Simple theory for the atomic-force microscope with a comparison of theoretical and experimental images of graphite

In this theory the atom-atom interactions within the sample are modeled with use of a force-constant matrix that is valid in the harmonic approximation. The tip-atom-sample interactions are modeled by a Lennard-Jones potential. Images for single-atom tips that are calculated from this theory, in which the atoms are allowed to relax, are similar to previous theoretical images that were calculated from a rigid-sample model. The asymmetric images produced by experiment could be reproduced theoretically with double-atom tips. All calculations were performed using a commercially available desk-top computer.