuremath{-}}$ 0.64, ${\mathrm{Cl}}^{\ensuremath{-}}$ 2.96, ${\mathrm{Br}}^{\ensuremath{-}}$ 4.16, ${\mathrm{I}}^{\ensuremath{-}}$ 6.43, ${\mathrm{Ca}}^{++}$ 1.1, ${\mathrm{Sr}}^{++}$ 1.6, ${\mathrm{Ba}}^{++}$ 2.5, ${\mathrm{O}}^{\ensuremath{-}\ensuremath{-}}$ 0.5-3.2, ${\mathrm{S}}^{\ensuremath{-}\ensuremath{-}}$ 4.8-5.9, ${\mathrm{Se}}^{\ensuremath{-}\ensuremath{-}}$ 6.0-7.5, ${\mathrm{Te}}^{\ensuremath{-}\ensuremath{-}}$ 8.3-10.2, ${\mathrm{Ag}}^{+}$ 2.4, ${\mathrm{Cu}}^{+}$ 1.6, ${\mathrm{Cu}}^{++}$ 0.2, ${\mathrm{Zn}}^{++}$ 0.8, ${\mathrm{Cd}}^{++}$ 1.8, ${\mathrm{Ge}}^{4+}$ 1, ${\mathrm{Sn}}^{4+}$ 3.4, ${\mathrm{Pb}}^{++}$ 4.9. Values represented by a spread indicate ions that cannot be treated additively.