We studied friction and stick-slip phenomena on bare and lubricated silicon samples by measuring the torsional contact resonances of atomic force microscope cantilevers. A piezoelectric transducer placed below the sample generates in-plane sample surface vibrations which excite torsional vibrations of the cantilever. The resonance frequencies of the vibrating beam depend on the tip-sample forces. At low lateral surface amplitudes the cantilever behaves like a linear oscillator with viscous damping. Above a critical surface amplitude, typically 0.2 nm, the amplitude maximum of the resonance curves does not increase any more and the shape of the resonance curves changes, indicating the onset of sliding friction. The critical amplitude increases with increasing static cantilever load. For a bare silicon sample it is higher than for the lubricated silicon. Microslip known from macroscopic contacts causes energy dissipation in the atomic force microscope tip-contact before sliding friction sets i

Torsional and lateral vibrations of atomic force microscope (AFM) cantilevers can be used to measure elastic and frictional properties on a nanoscale. Recently a new dynamic operation mode called Torsional Resonance mode (TRmode) has been introduced. This paper describes the physical base of the TRmode and compares it to related dynamic AFM modes. In the theoretical part the torsional equation of motion of the cantilever beam is analysed. In the experimental part the contrast of images is interpreted based on the equation of motion. The route to quantitative measurements of contact stiffness, elastic moduli and friction is laid out.

Dynamic techniques exploiting the vibration of atomic force microscope (AFM) cantilevers are often superior to quasi-static operation, in particular with respect to the signal-to-noise ratio. Tapping mode, magnetic force microscopy or torsional resonance (TR)-mode for example exploit the resonance amplification of bending or torsional modes of the cantilever. In atomic force acoustic microscopy (AFAM) and related techniques aiming to measure elasticity or adhesion quantitatively on a nanometre scale, the cantilever vibrates while the tip is in contact with a sample surface. The higher vibration modes are included in the evaluation. Well-defined resonance maxima of the cantilever are a prerequisite for all resonance techniques. To allow their handling, microscaled commercial cantilevers are fabricated in one piece with a holder of millimetre dimensions providing the base to which the cantilever beam is suspended. Here, we examine experimentally and theoretically how the cantilever holder influences the vibration of the cantilevers.

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Using scanning probe techniques, surface properties such as shear stiffness and friction can be measured with a resolution in the nanometer range. The torsional deflection or buckling of atomic force microscope cantilevers has previously been used in order to measure the lateral forces acting on the tip. This letter shows that the flexural vibration modes of cantilevers oscillating in their width direction parallel to the sample surface can also be used for imaging. These lateral cantilever modes exhibit vertical deflection amplitudes if the cantilever is asymmetric in thickness direction, e.g., by a trapezoidal cross section.