Lattice-Vibration Effects Due to Impurities in an Alkali Halide

Abstract

The Green's-function approach to the study of impurity effects on lattice vibrations is applied to alkali halides. Due to the strong phonon-photon interaction, some care must be taken in the application of the results for the pure crystal. A simplified approach for obtaining the impurity contribution to the lattice thermal conductivity is presented which leads to a phonon lifetime having resonance dips. Numerical calculations for NaI:${\mathrm{Li}}^{+}$, using a simple model for the interionic forces (which took into account the electronic polarization but not dipole deformation) and the "mass-defect approximation," revealed resonances at the frequencies 2.2, 2.5, 2.8, and 3.0×${10}^{13}$ ${\sec }^{-1\mathrm{}}$. An expression for the optical absorption is derived which reveals a peak of first order in the impurity concentration at the localized-mode frequency and peaks at the resonance frequencies proportional to the square of the impurity concentration. In the mass-defect approximation and in the above model, the localized-mode frequency of NaI:${\mathrm{Li}}^{+}$ lay at 4.28×${10}^{13}$ ${\sec }^{-1\mathrm{}}$, while that of NaI:${\mathrm{K}}^{+}$ lay at 1.76×${10}^{13}$ ${\sec }^{-1\mathrm{}}$. Using estimates of phonon and impurity-mode lifetimes, we conclude that these peaks should be easily observed.