van der Waals force between a spherical tip and a solid surface

We present a model for calculating the van der Waals interaction between a real surface and probe tip. The probe characterized by its dielectric constant is assumed locally spherical, and the description of the sample is based on a discrete atomic representation of the solid. This allows one to separate the van der Waals force into two different parts, which describe the continuum character and the corrugation of the surface, respectively. Numerical results corresponding to two different modes of imaging are proposed by varying two parameters: the radius of the probe and the distance of nearest approach. Finally, the model is used to discuss the structure sensitivity of the atomic force microscope on the (100) face of an ionic crystal.