Characterization of the mechanical properties of qPlus sensors

In this paper we present a comparison of three different methods that can be used for estimating the stiffness of qPlus sensors. The first method is based on continuum theory of elasticity. The second (Cleveland's method) uses the change in the eigenfrequency that is induced by the loading of small masses. Finally, the stiffness is obtained by analysis of the thermal noise spectrum. We show that all three methods give very similar results. Surprisingly, neither the gold wire nor the gluing give rise to significant changes of the stiffness in the case of our home-built sensors. Furthermore we describe a fast and cost-effective way to perform Cleveland's method. This method is based on gluing small pieces of a tungsten wire; the mass is obtained from the volume of the wire, which is measured by optical microscopy. To facilitate detection of oscillation eigenfrequencies under ambient conditions, we designed and built a device for testing qPlus sensors.