Specific heat of glasses at low temperatures

We have studied the specific heat of nitrate glasses ($T<\mathrm{}1\mathrm{}$ K) doped with water, lithium, and nitrite. We have found that there is a basic difference between doped crystals and doped glasses regarding the excess specific heat caused by the presence of the dopants. Dopants in glasses cause a change in the low-temperature specific heat only if the glass transition temperature $T_G$ changes upon admixing. The excess specific heat is found to be inversely proportional to $T_G$. Similar results have been observed on silica containing sodium and on neutron-irradiated silica, for which the important parameter is the fictive temperature $T_f$. It is concluded that the frozen-in disorder in the glass, which is measured by $T_G$ (or $T_f$), is an important factor in determining the density of states of low-energy excitations which are characteristic of the amorphous state.