Theory for the atomic force microscopy of layered elastic surfaces

A first-principles theory of atomic force microscopy (AFM) on layered elastic surfaces is presented. Substrate distortions due to the AFM tip and intercalant impurities are described within continuum elasticity theory, using elastic constants determined from ab initio density functional calculations. This theory is applied to graphite and local distortions in the vicinity of an AFM tip and/or an intercalant atom are calculated. Using this formalism, the effect of a finite size tip (or a graphite flake attached to the tip) on the substrate distortions and the resulting AFM image is discussed. Calculations show that the AFM should be a unique tool to determine the local surface rigidity and the healing length of graphite near structural impurities. Palladium is used as the finite size tip.