Nature of Ionic Deformations in Crystals; Application to an Analysis of the Magnetic Properties of the Alkali-Halide and Alkaline-Earth Oxide Crystals

Abstract

Absolute diamagnetic susceptibilities for the alkali-halide crystals are obtained theoretically and compared with the observed magnetic susceptibilities of these crystals in order to determine the crystalline paramagnetic susceptibilities. The paramagnetic susceptibilities obtained in this way are found to obey the linear relationship ${\ensuremath{\chi}}_{\mathrm{para}}=0.11 {\ensuremath{\chi}}_{\mathrm{dia}}$. Theoretical analysis confirms this relationship for the alkali halides and indicates, in addition, that (1) Virtually all of the increased kinetic energy which the ions acquire in the process of crystallization takes the form of rotational kinetic energy; (2) the angular deformations of the ions in all the alkali halides are the same in that the average eigenvalue of the square of the angular momentum operator per electronic orbital is constant for all these crystals; and (3) the general relationship between ${\ensuremath{\chi}}_{\mathrm{dia}}$ and ${\ensuremath{\chi}}_{\mathrm{para}}$ for an ionic crystal is of the form ${\ensuremath{\chi}}_{\mathrm{para}}=C{\ensuremath{\chi}}_{\mathrm{dia}}$, where $C$ is very nearly proportional to the average cohesive energy per ion of the crystal. The last conclusion is confirmed in the alkaline-earth oxides where $C\ensuremath{\approx}0.5$, in accord with the fact that the cohesive energies of these crystals are about five times those of the alkali halides. Furthermore, this analysis indicates that an ionic crystal with a large enough cohesive energy is paramagnetic, in agreement with observation.