Determining Spring Constants

Discussions by Two Authors:

1. Dirk Then, Institut fuer Physikalische und Theoretische Chemie, Tuebingen

2. Carl Masens, Department of Applied Physics University of Technology, Sydney, Australia

How to Determine the Spring Constant for a Cantilever
from the DI SPM Digest, by Dirk Then.

------- Forwarded Message Follows -------
From:          "maps" <>
To:            <>
Subject:       spring constant
Date:          Mon, 29 Jun 1998 10:19:18 -0300

How can I calculate the spring constant of the cantilever in the case of silicon nitride (triangle shaped) and cristal silicon (retangle shaped) grate?
Marcelo de A. Pereira-da-Silva

Dear Marcelo,

for a rectangular cantilever geometry it is easy to calculate the spring constant using the dimensions of the cantilever and  its Young's Modulus with the following equation

        k = (E*t^3*w) / (4*L^3)

where E is Young=B4s Modulus, t the thickness, w the width and L the length of the cantilever.
But there are a lot more accurate possibilities to determine the spring constant of a cantilever. For example one can calculate the spring constant from the thermal noise of a cantilever. Another posibility is to add a small mass at the apex of the cantilever. From the occuring resonance frequency shift you can calculte the spring constant.
For more details look at the following publications:

J.M. Neumeister, Rev. Sci. Instrum. 65, 1994, pp. 2527 J.P. Cleveland, Rev. Sci. Instrum. 64, 1993, pp. 403 H.-J. Butt, Microscopy 169, 1993, pp. 75 H.-J. Butt, Nanotechnology 6, 1995, pp. 1 G. Y. Chen,  Rev. Sci. Instrum. 65, (1994), pp. 2532 G. Y. Chen,  J. Appl. Phys. 77, (1995), pp. 3618

With best regards

Dirk Then
Dirk Then
Institut fuer Physikalische und Theoretische Chemie Auf der Morgenstelle 8
D-72076 Tuebingen
Tel: ++49(0)7071 / 29 78749
Fax: ++49(0)7071 / 29 5490

Revised:  March 11, 2000
Copyright © John W. Cross