Theory of the Dielectric Constants of Alkali Halide Crystals

TLDR

Classical theories of ionic crystal dielectric constants predict Szigeti relations, but their additivity assumption fails in refined models involving vacuum and crystal ion polarizabilities. The study investigates short‑range repulsive interactions between closed‑shell ions and develops an overlap‑integral interpretation of the Born‑Mayer potential. The authors model ions as rigid charged shells attached to cores by harmonic forces, using this framework to describe short‑range interaction and exchange‑charge polarizations that arise from charge redistribution, and to derive generalized Szigeti, Clausius‑Mossotti, and Lorenz‑Lorentz relations. Experimental data violate both Szigeti relations; the calculated effective charge ratio from the refined model shows that short‑range interaction and exchange‑charge polarizations partly explain the deviation from unity, while the first relation’s failure is attributed to inadequate compressibility treatment.

Abstract

The simple classical theories of the dielectric constants and compressibility of ionic crystals lead to two relations among the experimental quantities from which arbitrary parameters have been eliminated, the Szigeti relations. Neither is satisfied by the data, indicating the inadequacy of these simple theories. The short-range repulsive interaction between ions with closed shell electron configurations is investigated, and an approximate interpretation of the Born-Mayer potential in terms of overlap integrals is developed. These results are applied to the interaction of model ions consisting of rigid charged shells bound to cores by harmonic restoring forces. Using this model, polarization mechanisms neglected in the simple dielectric constant theory, the "short range interaction polarization," and the "exchange charge polarization" are described. Both arise from charge redistributions occurring when the ions move with resulting changes in electron overlaps. Applied to a crystal, these ion models permit the derivation of generalizations of the Szigeti, Clausius-Mossotti, and Lorenz-Lorentz relations. The $\frac{{e}^{*}}{e}$ of the second Szigeti relation can then be calculated and comparison with the $\frac{{e}^{*}}{e}$ values derived from experimental data imply that the above polarization mechanisms must be at least in part responsible for the deviation of this parameter from unity. The failure of the first Szigeti relation is discussed and attributed to the inadequacy of the treatment of compressibility. The additivity feature of the simple theory and its absence in the refined theory are discussed in relation to the so-called vacuum and crystal ion polarizabilities.