Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene

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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.




Haždijojić, M., Ćosić, M., & Rymzhanov, R. (2021). Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene. Journal of Physical Chemistry C, 125(38), 21030–21043.

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