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

TL;DR

This paper investigates how force gradients affect the mechanical dissipation and resonance behavior of quartz tuning fork sensors in atomic force microscopy, revealing a previously overlooked dissipation mechanism.

Contribution

It introduces the concept of force-gradient-induced dissipation and analyzes its impact on the quality factor and resonance frequency of tuning forks in AFM.

Findings

Force gradients alter the tuning fork's quality factor even with elastic interactions.

A second order term significantly influences resonance frequency shifts.

The dissipation signal may not directly reflect sensor-sample dissipation.

Abstract

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.