Force-gradient-induced mechanical dissipation of quartz tuning fork force sensors used in atomic force microscopy

Abstract

We have studied the dynamics of quartz tuning fork resonators used in atomic force microscopy taking into account the mechanical energy dissipation through the attachment of the tuning fork base. We find that the tuning fork resonator quality factor changes even in 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 dissipation through the attachment of the resonator base. This effect may yield a measured dissipation signal that can be different from 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.

Nanomechanical tuning forks fabricated using focused-ion-beam chemical vapor deposition

“…[17][18][19] The beam model is appropriate for calculating resonant frequencies, and the 2-degrees-of-freedom model is appropriate for describing frequency responses. In the work reported in this paper, we used a beam-with-torsional-spring(s) model to a) Electronic mail: ashiba@nanome.t.u-tokyo.ac.jp Fig.…”

Controlling the quality factor of a tuning-fork resonance between 9 and 300 K for scanning-probe microscopy

“…The tuning fork is therefore not balanced anymore but asymmetric. One expects changes in the response of the tuning fork as compared to a bare one as has already been reported before [32,33,34]. The elastic constant of quartz and its density are E = 8.68 × 10 10 N/m 2 and ρ = 2649 kg/m 3 , respectively.…”

“…Whereas the dominant mode is the fundamental anti-symmetric mode of the tuning fork, the second mode cannot be the fundamental symmetric mode because the symmetric and anti-symmetric modes are at least 10 kHz apart [33]. Even considering the asymmetry of the tuning fork because of the loaded prong using a two-coupled-oscillator model [32,33,34] cannot fully explain the observed resonance splitting. An explanation might be that the oscillation mode of the loaded prong alone changes with temperature due to the changing elastic properties of the glue that was used to attach the fiber.…”

“…One prong is l r = 3.9 mm long, t r = 600 µm thick, and w r = 330 µm wide. Since the tuning fork is excited electrically, we expect the so-called anti-phase mode to be the dominant oscillation mode [32,33,34]. In part of the experiments an optical fiber was glued to one prong of the tuning fork with epoxy glue for the use in temperature-dependent NSOM measurements.…”

Photo-thermal quartz tuning fork excitation for dynamic mode atomic force microscope

“…A quartz tuning fork prong is usually glued on a supplementary actuator which vibrates at the QTF resonance frequency. This mechanical setup decreases significantly the QTF quality factor (Q < 1000) due to prong imbalance, yet provides a reliable tip-sample distance control mechanism in scanning probe microscopies including AFM [14][15][16] or Scanning Near-field Optical Microscopy. 17 The photo-acoustical spectroscopy (PAS) is another field in which the QTF has been successfully used.…”