Effect of Dislocations on the Thermal Conductivity of Ice and Ice Clathrate

Abstract

Recently Ahmad and Phillips /I/ observed that the T2 dependence of the thermal conductivity of ice clathrates is due to the tunneling states arising from proton disorder 121. The thermal conductivity of ice clathrat'e was otherwise assumed to resemble the thermal conductivity of amorphous materials 131. The other important parameter to analyse their thermal conductivity is found to be the dislocation density of the order of 1014 rn-' in such materials which is quite higher than that normally found in non-metals in earlier calculations 141. In the present note we study the effect of dislocations on the thermal conductivity of ice clathrates at low temperatures when the dislocation density is large.The thermal conductivity of ice clathrate hydrates is found to be markedly different from that of ice between 40 K and room temperature unlike the properties such as sound velocity and electrical resistivity which are almost the same due to the similarities in their lattice structures. The clathrate hydrates are crystalline in 2 nature though the temperature dependence of the thermal conductivity curve is T dependent. It is therefore interesting to compare the results of the thermal conductivity of clathrates with that of ice as shown in Fig. 1. The thermal conductivity of ice and its clathrates is calculated by using the Callaway relation which can be summarized aswhere C(w,T) is the specific heat at temperature T, l(w,T) is the mean free path, and v(w,T) is the phonon velocity. Ahmad and Phillips /I/ have suggested that due to the typical characteristics of the density of phonons states, a constant v with Debye-like density of vibrational states is a good approximation to study the presence of dislocations and proton disorder in clathrates .Klinger and Rochas /5/ have analysed the thermal conductivity data of ice of linear dimensions by considering l ) Purulia, West Bengal, India. where the first term is the boundary scattering, the second is due to dislocation scattering, and the last *term represents the umklapp scattering processes. From the temperature dependence of the relaxation time for phonon-phonon scattering processes the value of s can vary from 1 to 4 . A best fit /6/ between theory and experiment can be obtained by including the normal phonon-phonon and isotopic scattering processes, the effective relaxation may then be expressed as T -l ( w ,~) = 1 + + DU 3 + B~U 2 3