Abstract:
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.
