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Diamagnetic Lateral Force Calibrator (D-LFC)

Lateral force calibration of AFM (LFM, FFM)

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Calibration Procedures

Data Processing

Calibration Procedures [top]

Through the previous four-step DIY, you must be anxious to see how this simple device can work on the sophisticated AFM system. Let's start with the demonstration by showing some of the videos I took using an optical microscope:  side view ,  top view

A schematic of the D-LFC is shown in Figure 7.  In the setup, the diamagnetic levitation system is mounted on the stage of the AFM base scanner. For the calibration, you just do the normal LFM measurement; the only thing different is that your sample is now replaced by the D-LFC. Once the AFM tip is engaged on the PG composite surface, the magnets together with the AFM base are reciprocated by the lateral scanner, while the normal load is held fixed by holding the normal PSPD output vn constant through the feedback controller. It should be noticed that we used the Park Scientific Instrument AutoCP AFM system. For those systems with a fixed sample holder but a moving probe, the magnets are stationary while the PG sheet moves together with the probe after the engagement. 

schematics of calibration

Figure 7. A schematic of the D-LFC

The lateral PSPD output vl is recorded against the lateral base displacement dx1. The displacement is related to the lateral force f by 

eq-5         (5)

where the base displacement can be decomposed dx1eq , into the displacements of the magnetic spring dx1m and the AFM tip dx1t. The tip displacement dx1t is caused by the compliance of the tip contact and the cantilever twist. It is typically within a few nanometers while the magnetic spring displacement is on the order of tens of micrometers. Therefore, the tip displacement can be neglected in (5). In this calibration procedure, the maximum reciprocating displacement of the lateral base displacement  dx1b is limited to induce a lateral force f well within the static friction force of the onset of slip.


Figure 8. A diagram showing the D-LFC principles for measuring the AFM force constants

Figure 8 shows an experimental measurement of the lateral PSPD output against the lateral displacement of the magnets on the AFM base reciprocated within 25 µm for contact between a mica specimen mounted on a levitated PG sheet and a spherical bead attached near the end of an AFM cantilever. The bead is made of boro-silicate glass coated with a 50 nm gold layer and has a diameter of 15 µm. The experimental data show that the response is linear and reversible within the thermal and feed-back noise band for forward and backward scanning of the base displacement.

Step-1: Use the D-LFC as your sample and collect the LFM data as normal. Multiple data sets should be collected for different normal loads (usually called set point) if you want the crosstalk force constant to be calibrated.

If everything is carried out correctly, you will get the data similar to those shown in Figure 9. 



Figure 9. D-LFC data of the lateral PSPD output under incremental normal loads

According to our experiences, this is the trickiest part of the calibration process. Here are some tips, you may find them useful (or you can contact me if you have some other weird problems): 

  • Use a larger scan size, i.e. larger spring displacement, as long as the probe doesn't slip relatively to the PG surface;
  • Put an acoustic cover if your AFM system has one; because the PG sheet is floating in air, it is susceptible to the acoustic noise; and if your system has a poor vibration isolation, you can try the data averaging if necessary;
  • If you observe a significant oscillation in vertical direction, that's due to the setting of feedback parameters; play with them you should be able to find the recipe for your own AFM system. The reason for this is that the feedback circuit could behave like an extra "electric spring" to make the D-LFC and your probe at around resonant status;
  • Use a reasonable slow scan rate; this would reduce the effect of the eddy current and the possible air perturbation, though our testing shows that the calibration results are not sensitive to them.

Data Processing [top]

The data processing is summarized in Figure 8. To simplify data processing, the AFM base displacement is approximated as the lateral spring displacement. Then it is multiplied by the spring constant k11o and converted to the lateral force , which is shown on the horizontal axis at the top of Fig. 8. Now we have a data set relating f and vl for a fixed value of vn. Recalling the equation (1) in Background in a difference form, 

eq-6aeq-6b      (6)

the inverse slop, dfdvl, of the data is the lateral force constant all. In addition, two response lines for two different vn's should be parallel to each other as shown by a dashed line in the figure. The crosstalk lateral force constant aln is given by aln-eq. Thus, experimental measurements of the responses vl's with respect to the lateral force (or spring displacement) for two different vn's can provide the values of both all and aln via two linear fittings. 


Up to here, you have gone through all the details of D-LFC. Hope you enjoy this scientific toy :)  
If you have any questions or comments, please don't hesitate to contact us. 


DIY Steps

Lateral Calibration