Effects of non-rotationally symmetric aberrations on the quantitative measurement of lattice positions in a graphene monolayer using high-resolution transmission electron microscopy

It is crucial to determine the position of lattice atoms in a monolayer specimen with high precision using high-resolution transmission electron microscopy (HRTEM). Image simulations indicate that the intensity centers of periodic lattice atoms in graphene may deviate from their intrinsic positions if non-rotationally symmetric aberrations (except for three-fold and six-fold aberrations) exist in the HRTEM imaging system. In this letter, we quantitatively compared the deviations caused by non-rotationally symmetric aberrations, which are equivalent to individually produce a π/4 phase shift in the wave aberration function at a given frequency of 7.2 nm(-1). A two-fold aberration caused a maximum shift of 0.3 Å, and in the images affected by the axial coma, graphene still maintained its hexagonal structure while all of the measured atomic positions deviated. Furthermore, we discovered that atoms on each sublattice tended to shift by similar distances in the image. Based on this rule, we retrieved the intrinsic bond length between neighboring carbon atoms by 'shifting' the measured atom positions in an experimental HRTEM image affected by residual aberrations.