A cellular model for the specific heat of amorphous solids at low temperatures

The wave equation for a non-homogeneous continuum with a statistical mass-density distribution is studied as a model for the vibrational specific heat of amorphous solids. The frequency spectrum is calculated for the simple case of small homogeneous cells separated from each other by hard and soft boundary walls distributed at random. The usual bulk mode density is enhanced by a positive constant term yielding the specific heat AT + BT³. From experimental values of the constants A, an upper limit of about 70 Å is calculated for the average cell diameter in vitreous SiO₂ and GeO₂.