Thermal properties of amorphous materials at low temperatures

Recent investigations of X-ray diffraction and electron micrograph studies reveal high density clusters separated by density deficient regions (voids) in amorphous materials. The low temperature specific heat and the thermal conductivity anomalies are explained on the basis of such a structure for amorphous materials. It is a generalisation of Debye's theory applied to most of the amorphous solids in the temperature range from 0 to 10 K. The anharmonic effects lead to the observed temperature dependence of the sound velocity. The thermal conductivity between 0 and 2 K is due to thermal diffusion, the plateau observed between 2 and 20 K is a consequence of the decrease in thermal conductivity due to three phonon processes compensated by intercluster diffusion, while beyond this range it is due to excitations within a cluster limited by the size of a cluster. Further the model predicts the coefficient of expansion about 100 times that found in the corresponding crystalline solids. An experimental verification of this result can be a good test for the model.