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Study of graphene by proton rainbow scattering

  • Regular Article – Atomic and Molecular Collisions
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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

Red arrows illustrate the incident and transmitted proton beams, respectively. From left to right are presented perfect graphene with isotropic thermal atomic motion, perfect graphene with anisotropic atomic thermal vibrations, and defective graphene with isotropic thermal vibrations of atoms. Blue surfaces are illustrations of the interaction potential isosurfaces in the vicinity of individual carbon atoms. Black spheres are carbon atoms. Corresponding angular distributions of the transmitted proton beams are presented below. The associated rectangular insets depict enlarged views of the central parts of corresponding distributions. Angular yields are expressed in the logarithmic scale and presented by the associated colormap

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

Authors acknowledge the support of the Ministry of Science, Technological Development and Innovation of Serbia under the contract No. 451-03-47/2023-01/200017.

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Authors and Affiliations

  1. Laboratory of Physics, “Vinča” Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, P. O. Box 522, 11001, Belgrade, Serbia

    M. Hadžijojić & M. Ćosić

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  1. M. Hadžijojić
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Contributions

M. H. and M. Ć. developed the theoretical framework and performed all calculations. The investigation was supervised by M. Ć, and M. H. wrote the first draft of the manuscript. Both authors commented on the manuscript and approved its final version.

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Correspondence to M. Hadžijojić.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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T.I.: Physics of Ionized Gases and Spectroscopy of Isolated Complex Systems: Fundamentals and Applications. Guest editors: Bratislav Obradović, Jovan Cvetić, Dragana Ilić, Vladimir Srećković and Sylwia Ptasinska.

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Hadžijojić, M., Ćosić, M. Study of graphene by proton rainbow scattering. Eur. Phys. J. D 77, 86 (2023). https://doi.org/10.1140/epjd/s10053-023-00664-y

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