Lattice-Dynamical Calculation of the Surface Specific Heat of a Crystal at Low Temperatures

Abstract

A lattice-dynamical calculation of the surface contribution to the low-temperature specific heat of a crystal is presented. The free boundary surfaces of a crystal are treated as a perturbation of an unperturbed crystal in which the atomic displacements satisfy the cyclic boundary condition. The general theory developed in this paper is illustrated by applying it to a nearest- and next-nearest-neighbor central-force model of a simple cubic crystal, whose force constants are chosen in such a way that it is elastically isotropic in the long-wavelength limit. The result for the low-temperature surface specific heat obtained here agrees with the results of earlier calculations by Dupuis, Mazo, and Onsager, and by Stratton, which were based on elasticity theory.