Heat Capacity of Ice at Low Temperatures

The heat capacity of normal hexagonal ice has been measured over the temperature range 2° to 27°K with an estimated precision varying between ±2% at the lowest temperatures and ±0.2% at the higher temperatures. The results agree satisfactorily with those of earlier measurements in the region T 10°K, and do not significantly affect the value of the residual entropy of ice calculated by Giauque and Stout W. F. Giauque and J. W. Stout, J. Am. Chem. Soc. 58, 1144 (1936). Although the new results do not influence the existing thermodynamic description of ice, they provide information which is important in understanding its vibrational properties. In the first place, extrapolation of the results to T=0°K yields a value of Θ0, the Debye characteristic temperature corresponding to continuum behavior. This is found to agree satisfactorily with Θ (elastic) estimated from the elastic constants of ice. In the second place, complete ΘD(T) curves can be constructed, and an examination of these, computed for different sizes of vibrational unit, enables the gross features of the lattice frequency spectrum of ice to be determined. The conclusion reached is that the three components of the spectrum, due respectively to translational and rotational vibrations of the water molecule and to intramolecular vibrations, are well separated. The contribution of the librational modes to the thermodynamic properties can be approximated rather well by a single frequency of 620 cm—1.