AVS 49th International Symposium
    Nanometer Structures Monday Sessions
       Session NS-MoM

Paper NS-MoM9
Towards the Sensing of Atomic Interactions by Nanoindentation with Extremely Sharp Tips

Monday, November 4, 2002, 11:00 am, Room C-207

Session: Nanomechanics
Presenter: J. Fraxedas, ICMAB-CSIC, Spain
Authors: J. Fraxedas, ICMAB-CSIC, Spain
S. Garcia-Manyes, CBEN and University of Barcelona, Spain
P. Gorostiza, University of California, Berkeley
F. Sanz, CBEN and University of Barcelona, Spain
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A force F applied to a surface acts directly on the surface atoms and is transmitted to the bulk atoms via the crystal lattice. The bonds play thus a crucial role in the mechanical response because of their strength and spatial distribution. For a point force only few atoms are involved. In this case the elastic deformation of the surface critically depends on in-plane interactions. In order to demonstrate the relevance of such interactions we have done nanoindentation experiments on 2D materials and ionic single crystals with an AFM. The stiffness k of the crystal and an estimated radius d@sub s@ of the elastically perturbed surface can be evaluated from expression F(@delta@)=k@delta@(1-d@sub s@/@sr@(@delta@@super 2@+d@sub s@@super 2@)),@footnote 1@ where @delta@ stands for the surface deformation. k is related to the Debye frequency @omega@@sub D@ (k@sub D@=m@omega@@sub D@@super 2@), where m represents the mean atomic mass. The calculated values of k@sub D@ are very close to the experimentally derived values of k (i. e., k=84±13 Nm@super -1@ and k@sub D@=86 Nm@super -1@ for NaCl). Nanoindentation thus reveals the collective behavior of nanoscale volumes since many atoms are involved in the process (ca. 140 ion pairs for the alkali halides). We observe that k/d@sub s@=c@sub 11@, where c@sub 11@ represents the (1,1) component of the elastic tensor. Feynman developed a simple model relating the anion-cation interatomic interaction k@sub ac@ to elastic constants for small strains for NaCl-type crystals assuming central forces.@footnote 2@ Within this approximation we obtain k@sub ac@<13 Nm@super -1@, in good agreement with k@sub ac@=10-12 Nm@super -1@, obtained in the harmonic limit from long wavelength TO phonon frequencies. @FootnoteText@ @footnote 1@ J. Fraxedas, S. Garcia-Manyes, P. Gorostiza, F. Sanz, Proc. Natl. Acad. Sci. USA 99, 5228 (2002)@footnote 2@ R. P. Feynman, R. B. Leighton, M. Sands in The Feynman Lectures on Physics (Addison-Wesley, 1964), pp. 10.