LV. A surface contribution to the Debye specific heat

Abstract

The vibrations of a bounded lattice are identified with those of an elastic medium (isotropic, arbitrary elastic constants) having stress free surfaces. The densities of the representative points in wave number space for the four possible types of vibration are estimated. These estimates are carried one step further than the usual (Debye) method by including terms proportional to the surface. Summing over the densities, the total number of excited modes and the intrinsic energy of the lattice vibrations are obtained in the usual manner. From these we calculate surface terms for the Debye temperature and specific heat and for the free energy of the lattice vibrations.