Study of graphene by proton rainbow scattering

Abstract

We have studied the transmission of 5 keV protons through graphene. Proton dynamics was modeled by classical theory. Proton trajectories define a mapping of the set of initial proton positions to the set of scattering angles. Singularities of the Jacobian associated with the introduced mapping form curves known as the rainbow lines. The differential cross section is infinite along the rainbow lines, making the proton count significantly larger along the rainbow pattern. Hence, rainbows dominantly determine the shape and size of the angular distribution of transmitted protons. It was found that reorientation of the graphene with respect to the incident beam direction and deformation of the graphene crystal lattice induce the transformation of the proton rainbow pattern. We thoroughly studied the morphological properties of the proton rainbow pattern. It was shown that angular distribution and the corresponding rainbow pattern could be used to determine the covariance matrix of atomic thermal displacements and to characterize point defects present in graphene. Graphical abstract: [Figure not available: see fulltext.] © 2023, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.