Computer Studies of Copper Atom Ranges in Copper Lattices

We have used an n-body collision computer simulation model with a Gibson #2 potential to examine various ways in which the lattice nature of the slowing down material influences the motion of a medium-energy copper atom. For normal incidence upon a (110) surface, we found that the lattice has a significant effect upon the scattering angle when a 10-keV copper atom strikes an atom of a copper lattice. The channel area, which comprises approximately 40% of the representative area in this orientation, is quite insensitive to the copper atom's energy above 1 keV. Total ranges are significantly longer than those reported by Robinson and Oen from calculations based upon a binary collision model. Below 1 keV, total ranges closely approximate the E32 law reported by Kornelsen et al. Above 1 keV dE/dx=A−B/E appears to describe the motion at all positions in the channel if the values of A and B are specified for the initial point at which the atom enters the channel. This behavior above 1 keV is clearly nonphysical. To be meaningful, even at intermediate energies, computer range studies must include inelastic energy losses. Lattices are known to focus atoms incident near the [110] direction into [110] channels. This mechanism was studied at the center of the channel with 1-keV atoms. The effect is anisotropic in the azimuthal angle, but we found that atoms inside a 10° cone were always focused, and that 20° focusing occured in one orientation. Angular focusing was less effective at higher energies. Transverse oscillations in the channel were also considered. The ``wavelengths'' are proportional to E½, but oscillations are usually not symmetric about the channel axis. Transverse motion is approximately harmonic, but the ``vertical'' and ``horizontal'' frequencies are never commensurable. We have evidence for a skimming mechanism in which high energy atoms are confined between (111) planes, or to a lesser extent between (100) planes. Trajectories of 5-keV knock-on atoms are shorter than 40 Å unless the moving atom skims. One true channel event was found in 120 trials in which the moving atom started from a lattice site.