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A combined Monte Carlo (MC) and Molecular Dynamics (MD) approach enables us to study in detail effects of different stages of swift heavy ion (SHI) track formation. The MC model (TREKIS [1]) describes excitation of the electronic system and energy transfer to the lattice providing initial conditions for the MD simulations of subsequent lattice response. We discuss here the kinetics of individual track formation, tracks overlap and surface modifications in some amorphizable (YAG, Mg2SiO4) and non-amorphizable (Al2O3, MgO, CaF2) solids irradiated with SHIs. High-resolution transmission electron microscopy analysis of samples irradiated with Xe and Bi ions is used to validate the developed model and to investigate the link between the basic properties of the studied materials and the kinetics of structural changes of the targets. We demonstrate the following: 1) The size and morphology of individual latent tracks and tracks overlap at high fluences are strongly affected by recrystallization of the transiently disordered zone [2]. 2) Different spectra of electrons generated by ions of different energies result in a velocity effect of track formation and a mismatch between the position of the maximal damage and the Bragg peak of the projectile energy loss [3]. 3) Protrusion of molten material and a final structure of surface defects induced by an SHI are governed by mobility of target atoms, surface tensions and recrystallization of a material during the ultra-short cooling period [4]. 4) A target thickness affects formation of surface defects under SHI irradiation: the thinnest layers form a through hole, semispherical and spherical hillocks are created after an ion impact at medium thicknesses, whereas nanoparticle emission occurs from thick layers [5]. 5) Impact of an SHI under a grazing incidence results in formation of a groove-like structure vs. a chain of nanohillocks depending on material and irradiation properties. It can be concluded that hydrodynamic (Rayleigh

We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.

We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.

The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.