Dynamics of systems with two interfaces

Systems with two interfaces (sandwich $\mathrm{ABC}$, planar defect, film) are considered. A symmetrization scheme is used to obtain the symmetrical ($S$) and antisymmetrical ($A$) modes of the planar defect and the thin film for arbitrary thickness. When medium $B$ is very thin ($h{k}_{\parallel }\ll 1$), we obtain the eigenmodes of the planar defect in analytical form, clarifying some discrepancies previously existing in the study of such a system. The interaction energy of point defects is obtained in closed form. The particular case of two adatoms is considered.