Simple Classical Model for the Scattering of Gas Atoms from a Solid Surface

TLDR

The model builds on features previously introduced by Goodman. The study proposes a simple classical model to describe gas atom scattering from solid surfaces and determines its characteristics. The model assumes an impulsive repulsive force between gas and surface atoms, a uniform in‑plane potential that preserves tangential velocity, surface atoms as independent particles in square‑well potentials, and a Maxwellian velocity distribution for the surface atoms. The model, having no adjustable constants, yields angular distributions that qualitatively match experiments, correctly predicting the scattering pattern’s dependence on incidence angle, temperature, and masses, and revealing that surface temperature is a significant parameter.

Abstract

A simple classical model for the scattering of gas atoms from a solid surface is proposed and its characteristics are determined. The principal assumptions are (1) the interaction of a gas atom with a surface atom is represented by an impulsive force of repulsion, (2) the gas—surface intermolecular potential is uniform in the plane of the surface (hence the interaction does not change the tangential velocity of the gas particle), (3) the surface atoms are represented by independent particles confined by square-well potentials, (4) the surface atoms have a Maxwellian velocity distribution. The model incorporates many of the same features as that proposed by Goodman. As a result of these assumptions, the model is simplified to the extent that it contains no adjustable constants. Results are obtained for the angular distribution of the scattered particles. Significant quantitative results are not expected from such a simple model, but the qualitative behavior of the model does agree surprisingly well with the experimental results. The model correctly predicts the general appearance of the scattering pattern and its dependence on the angle of incidence of the beam and on the temperatures and masses of the gas and surface atoms. We conclude that, contrary to the assumption often made in theoretical studies of gas—surface interactions, the temperature of the surface is a significant parameter when considering the existing experimental data.