Numerical solution of the inverse problem of reconstructing phonon density of states from experimental heat capacity

A method is proposed to numerically solve the inverse problem of reconstructing phonon density of states g(ω) based on the experimental heat capacity C(T). A feature of this method is that, at the initial step, we calculate the g(ω) behavior at low and cutoff frequencies. The method is considered for several model objects of varying complexity. The phonon density of states of copper has been calculated and compared with published data. Analysis demonstrates that up to three peaks can be distinguished in g(ω) with correct description of their shapes. The new method can be used for a widest class of solids provided that very precise data on C(T) in a wide range of low temperatures are available.