Trapping and Energy Transfer in Atomic Collisions with a Crystal Surface

Abstract

The condensation of atoms on a solid is examined by calculating the critical energy for trapping of a particle of arbitrary mass and force constant colliding with a linear lattice. In the harmonic approximation and using classical mechanics, the maximum kinetic energy for trapping is found to depend strongly upon the well depth, in qualitative agreement with experiment. For a gas atom colliding with its own lattice (that is, force constant ratio β=1 and mass ratio μ=1) capture occurs at translational energies up to 25 times the binding energy. For β=0.2, this critical energy has diminished to 1.3 times the dissociation energy Q of the homogeneous lattice. The dependence of the critical energy on force constant is not monotonic, however—there is a maximum at β∼0.75. At β=0.75 and μ=1, for example, the incident energy must exceed ∼31Q to prevent trapping. Most of the energy exchange occurs during the repulsive part of the collision. For this part of the collision interval, the presence of a trapping potential has little effect. However, the energy exchange occurring when the particle rebounds through the attractive part of the potential is sensitively dependent upon the force constant. For β<0.5, the incident particle loses energy equal to ∼0.5 times its binding energy. As β increases, the energy loss diminishes and after β∼0.75 the incident particle actually gains in total energy. The accommodation coefficient for systems with repulsive interactions only does not show such specificity; for β>0.2 the energy exchange is dictated primarily by the mass ratio. The coefficients calculated for hard-sphere collisions provide an acceptable approximation when β>∼0.5.