Infra-red and Raman spectra of glasses. Part 1.—Theory for the translational lattice vibrations

Abstract

A theory of the absorption and scattering of light by the translational vibrations of orientationally disordered crystals has been extended to the “acoustic” vibrations of a vitreous solid. With certain simplifying assumptions, the integrated absorptivity of each normal vibration should be proportional to the square of its frequency and independent of its precise form. Hence the optical density, or the absorptivity, divided by the frequency squared should be closely related to the density of vibrational states. In the region of the sound waves the absorptivity should be proportional to the fourth power of the frequency. On the basis of the same assumptions, the Raman intensity is the sum of a term proportional to the frequency squared and independent of the precise form of the vibration and a term that depends upon the normal coordinate. At sufficiently low frequencies that the vibrations can be represented by plane waves, the latter term becomes zero, and the intensity of Raman scattering should be proportional to the third power of the frequency. Localized vibrations such as are caused by impurities and defects are not included in this treatment.