Gruneisen Function Research Articles

Grüneisen functions for axial crystals

Abstract For axial crystals there are only two independent non-zero Gruneisen functions, γ1 = γ2 and γ3—even for those axial crystals which have non-zero elastic constants c Λμ for Λ = 1, 2, 3 and μ = 4, 5, 6. The results γ1 = γ2 and γ4 = γ5 = γ6 = 0 follow from the symmetry in the same way as the corresponding results for the thermal expansion coefficients. The expressions for γ1 and γ3 given by Barron and Munn (1967) are valid for all axial crystals.

The thermodynamic and vibrational properties of H2O ice and D2O ice

The thermodynamic properties of H2O ice and D2O ice have been analysed in terms of the effective harmonic spectrum of lattice vibrations. In this approximation the vibrations are treated as harmonic, but with frequencies which are both volume and temperature dependent. Analysis of the heat capacity then gives properties of the effective spectrum at 0 °K, and the average temperature dependence of the spectrum at constant volume. It has been shown that the parts of the spectrum associated with translational and librational motion of the molecules are distinct, and their contributions to the thermodynamic properties may be separated. The momentsv-2,v-1,v,v2,v4andv6together with the geometric mean frequencyvghave been derived for the separate parts of the spectrum. The reduced librational moments, (vnL)1/n, are independent ofnwithin the experimental uncertainty. This shows that the spectrum of librational frequencies consists of a fairly sharp and symmetrical band. From the very low temperature data the coefficients of the terms inv2,v4andv6in the low frequency expansion of the translational spectrum have been derived, together with the position and approximate weight of the first peak in the spectrum. The ratios of the moments for H20 and D2O show that the intermolecular forces are stronger for D2O than for H2O. From the thermal expansion data, by analysing the Gruneisen function y(T, V) =βV/XsCp, values for some of the parameters y(n) = — (l/n)dlnvn/dlnV, which describe the volume dependence of the moments, have been obtained for the separate parts of the spectrum. These are useful in estimating the volume dependence of various crystal properties. The properties of the effective harmonic spectrum and its average total temperature dependence (including thermal expansion effects) are in good agreement with the results of a variety of spectroscopic experiments. The moments derived from the thermodynamic data have been used to calculate the mean square amplitudes of vibration of O, H and D atoms and the results are in good agreement with the results of X-ray and neutron scattering experiments.