Anharmonicity of the Lattice Oscillations in the Alkali Halide Crystals

Abstract

THE oscillations of the two interpenetrating lattices of the alkali and the halide ions respectively, in alkali halide crystals, with respect to each other, have been studied in detail, particularly in relation to the infra-red and the Raman spectra of the crystals, and the contribution of the electric dipole moments associated with these oscillations to the dielectric constants of the crystals. These oscillations are presumed to be anharmonic—the anharmonicity being attributed sometimes to the size of the amplitude of the oscillations—and the anharmonicity is invoked to explain the occurrence of certain combination frequencies in Raman spectra, and the temperature variation of the specific heat at constant volume at high temperatures. No attempt, however, seems to have been made to estimate the magnitude of the anharmonicity, though it can be done readily on the basis of any simple model of the crystal, as, for example, Born's, which regards the lattices of the positive and the negative ions respectively as held together by electrostatic forces between the ions, and by Van der Waals forces of repulsion between them, which die down much more rapidly with distance than the electrostatic forces. (The inclusion of forces due to the polarizabilities of the ions does not appreciably affect the results.)