Mechanical model of tuning forks used in scanning probe microscopes

Quartz tuning forks have been widely used as force sensors in scanning probe microscopes. The anti-phase and in-phase eigenmodes of a tuning fork are involved during microscope operations. Dynamic characteristics of both eigenmodes are studied by experiments and finite element analysis simulations. It is demonstrated that elastic couplings exist between not only both the prongs but also two prongs and the base of the tuning fork. Experimental results show that the coupling between both the prongs increases the anti-phase mode eigenfrequency while the coupling between two prongs and the base of the tuning fork decreases the in-phase mode eigenfrequency. A mechanical model of the tuning fork is introduced and simplified. Parameters of the simplified model are calculated, which is described as a four-springs-three-point-masses system. The quantitative relation between the effective mass of one prong and the eigenfrequency of the anti-phase mode of the mechanical model is in good agreement with that of finite element simulations.