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Impacts of swift heavy ions of different energy loss in amorphous and crystalline Lennard-Jones (LJ) thin films (2–60 nm) were simulated using classical molecular dynamics to study cratering and sputtering in model molecular thin films. Crater size is determined mostly by evaporation and melt flow from the hot ion track, while rim size is determined both by melt flow and by coherent displacement of particles due to the large pressure developed in the excited region, with minor influence of particles from the substrate. Sputtering yields from both crystalline and amorphous samples are similar (including the scaling with energy loss), due to the extremely high temperature and disordered condition of the track region from where most ejected particles originate in the early stages of the track evolution. Cratering, however clearly depends on the crystallinity of the film. Craters and rims are much smaller in crystalline films mainly due to faster energy dissipation, higher stress threshold for plasticity and smaller free-volume in the ordered phase. We also found a large dependence of the induced surface effects on film thickness below a critical thickness value. The pressure pulse due to the ion impact is weaker and cooling of the excited track is more efficient in short tracks, both contributing to the decreased radiation damage efficiency on ultrathin layers. Despite the simplicity of the LJ model, the simulations in the amorphous films reproduce remarkably well several of the experimental features seen recently on polymer thin and ultrathin films irradiated by swift heavy ions. Fil: Gutierres, L. I.. Pontificia Universidade Católica do Rio Grande do Sul; Brasil Fil: Lima, N.W.. Pontificia Universidade Católica do Rio Grande do Sul; Brasil Fil: Thomaz, R. S.. Pontificia Universidade Católica do Rio Grande do Sul; Brasil Fil: Papaléo, R. M.. Pontificia Universidade Católica do Rio Grande do Sul; Brasil Fil: Bringa, Eduardo Marcial. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina