Determination of the static spring constant of electrically-driven quartz tuning forks with two freely oscillating prongs.

Quartz tuning forks have become popular in nanotechnology applications, especially as sensors for scanning probe microscopy. The sensor's spring constant and the oscillation amplitude are required parameters to evaluate the tip-sample forces; however, there is certain controversy within the research community as to how to arrive at a value for the static spring constant of the device when working in shear mode. Here, we present two different methods based on finite element simulations, to determine the value of the spring constant of the sensors: the amplitude and Cleveland methods. The results obtained using these methods are compared to those using the geometrical method, and show that the latter overestimates the spring constant of the device.