Density of states and specific heat of elastic vibrations in layer structures

On the basis of a determination of normal modes in materials consisting of periodic arrangements of macroscopic layers (of period d), the low frequency density of states and the corresponding low temperature specific heat were calculated numerically. The average temperature dependence of the latter changes in the vicinity of a characteristic temperature T₀ (proportional to 1/d), from a low temperature (α₀T³)- to a higher temperature (αT³+βT²)- law. Depending on the material parameters, β may be positive (especially if Stonely waves are present) or negative. The coefficients α and α₀ can differ by a factor larger than 2. Characteristics of thick and thin layers and the implications of the results on the interpretation of experimental data are discussed.