Saturation of the ion-hammering effect for large non-hydrostatic capillarity stresses in colloidal silica nanoparticles

We investigate the role of capillarity stresses on the ion-hammering phenomenon when sub-micrometer colloidal particles are considered. To this end, nearly monodisperse, chemically synthesized silica (SiO₂) colloids (100, 300 and 600 nm) were irradiated at room temperature (300 K) with 4 MeV Au ions for fluences up to Φ = 1.8 × 10¹⁶ cm⁻². It has been taken for granted that the transverse dimension of an ion-deformable amorphous material grows exponentially with the irradiation fluence, L(φ) = L₀exp[A₀Φ]. Here, we show that for sub-micrometer particles the irradiation-induced deformation saturates for larger fluences, L(φ)→const. The saturation fluence depends on the initial dimension of the colloidal nanoparticles: the smaller the dimension of the colloids, the lower the saturation fluence. Experimental data are successfully accounted for by having recourse to a phenomenological model first developed by Klaumünzer and further elaborated by van Dillen. We also estimate the evolution with fluence of the principal stresses inside the particles, σ₁₁(φ) = σ₂₂(φ) and σ₃₃(φ), and we show that they evolve toward a steady-state value following a sigmoidal-like behavior. Furthermore, when stresses induced by the surface curvature become non-negligible the approximation often made that the deformation strain rate, A₀ = dL/L dΦ, remains constant upon irradiation is no longer valid. We show that A₀ evolves with the irradiation fluence, e.g. A₀→A(Φ), and we relate this behavior to the evolution of the stresses upon irradiation. Finally, this work allows us to define the limits of the ion-hammering effect when the non-hydrostatic capillarity stresses become important.