The dynamics of simple cubic lattices—II: The effects of surface impurities on the lattice motion

Abstract

The lattice dynamics of simple cubic lattices which have impurity atoms on their surfaces are studied. An n-dimensional semi-infinite lattice model is used as a model of a solid surface and the response of an impurity atom on the surface to an initial disturbance is considered, a solution in terms of well-known functions being obtained for the one-dimensional case. A method of dealing with n-dimensional lattices is discussed and the three-dimensional lattice is considered in detail. The most important result is the appearance of special “surface modes” of vibration which are localized around the impurity atom. It is suggested that the “special modes” may greatly affect the energy transfer between a gas atom and a solid surface during a collision. Applications to experiment of the theory presented in this paper will be made in a later publication.