Effect of interatomic interaction, surface orientation and direction of propagation on the properties of single-component surface waves

In the framework of the discrete lattice model the dispersion relation and penetration depth of surface waves are obtained for arbitrary values of the two-dimensional wave vector. Primitive, face-centered and body-centered cubic crystals with differently oriented surfaces are considered taking into account the interaction between the nearest and next nearest neighbors. It is shown that depending on the direction of the two-dimensional wave vector, the penetration depth is varied through a wide range from an infinitely large value (when the surface wave tran forms into a bulk one) to the thickness of a few subsurface atomic layers. In the limit of large wave numbers the penetration depth depends essentially on the interaction between the next nearest neighbors. Two-part single-component surface waves can exist: the amplitude of the first part decreases monotonously with the distance from the surface and the amplitude of second part decreases in a non-monotonous way.