Tuning fork force measurement

As mentioned in a previous post, we want to include a quartz tuning fork to be able to directly measure force in-situ TEM. From the easy PLL system that controls the tuning fork a output signal proportional to the frequency shift that occurs due to an mechanical interaction force applied to the tuning force.
According to the PLL manual the frequency shift dF is given by:

dF=K*U

(1)

were U is the detector output signal voltage on the PLL system. Here was K=12.9°/V. If the measured spring Kts constant is low compared to the spring constant Kquartz of the tuning fork, shift in the measured spring constant over one cycle of the amplitude on the tuning fork can be neglected and if so the measured spring constant due to the applied force is given by:

Kts=2*Kquartz*dF/F0

(2)

Were F0 is the resonance frequency of the tuning fork. The result from contacting the tuning fork with the TEM-SPM probe is shown in the plot below were the measured spring constant (of the applied force) is plotted as function of the probe movement. Red and blue curves corresponds to probe moved in forward direction, i.e against the tuning fork, and in reverese direction, i.e away from the tuning fork.

If one integrate (sum) the measurement points one will get the applied force as function of probe movement, as seen in plot below.

One can notice that the forward and reverse curves do not follow the same path in the close-contact region, i.e to the right in plots.