Calibrating conservative and dissipative response of electrically-driven quartz tuning forks

Determining sensor parameters is a prerequisite for quantitative force measurement. Here we report a direct, high-precision calibration method for quartz tuning fork (TF) sensors that are popular in the field of nanomechanical measurement. In the method, conservative and dissipative forces with controlled amplitudes are applied to one prong of TF directly to mimic the tip-sample interaction, and the responses of the sensor are measured at the same time to extract sensor parameters. The method, for the first time, allows force gradient and damping coefficient which correspond to the conservative and dissipative interactions to be measured simultaneously. The calibration result shows surprisingly that, unlike cantilevers, the frequency shift for TFs depends on both the conservative and dissipative forces, which may be ascribed to the complex dynamics. The effectiveness of the method is testified by force spectrum measurement with a calibrated TF. The method is generic for all kinds of sensors used for non-contact atomic force microscopy (NC-AFM) and is an important improvement for quantitative nanomechanical measurement.