Abstract
Scanning probe microscopy techniques enable one to investigate surface properties such as contact stiffness and friction between the probe tip and a sample with nm resolution. So far the bending and the torsional eigenmodes of an atomic force microscope cantilever have been used to image variations of elasticity and shear elasticity, respectively. Such images are near-field images with the resolution given by the contact radius typically between 10 nm and 50 nm. We show that the flexural modes of a cantilever oscillating in the width direction and parallel to the sample surface can also be used for imaging. Additional to the dominant in-plane component of the oscillation, the lateral modes exhibit a vertical component as well, provided there is an asymmetry in the cross-section of the cantilever or in its suspension. The out-of-plane deflection renders the lateral modes detectable by the optical position sensors used in atomic force microscopes. We studied cracks which were generated by Vickers indents, in submicro- and nanocrystalline ZrO2. Images of the lateral contact stiffness were obtained by vibrating the cantilever close to a contact-resonance frequency. A change in contact stiffness causes a shift of the resonant frequency and hence a change of the cantilever vibration amplitude. The lateral contact-stiffness images close to the crack faces display a contrast that we attribute to altered elastic properties indicating a process zone. This could be caused by a stress-induced phase transformation during crack propagation. Using the contact mode of an atomic force microscope, we measured the crack-opening displacement as a function of distance from the crack tip, and we determined the crack-tip toughness Ktip. Furthermore, K1c was inferred from the length of radial cracks of Vickers indents that were measured using classical scanning acoustic microscopy
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Binnig, C.F. Quate, and Ch. Gerber, “Atomic Force Microscope”, Phys. Rev. Lett., 56, 930 (1986).
V. Scherer, M. Reinstädtler, and W. Arnold, “Atomic Force Microscopy with Lateral Modulation” in Applied Scanning Probe Methods, Eds. H. Fuchs, B. Bhushan, and S. Hosaka (Springer, Berlin, 2003), pp. 76–115, and references therein.
B. Bhushan, in Handbook of Nanotechnology, edited by B. Bhushan (Springer, Berlin, 2004), pp. 497ff, and references therein.
C.M. Mate, G.M. McClelland, R. Erlandsson, and S. Chiang, “Atomic-scale friction of a tungsten tip on a graphite surface”, Phys. Rev. Lett., 59, 1942 (1987).
T. Göddenhenrich, S. Müller, and C. Heiden, “A lateral technique for simultaneous friction and topography measurements with the atomic force microscope”, Rev. Sci. Instrum., 65, 2870 (1994).
A. Caron, U. Rabe, M. Reinstädtler, J.A. Turner, and W. Arnold, “Imaging using lateral bending modes of atomic force microscope cantilevers”, Appl. Phys. Lett. 85, 6398 (2004).
U. Rabe, S. Amelio, E. Kester, V. Scherer, S. Hirsekorn, and W. Arnold, “Quantitative Determination of Contact Stiffness Using Atomic Force Acoustic Microscopy”, Ultrasonics, 38, 430 (2000), and reference contained therein.
A.A. Griffiths, “The Phenomena of Rupture and Flaw in Solids”, Phil. Trans. R. Soc. London, A221, 163 (1920).
T.L. Anderson, Fracture Mechanics - Fundamentals and Applications, Chapter 6: Fracture Mechanics in Nonmetals, Boston: CRC Press (1991).
E. Babilon, G. Kleist, R.W. Steinbrech, and H. Nickel, “Untersuchung von Mikrorissfeldern in der Umgebung eines Makrorisses in Al2O3-Keramik mittels der Röntgenkleinwinkelstreuung”, Konferenzberichte des FZ Jülich, 7, Eds. H. Nickel and R.W. Steinbrech, 175 (1991).
W. Arnold, G. Weides, and S. Faßbender “Measurement of Elastic Properties Related to the R-Curve-Behavior of Ceramics”, Proc. Asian Pacific Conf. Fract. & Strength 2001 and Int. Conf. Adv. Technol. in Exp.. Mech., Jap. Soc. of Mech. Eng., Tokyo, 2001, 517.
F.F. Lange, “Transformation Toughening. Part 1: Size Effects Associated with the Thermodynamics of Constrained Transformations”, J. Mat. Sci.,17, 225 (1982).
G.R. Irwin, “Fracture”, Handbuch der Physik, Springer Verlag, Berlin, 6, 551, (1958).
B.R. Lawn, “Fracture of Brittle Solids – Second Edition”, Sol. State Sci. Ser. Cambridge University Press, (1993).
J. Rödel, G. Kelly, and B.R. Lawn, “In-Situ Measurements of Bridged Cracked Interfaces in the SEM”, J. Am. Ceram. Soc.,73, 3313 (1990).
D. Munz, and T. Fett, Mechanisches Verhalten keramischer Werkstoffe, in Werkstoffforschung und –Technik, B. Ilschner (Ed.), Springer, Heidelberg, 1989.
G.A.D. Briggs, “Scanning Acoustic Microscopy”, Oxford University Press, 1992.
AFM – Digital Instrument, www.veeco.com.
K. Yamanaka, H. Ogiso, and O. Kosolov, “Analysis of Subsurface Imaging Effect of Contact Elasticity in the Ultrasonic Force Microscopy”, Jpn. J. Appl. Phys., 33, 3197 (1994).
M. Kopycinska-Müller, M. Reinstädtler, U. Rabe, A. Caron, S. Hirsekorn, and W. Arnold, “Ultrasonic modes in atomic force microscopy”, Proc. 27th Int. Symp. Acoustical Imaging, Kluwer Plenum Press, Eds. W. Arnold and S. Hirsekorn, 699–704 (2004).
M. Reinstädtler, U. Rabe, V. Scherer, U. Hartmann, A. Goldade, B. Bhushan, and W. Arnold, “On the nanoscale measurement of friction using atomic force microscope cantilever torsional resonances”, Appl. Phys. Lett., 82, 2604 (2003).
J. Eichler, “Mechanical Properties of Nanocrystalline Zirconia”, Ph.D. Thesis, Fachbereich Material- und Geowissenschaften, University of Technology, Darmstadt, Germany (2004).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Caron, A., Rabe, U., Rödel, J., Arnold, W. (2007). Near-Field Acoustical Imaging using Lateral Bending Mode of Atomic Force Microscope Cantilevers. In: André, M.P., et al. Acoustical Imaging. Acoustical Imaging, vol 28. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5721-0_4
Download citation
DOI: https://doi.org/10.1007/1-4020-5721-0_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5720-5
Online ISBN: 978-1-4020-5721-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)