Elastic properties of amorphous solids below 100 K

We have performed a survey of the available literature on the speed of sound at temperatures above 5 K in amorphous solids. We have compared the slope, β, of the linear variation in the speed of sound at these temperatures with the temperature independent internal friction below 10 K, Q₀^-1, and find that, empirically, β = 0.5 Q₀^-1/K. This suggests that the low temperature properties of amorphous solids are connected with their universal behavior at higher temperatures. Additionally, we have extended our survey to crystals with glass-like properties as well as to quasicrystals. We find that the same relationship that exists in amorphous solids between Q₀^-1 and β exists in these solids as well. A model to explain this very general empirical relation does not seem to exist.