Theory for the Atomic Force Microscopy of Deformable Surfaces

We present a theory for the atomic force microscopy (AFM) of deformable surfaces and apply it to graphite with and without intercalated atoms. Using continuum elasticity theory for graphite layers, with parameters obtained from ab initio calculations, we determine quantitatively local distortions in the vicinity of a sharp AFM tip as a function of the applied force. Our calculations show that AFM should be a unique tool to determine local surface rigidity and to measure the healing length of graphite in the vicinity of intercalated impurities or steps.