On the determination of the phonon density of states from the specific heat

A new method is described for obtaining information on the phonon frequency spectrum g( omega ) from the phonon specific heat Cph(T). A rapidly convergent function G(T) is first generated from Cph(T), (G(T) approximately 1/T11 at high temperature T), and a spectrum g( omega ) is obtained from a least-squares fit to G(T) of a set of functions similarly derived from the Einstein specific heat function. The resolution (half width at half height) of 0.18 of the frequency is comparable to that of existing direct methods for the determination of g( omega ) such as incoherent inelastic neutron scattering. The geometric mean frequency and integer and non-integer negative and positive moments of g( omega ) may be accurately determined from suitable temperature integrals of G(T). The method is simple to apply and can be used if specific heat measurements of reasonable accuracy are available up to theta D/2.