J.R. Hardy, A.M. Karo, Phys. Rev. B26, 3327 (1982)

We have made a detailed theoretical study of the long-wavelength absorption of NaCl, KCl, KBr, and KI, associated with two-phonon difference processes caused by third-order anharmonic terms in the lattice potential energy. It was found that a simple nearest-neighbour approximation to the anharmonicity, combined with lattice-dynamical eigenfrequencies and eigenvectors generated with the use of a deformation dipole model, can generally account for most of the use of the observed absorption. This agreement was obtained without the use of any disposable parameters, as the form of the first-neighboru potential was predetermined. It was also found that discrepancies between theory and experiment can generally be explained by invoking three-phonon processes and, when these contributions are subtracted from the experimental data, the resultant agreement between theory and experiment is excellent. The effect of lifetime broadening of the final-state phonons were also considered. At the longer wavelengths these may be responsible for part of the discrepancy between theory and experiment. Specifically, for NaCl at 3.09 mm., clear evidence was found of an anomalous contribution to the measured absorption which could have such an origin. However, for KI, which has a "window" in its two-phonon absorption at long wavelength, it is clear that the three-phonon absorption is dominant at low frequencies. Our findings enable us to present certain criteria as to the requirements necessary for a material to process high transparency in the millimeter-wavelength region. In addition to obtaining theoretical results for the long-wavelength absorption of the four crystals studied, we have also calculated the damping function over the whole, two-phonon range and we thus present results for both summation and difference processes.