The far-infrared spectrum of ice Ih in the range 8–25 cm−1. Sound waves and difference bands, with application to Saturn’s rings

Abstract

The absorption spectrum of single crystals of ice Ih with the light traveling perpendicular or at 5° to the c axis has been measured in the frequency range 8–25 cm−1 at 80, 100, 150, and 202 K. At high frequencies, the absorptivity is proportional to the fourth power of the frequency, and is caused by fundamental hypersonic waves having wavelengths of about 100 Å. At low frequencies, it is probably caused by difference bands from the translational lattice vibrations. The theory of the intensity of binary combination bands of ionic crystals has been specialized to the low-frequency difference bands. Ice Ih has been assumed to have the same absorptivity as ice Ic, and ice Ic has been represented by an ordered crystal that resembles sphalerite. The model fits the measured absorptivity of ice Ih assuming that the difference bands arise mostly from the strong first-order band centered at ∼230 cm−1. The acoustic branches do not contribute significantly. The absorptivity, extrapolated to 3.0 cm−1 and interpolated to 85 K by means of the theory, was used to determine the mean thickness of ice in Saturn’s rings from the measured thermal component of the brightness temperature of the rings. If the slab model is used and scattering is neglected, the mean thickness is 30±10 cm.