We experimentally discovered that Al2O3 and MgO exhibit well-pronounced nanometric modifications on the surfaces when irradiated under grazing incidence with 23 MeV I beam, in contrast to normal incidence irradiation with the same ion beam when no damage was found. Moreover, ions in these two materials produce notably different structures: grooves surrounded with nanohillocks on MgO surfaces vs. smoother, roll-like discontinuous structures on the surfaces of Al2O3. To explain these results, detailed numerical simulations were performed. We identified that a presence of the surface inhibits recrystallization process, thereby preventing transient tracks from recovery, and thus forming observable nanopatterns. Furthermore, a difference in the viscosities in molten states in Al2O3 vs. MgO explains the differences in the created nanostructures. Our results thus provide a deeper understanding of the fundamental processes of surface nanostructuring, potentially allowing for controlled production of periodic surface nanopatterns.