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

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.