Thermal expansion of glasses at low temperatures

The linear thermal expansion coefficient (..cap alpha.. = (par. deltalnL/par. deltaT)/sub p/) was measured at temperatures to 1.2K for two amorphous solids, fused silica and PMMA (polymethylmethacrylate, plexiglas), using a parallel plate capacitor differential dilatometer. The low temperature expansion coefficients for these solids have the same temperature dependences as the specific heats, and show a contribution which is linear in the temperature and which can be associated with the postulate of a broad distribution of two level states. The Grueneisen parameters which are associated with this contribution are comparable for the two solids (Y approx. = -16), and suggest a further indication of common behavior for amorphous solids at low temperature. Large magnitudes for Grueneisen parameters (/..gamma../ > 5) generally are associated with tunneling models. A symmetric double harmonic oscillator tunneling model can be used to understand the sign and magnitude of ..gamma.. for these solids. This model is inconsistent with other thermal and thermodynamic data for fused silica. The existence of similar negative and large magnitude Grueneisen parameters for these two amorphous solids places an additional constraint on theories for the low temperature properties of glasses.