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I have an atomic force microscope with a tuning fork-based sensor. This tuning fork has a probe tip on it that feels a force from the sample that it scans over. Since the tuning fork and probe tip are coupled, the force on this tip affects the tuning fork.

Why does such a force change the resonance frequency of the tuning fork? For instance, a repulsive force between the probe tip and the sample increases the tuning fork's resonance frequency from its free-space value. However, an attractive force decreases the resonance frequency. I'm just a bit confused about why only repulsive forces increase the rate. I assume that it is related to the electric field generated by the potential difference between the probe tip and sample.

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It's not the force that changes the resonant frequency, it's the gradient of force vs. distance. Despite the name, AFMs actually measure force-gradient not force.

It is possible to operate AFMs in a force-sensing mode where the deflection angle of the cantilever is measured by laser reflection. But the preferred mode is to excite the cantilever at its resonant frequency and then measure the changes in phase angle between the driving frequency and the cantilever motion. This is the most sensitive way of measuring changes in the mechanical resonant frequency.

The force gradient from the surface adds to the natural stiffness of the cantilever. Both can be expressed in Newtons per meter of tip deflection. When the force is pushing the tip away from the surface, the force gradient acts to add to cantilever stiffness and increase the resonant frequency. The reverse is true when the tip is attracted towards the surface.

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  • $\begingroup$ Oh okay, the concept of added stiffness helps. So a positive force gradient (grad(F) > 0) increases the "spring constant" k for the tuning fork or cantilever? While a (grad(F) < 0) decreases this k? $\endgroup$ Mar 3, 2021 at 18:38
  • $\begingroup$ Also, if it is the force-gradient that is measured, and the force is the (-grad(U)), where U is a potential scalar field, then AFM measures the concavity of the potential well between the sample and tip? $\endgroup$ Mar 3, 2021 at 18:41
  • $\begingroup$ @ExactPlace441 Yes and yes. It comes up as more of a concern in MFM [2] H. Hug et al., “Quantitative magnetic force microscopy on perpendicularly magnetized samples”, J. App. Phys., Vol. 83, No. 11-1, pp. 5609- 5620, June 1998 [3] U. Hartmann , “Magnetic Force Microscopy”, Annual Review of Materials Science, Vol. 29, pp. 53-87, August 1999 $\endgroup$
    – Roger Wood
    Mar 3, 2021 at 20:55

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