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For the past few years, there has been a rapid rise in the use of ion beam technology for surface nanostructuring of various materials. For LiNbO3 single crystals, we have observed surface nanostructures after surpassing a potential energy ≈35 keV of the incident ion. Here, we introduce plasma expansion approach, based on a dimensionless self-similar parameter, to explain the main features of the mechanism responsible for the created structures. The analysis of the results reveals that the temperature ratio between ions-to-electrons does not change the profile of the expansion at early time. However, increasing the temperature ratio makes the expansion domain longer; nevertheless, a further rising leads to decrease the expansion range. Furthermore, the niobium ions exhibit a dominant effect, in comparison to lithium ions, for the modification of the plasma-expanded region. Keywords: Plasma expansion approach, Surface nano-structures, Fluid model