Theory for the atomic force microscopy of layered elastic surfaces

The authors present a first-principles theory of atomic force microscopy (AFM) on layered elastic surfaces. 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. They apply this theory to graphite and calculate local distortions in the vicinity of an AFM tip and/or an intercalant atom. Using this formalism, they discuss the effect of a finite size tip (or a graphite flake attached to the tip) on the substrate distortions and the resulting AFM image. The authors 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.