Shell Model Treatment of the Vibrations of Crystals Containing Substitutional Defects I. U‐Center Localized Modes

A shell model treatment of the harmonic vibrations of lattices containing substitutional defects is given and is applied to the problem of the infrared‐active localized modes of U‐centers in alkali halide crystals. Long‐range effects due to the shell motions and to altered core and shell charges are included, as are the effects of spherical deformations of the ions. For a U‐center polarizability of 1.9 Å3 and a shell charge of −e it is found that the fractional decreases in the defect's nearest neighbor shell‐shell and isotropic core‐shell spring constants are between 0.30 and 0.55 and greater than 0.75, respectively, for U‐centers in nine different alkali halides.