Atomic-force-microscope study of contact area and friction onNbSe2

We have used an ultrahigh vacuum atomic-force microscope to study the variation in contact radius and friction with applied force between a silicon tip and a ${\mathrm{NbSe}}_{2}$ sample. The data are compared to the Maugis-Dugdale theory, which is the appropriate continuum mechanics model for the properties and size of the tip-sample contact. The lateral stiffness of the tip-sample contact is related to the radius of the tip-sample contact through the shear moduli of the materials and we have used this relationship to measure directly the variation in contact radius with applied load. The contact radius measured in this way is found to be in agreement with the Maugis-Dugdale theory using the bulk values of the shear moduli. We also measured the variation in friction force with applied load using the same silicon tip. The variation in friction force with applied normal force is found to follow the variation of the contact area as predicted by the Maugis-Dugdale theory [D. Maugis, J. Colloid Interface Sci. 150, 243 (1992)], which supports the hypothesis that for a single asperity contact, the frictional shear stress \ensuremath{\tau} is constant. The value of the shear stress is found to be \ensuremath{\tau}\ensuremath{\approx}6\ifmmode\times\else\texttimes\fi{}${10}^{8}$ N/${\mathrm{m}}^{2}$, which is comparable to the estimated theoretical shear strength of ${\mathrm{NbSe}}_{2}$.