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Journal of Nanotechnology
Volume 2013, Article ID 761031, 10 pages
Research Article

On the Tapping Mode Measurement for Young’s Modulus of Nanocrystalline Metal Coatings

Edward E. Whitacre, Jr. College of Engineering, Mechanical Engineering, Texas Tech University, P. O. Box 41021, Lubbock, TX 79409-1021, USA

Received 7 June 2013; Revised 26 July 2013; Accepted 27 July 2013

Academic Editor: Carlos R. Cabrera

Copyright © 2013 H. S. Tanvir Ahmed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Young’s modulus of nanocrystalline metal coatings is measured using the oscillating, that is, tapping, mode of a cantilever with a diamond tip. The resonant frequency of the cantilever changes when the diamond tip comes in contact with a sample surface. A Hertz-contact-based model is further developed using higher-order terms in a Taylor series expansion to determine a relationship between the reduced elastic modulus and the shift in the resonant frequency of the cantilever during elastic contact between the diamond tip and sample surface. The tapping mode technique can be used to accurately determine Young’s modulus that corresponds with the crystalline orientation of the sample surface as demonstrated for nanocrystalline nickel, vanadium, and tantalum coatings.