Theoretical Investigations of Gas–Solid Interaction Phenomena. II. Three-Dimensional Treatment

Abstract

A three‐dimensional, classical study of gas–solid surface interaction phenomena is reported. An independent‐oscillator lattice model is assumed to represent the crystal surface. Nine movable lattice sites are connected to fixed points by harmonic springs in a geometry chosen to represent either the (100) or (111) planes of a Ni crystal. The interaction potential is constructed from nine pairwise Morse potentials operating between the incident gaseous atom and the nine movable lattice points. Energy‐transfer coefficients (ETC) and spatial distributions are calculated as a function of incidence angle, gaseous beam velocity and temperature, surface temperature, gaseous atom mass, lattice force constant, and attractive well depth and curvature by numerical solution of the 60 differential‐motion equations. The results indicate that the ETC should decrease with increasing incidence angle, decreasing attractive well depth and curvature, increasing lattice force constant, and decreasing isotopic mass of the incident gaseous atom. As the surface temperature approaches and exceeds the gaseous beam temperature, the ETC is also predicted to decrease. The rate of decrease of the ETC with incidence angle seems sufficient to justify the normal component model in contrast to previous two‐dimensional results. Energy transfer is found to be favored for collisions near lattice sites. The calculated ETC values are virtually independent of the crystal plane being attacked. The calculated three‐dimensional spatial distributions exhibit peak maxima and half‐widths characteristic of experiment. The distributions are strongly dependent upon incidence angle and, under certain conditions, exhibit a “bimodal” structure. This structure is observed to decrease with increasing beam and surface temperatures, decreasing incidence angle, and decreasing attractive well. Subspecular shifts of calculated peak maxima are predicted for increasing surface temperature. The angular distributions in planes parallel to the surface are peaked at the in‐plane angle and decrease rapidly on either side of it. This effect becomes more pronounced as the incidence angle and the beam temperature are increased and as the attractive well depth is decreased. Insofar as comparison with experiment is possible, virtually all results are in qualitative to semi‐quantitative agreement with available experimental data.