Green’s-tensor approach in the theory of the surface or interface vibrational contribution to thermodynamic properties of solids

We present a theory of the surface or interface contribution to vibrational thermodynamic properties of solids. We express the thermodynamic quantities such as the free energy and specific heat in terms of the surface or interface density of vibrational states. We derive a simple analytic expression for this function in terms of a static Green’s tensor of the system. We redefine the dynamical Green’s tensor compared with some earlier works, requiring that it correspond to a Hermitian differential operator. In order to calculate the free energy, we modify the Debye model to apply it to surface or interface problems. The free energy and specific heat are calculated for the cases of an isotropic solid bounded by a stress-free planar surface and two isotropic solids separated by a flat interface. © 1996 The American Physical Society.