Mapping nanoscale elasticity and dissipation using dual frequency contact resonance AFM

We report on a technique that simultaneously quantifies the contact stiffness and dissipation of an AFM cantilever in contact with a surface, which can ultimately be used for quantitative nanomechanical characterization of surfaces. The method is based on measuring the contact resonance frequency using dual AC resonance tracking (DART), where the amplitude and phase of the cantilever response are monitored at two frequencies on either side of the contact resonance. By modelling the tip–sample contact as a driven damped harmonic oscillator, the four measured quantities (two amplitudes and two phases) allow the four model parameters, namely, drive amplitude, drive phase, resonance frequency and quality factor, to be calculated. These mechanical parameters can in turn be used to make quantitative statements about localized sample properties. We apply the method to study the electromechanical coupling coefficients in ferroelectric materials and the storage and loss moduli in viscoelastic materials.