document: The final contribution to the force is the van der Waals interaction. It includes the following contributions: (i) between the macroscopic Si tip of conical shape with the sphere of radius R at the end [27] and semi-infinite substrate; (ii) the dispersion forces between the atoms in the sample treated atomistically; and (iii) the interaction between the macroscopic part of the tip and the sample atoms. The first contribution is calculated analytically [27]. In fact, the macroscopic contribution to the van der Waals force is the same in each of the three systems described below, as it depends only on the tip–surface separation, macroscopic sphere radius, cone-angle and Hamaker constant of the system [27]. All these quantities are identical in each system we look at, so that the van der Waals force acts as a background attractive force independent of the microscopic properties of the system [8]. The Hamaker constant needed for the calculation of the macroscopic van der Waals force is estimated to be 0.5eV [32].
extractive_keyphrases: atoms calculation dispersion forces macroscopic part of the tip macroscopic si tip macroscopic van der waals force tip–surface separation van der waals force van der waals interaction
abstractive_keyphrases: sample atoms semi-infinite substrate