Anisotropic plastic deformation by viscous flow in ion tracks

A model describing the origin of ion beam-induced anisotropic plastic deformation is derived and discussed. It is based on a viscoelastic thermal spike model for viscous flow in single ion tracks derived by Trinkaus and Ryazanov. Deviatoric (shear) stresses, brought about by the rapid thermal expansion of the thermal spike, relax at ion track temperatures beyond a certain flow temperature. Shear stress relaxation is accompanied by the generation of viscous strains. The model introduces differential equations describing the time evolution of the radial and axial stresses, enabling an exact derivation of the viscous strains for any ion track temperature history $T\left(t\right)$. It is shown that the viscous strains effectively freeze in for large track cooling rates, whereas reverse viscous flow reduces the net viscous strains in the ion track for smaller cooling rates. The model is extended to include finite-size effects that occur for ion tracks close to the sample edge, enabling a comparison with experimental results for systems with small size. The “effective flow temperature approach” that was earlier introduced by Trinkaus and Ryazanov by making use of Eshelby’s theory of elastic inclusions, follows directly from the viscoelastic model as a limiting case. We show that the viscous strains in single ion tracks are the origin of the macroscopic anisotropic deformation process. The macroscopic deformation rate can be directly found by superposing the effects of single ion impacts. By taking realistic materials parameters, model calculations are performed for experimentally studied cases. Qualitative agreement is observed.