Force-gradient-induced mechanical dissipation of quartz tuning fork   force sensors used in atomic force microscopy
  We have studied the dynamics of quartz tuning fork resonators used in atomic force microscopy taking into account mechanical energy dissipation through the attachment of the tuning fork base. We find that the tuning fork resonator quality factor changes even for the case of a purely elastic sensor-sample interaction. This is due to the effective mechanical imbalance of the tuning fork prongs induced by the sensor-sample force gradient which in turn has an impact on the dissipation through the attachment of the resonator base. This effect may yield a measured dissipation signal that can be different to the one exclusively related to the dissipation between the sensor and the sample. We also find that there is a second order term in addition to the linear relationship between the sensor-sample force gradient and the resonance frequency shift of the tuning fork that is significant even for force gradients usually present in atomic force microscopy which are in the range of tens of N/m. 
Andres Castellanos-Gomez, Nicolas Agra\"it and Gabino Rubio-Bollinger
cond-mat.mes-hall