Optical Spectra of Orientationally Disordered Crystals. II. Infrared Spectrum of Ice Ih and Ice Ic from 360 to 50 cm−1

The far-infrared spectra in the range 360–50 cm−1 of ice Ih and ice Ic made from H2O and from D2O, and of vitreous ice made made from H2O have been investigated. The spectra are due to essentially purely translational vibrations, and have been interpreted using the theory of the spectra of orientationally disordered phases developed in the preceding paper. There are peaks at 229.2 and 164 cm−1 that are due (in ice Ic) to maxima in the density of vibrational states due to the transverse optic and longitudinal acoustic vibrations, respectively, and a shoulder at 190 cm−1 due to the maximum in the longitudinal optic vibrations. There is also a peak just below 50 cm−1 in the spectrum of optical density divided by the square of the frequency that is due to the maximum in the transverse acoustic vibrations. Corresponding assignments are proposed for ice Ih. The Raman spectrum can in principle yield similar information, and agrees with the infrared spectrum in so far as the measurements can be compared. Some of the observed frequencies can be fitted reasonably well with a simple nearest-neighbor bond-stretching and angle-bending potential field, but there is absorption at sufficiently high frequencies to indicate that long-range forces are important in determining the translational lattice vibrations of ice. The effects of temperature and of deuterium substitution on the spectrum are discussed.