Third-Order Anharmonic Interactions of Infrared Phonons in the Alkali Halides

The third-order anharmonic processes which destroy infrared phonons in alkali halides are studied. The three-phonon processes are shown to give a theoretical linewidth of ∼${10}^{12}$ ${\sec }^{-1\mathrm{}}$ for the fundamental infrared resonance of NaCl at 300°K, which is in reasonable agreement with the experimental value of 2.5×${10}^{12}$ ${\sec }^{-1\mathrm{}}$ because of approximations that have been made. The selection rules for these processes will be discussed for a model where the ions interact via central forces. It is shown that the far-infrared absorption for processes at symmetry points on the zone boundary vanishes for transitions between two acoustic or two optical branches and is much stronger for transitions between a transverse acoustic and a transverse optical branch than for transitions between a longitudinal acoustic and a transverse optical branch. This could account for the selection rules observed by Stolen and Dransfield in their far-infrared absorption experiments with NaI, KI, and KBr.