Direct measurement of interatomic force gradients using an ultra-low-amplitude atomic force microscope

Abstract
Interatomic force gradients between a W tip and a 7×7 reconstructed Si(111) surface were measured using an off–resonance, ultra–low–amplitude atomic force microscope (AFM) technique. The amplitudes used were less than 1 Å (peak–to–peak), which allowed direct measurement of the interaction force gradients as a function of separation. The force gradient curves are shown to consist of an attractive van der Waals part and short–range attractive and repulsive interactions. The van der Waals background can be subtracted, leaving a short–range interaction with an energy parameter of 1.9–3.4 eV and an interaction length–scale of 0.54–1.26 Å, characteristic of a single atomic bond. This correlates well with our observation of single–atom resolved force gradient images. In general, the interaction is reversible up to the zero intercept of the force gradient (inflection point of the energy). Beyond this point hysteresis tends to be observed and the onset of inelastic deformation can be clearly discerned. An analysis of the atomic scale contact gives reasonable values for the interfacial energy, yield strength, and the energy per atom needed to initiate plastic deformation.