Tunneling models and the experimental thermal expansivities of fused silica and poly(methylmethacrylate) (PMMA) below 4 K

Linear-thermal-expansivity data are given to 1.5 K for the two different amorphous solids, fused silica (amorphous SiO₂) and PMMA [poly(methylmethacrylate)]. Both solids exhibit a negative expansivity contribution at low temperatures which is linear in the absolute temperature and which corresponds to a common Gr\"uneisen parameter, γ₁=-16. A calculation is given for the corresponding expansivity which would be expected for a continuous distribution in energy of two-level states using both symmetric and asymmetric tunneling models. Inconsistencies between the postulates which must be made to explain the present results and those required to explain other low-temperature properties of amorphous solids lend support to the conclusion from other experiments that the tunneling model does not explain satisfactorily the low-temperature properties of amorphous solids.