iPhone¹, Web App¹ & Global Calibration Initiative^2*

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Experimental determination of the spring constants of Atomic Force Microscope (AFM) cantilevers is of fundamental importance in many applications of the AFM. For rectangular AFM cantilevers, both the normal and torsional spring constants can be measured using the unloaded resonance techniques detailed below.

The method of Sader et al. (Rev. Sci. Instrum., 70, 3967 (1999)), commonly referred to as the Sader method, enables the normal spring constant to be determined using only the plan view dimensions of the cantilever, its fundamental resonant frequency and quality factor in air.
[ background theory ]

The Sader method was extended to enable simultaneous calibration of the torsional spring constant of rectangular AFM cantilevers (Rev. Sci. Instrum., 75, 1988 (2004)). This extension, referred to as the Torsional Sader method, enables calibration of the torsional spring constant using an identical experimental methodology.
[ background theory ]

Recently, the physical basis for the method was elucidated and its extension to small elastic bodies of arbitrary shape presented (J. Appl. Phys., 97, 124903 (2005)). This was also applied to a series of commercially available non-rectangular cantilevers (Rev. Sci. Instrum., 83, 103705 (2012)).
[ background theory ]

The advantages of these techniques are that they are rapid to use, simple to implement experimentally, and importantly, are non-invasive and non-destructive. In order to assist users who would like to make use of these techniques, Java applets, iPhone and Wolfram CDF Player web apps, have been created which perform the calculations online.
[ online calibration ]

In addition, Mathematica ® notebooks for calculating the spring constants using the aforementioned techniques are available for download.
[ Mathematica files ]