Collimators are widely used to define MeV ion beams. Recent studies have shown the capability of collimators to define beams of MeV ions with sub-100 nm dimensions. Such nanometer beams have potential applications in MeV ion-beam lithography, which is the only maskless technique capable of producing extremely high aspect-ratio micro- and nanostructrures, as well as in high-resolution MeV ion-beam-based tomography. The ion scattering from the collimator edges that define the beam can be a resolution-restricting factor in these applications. Scattering processes at edges are difficult to study using conventional simulation codes because of the complicated geometry. In this part of the work, the authors used the GEANT4 toolkit as a simulation tool for studying the behavior of ions impinging onto, or in close proximity to, a single straight aperture edge. Results from simulations are presented for realistic beams of 3 MeV He ions with 0.2-1 mrad divergence incident on a 100-mu m-thick Ta plate. The contribution from grazing scattering of ions impinging under glancing angles of incidence < 1 degrees on the slit-edge surface plane can degrade the beam spot size and shape. Ray-tracing simulations were also performed to investigate the trajectories of ions impinging on the aperture edge and in close proximity to it.