On the Dispersion of Phonons in Metals

The measured dispersion law for copper and aluminium is used to find the corresponding heat capacity at constant volume with out recourse to a force-constant model for interpolation purposes. The discussion is confined to the harmonic approximation. Thermal expansion of the lattice is allowed for by the usual thermodynamic relations which are presented in a particularly convenient form . The use of perturbation theory is examined in some detail. It is found that while it may be made plausible from certain experimental results on slow neutron scattering, a theoretical justification is absent.