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The University of Melbourne  Atomic Force Microscope Cantilevers
(Calibration method of Sader)

The University of Melbourne
Sader Research Group
Online calibration Online calibration Online calibration
Sader Method - iPhone, Web App & Global Calibration Initiative*
*Released 26 May 2016

Bibliography on AFM Cantilevers and Force Measurements

calibration Mathematica files Mathematica files


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 ]

These methods can also be used to indirectly determine the spring constants of non-rectangular cantilevers, provided a reference rectangular cantilever is available. Conditions for this latter implementation are detailed in the above references.

CM Group - Home - Background theory - Online calibration - Mathematica files

Created: 18 September 2003
Last modified: 27 May 2017
Authorised by: Head, School of Mathematics and Statistics.
Maintained by: John Sader, School of Mathematics and Statistics.