ABSORPTIVITY OF ICE I IN RANGE 4000-30 CM-1

The absorbance of several samples of ice Ih has been measured in the range 4000-30 cm-1, and scaled to that of a particular film of unknown thickness. The thickness of the film has been calculated by two methods, first from the known absorptivity at 4940 cm-1, and second by equating the appropriate Kramers-Kronig integral to the known infrared contribution to the microwave refractive index. The two thicknesses agreed well and allowed the absorptivity to be obtained in the range 4000-30 cm-1. The complex refractive index and permittivity and the normal incidence reflectivity have been calculated from the absorptivity. About three-quarters of the infrared contribution to the microwave refractive index is caused by the translational lattice vibrations and about 15% by the rotational vibrations; the O-H stretching bands which absorb very strongly contribute relatively little. The maximum of the density of states in the transverse acoustic branch is at 65 cm-1 rather than below 50 cm-1 as reported earlier. Below 50 cm-1 the absorptivity is roughly proportional to the fourth power of the frequency. This arises because the vibrations here are short-wavelength sound waves with a density approximately proportional to the square of the frequency, and the integrated intensity of absorption by one vibration is proportional to the square of the frequency. A theory of the contribution of the translational lattice vibrations to the microwave permittivity is given based on the theory of the absorption by orientationally disordered crystals given in an earlier paper. From the theory and the experimental measurements reported in this paper the dipole-moment derivative for the relative displacement of two water molecules in ice along their line of centers (or equivalently the effective charge of a water molecule) is about 0.3 electronic charges.