Infrared absorption by the higher-order-dipole-moment mechanism

The simple model consisting of a one-dimensional chain of alternating rigid positive ions and shell-model negative ions connected by anharmonic forces gives insight into the Lax-Burstein nonlinear-dipole-moment mechanism (LB) of multiphonon absorption, especially in relation to the anharmonic-potential mechanism (AP) in polar crystals. The model and general considerations suggest that LB dominates AP in the high-frequency region of current interest and that the LB and AP Hamiltonians have opposite signs. The resulting minimum in the absorption coefficient $\beta$ should be observable if it were in the region of exponential decay of $\beta \left(\omega \right)$. The most likely explanation for the apparent lack of the minimum in experiments is that it occurs at the observed minimum nearest the reststrahlen peak in $\beta \left(\omega \right)$. Even though the accuracy of the results from the model is not expected to be great, the minimum is in the two-phonon region, though not as close to the peak as the first observed minimum. Since a larger value of LB corresponds to a minimum nearer the peak, this explanation results in theoretical values of $\beta$ at high $\omega$ that are considerably greater than experimental values in the alkali halides. In spite of this difficulty, it is unlikely that LB is negligible in the high-frequency region if shell models are believable in general. Possibilities of a positive LB-to-AP ratio, which would alleviate the difficulty, are shown to exist but to be unlikely.