The relation between simple analytic models for optical spectra of disordered solids

Several analytical models for infrared and Raman spectra of disordered solids, which predict widely different frequency dependence for the intensities of infrared absorption and Raman scattering, are examined. They are shown to be special cases of a more general formalism, and the assumptions required to obtain each model are examined. The frequency dependence of the infrared and Raman intensities of the vibrations of fully disordered materials are quite different because of the inherently different short-range correlations of effective charge and permittivity. The intensity of infrared absorption of a single oscillator is independent of the frequency if the change of dipole moment is due to the motion of permanent charges that are not correlated with one another. Raman scattering is analogous to infrared absorption caused by induced charges, and for maximum disorder the intensities of infrared absorption and reduced Raman scattering by a single oscillator are both proportional to the square of the frequency. Raman scattering cannot have an intensity that is independent of the frequency, except of course for narrow bands of oscillations. The Debye–Hückel distribution of charges is discussed as an example of infrared absorption of distributions of permanent charges intermediate between random charges and random ion pairs. The Debye–Hückel distribution of, for example, ammonium fluoride dissolved in ice can be tested by measuring the absorptivity of the sound waves.