Computer studies of fast ion trajectories in crystals

A computer program has been developed which follows the trajectories of fast ions in crystals, based on the assumption of classical dynamics and binary collisions. Initial work has been directed at various aspects of proton channeling in copper in the energy range 5–500 keV. The critical angle and distance of closest approach in a perfect lattice have been evaluated for both rows and planes and compare well with the predictions of the continuum model as developed by Lindhard (1965). We also discuss the overlap of close-packed rows and planes, and the modifications necessary to the basic theory when thermal vibrations are introduced. Experiments have been simulated directly by obtaining a statistical analysis of the velocity distribution of protons reflected from a (100) face of copper and transmitted through a thin (~1800 Â) crystal. In reflection, distinct minima were obtained along directions corresponding to close-packed rows and planes, in good agreement with experimental "blocking patterns" (Nelson 1967a). Transmission patterns also revealed a lack of large-angle scattering parallel to close-packed planes, analogous to the white arms observed experimentally with thinner crystals.