Classical Theory for the Interaction of Gas Atoms with Solid Surfaces

A classical theory for the interaction of gas atoms with solid surfaces is presented. The principal assumptions of the model used are: (1) The surface atoms involved in the collisions can be represented as independent one-dimensional oscillators; (2) the gas atoms interact with the surface through a stationary square-well attractive potential and an exponential repulsive potential; (3) the surface is flat so that the tangential velocity component of the gas atom is unchanged; (4) the surface oscillators have an equilibrium energy distribution at the temperature of the solid. This model represents a logical successor to the “hard-cube” model introduced by Logan and Stickney and allows the important effects involving the collision time and the natural frequency of the surface atoms to be taken into account. An approximate closed-form expression is obtained for the angular distribution of particle flux for a monoenergetic atomic beam scattered from a surface. For physically reasonable values of the well depth and range of the exponential potential, good quantitative agreement is obtained with available experimental data for the angular position of the maximum of the scattering distribution. Satisfactory agreement with experiment is even obtained in a case where the gas atom is heavier than the surface atom (Xe on Ag); in a case such as this the hard-cube model would not give reasonable results. Values are also obtained for the fraction of incident gas atoms which are initially trapped on the surface.