Far Infrared Properties of Lattice Resonant Modes. I. Isotope Shifts

The frequency shift of a lattice resonant mode associated with the isotopic substitution of an impurity ion has been measured for NaCl: ${\mathrm{Cu}}^{+}$, KI: ${\mathrm{Ag}}^{+}$, and KBr: ${\mathrm{Li}}^{+}$. For all three systems, the experimental frequency shifts can be described satisfactorily by an Einstein oscillator representation for the resonant mode with the oscillator mass set equal to the impurity-ion mass. The model of Benedek and Nardelli and also Klein does not account for the experimental results of NaCl: ${\mathrm{Cu}}^{+}$ or KBr: ${\mathrm{Li}}^{+}$. The inclusion of anharmonic forces does improve the agreement between theory and experiment, but a large discrepancy still exists for KBr: ${\mathrm{Li}}^{+}$.