Interaction between a spherical probe and an atomic lattice: implication for atomic force microscopy on graphite and diamond

Abstract

This work describes a new method for calculating the van der Waals interaction between a real surface and a spherical probe placed in its neighbourhood. The essence of the method is similar to that developed in physisorption calculations since it relies on the knowledge of a reduced number of parameters characterising the probe and the surface. The long range interaction energy (dispersive plus inductive) is obtained within the scheme of a nonlocal theory expressed in terms of generalised electric susceptibilities of the two partners. Short range interaction is then included through an atom-atom empirical pair potential. The discrete structure of each plane of the solid is described with an increasing accuracy by increasing the order of the Fourier expansion in the reciprocal planar lattice. This allows us to separate the van der Waals force probe-sample in two parts describing the continuum character and the corrugation of the surface, respectively. Numerical results are proposed by varying two parameters: the radius of the probe and the distance of nearest approach. Implications for atomic force microscopy on graphite and diamond are also discussed.